A ROAD NETWORK SHORTEST PATH ANALYSIS: APPLYING TIME-VARYING
TRAVEL-TIME COSTS FOR EMERGENCY RESPONSE VEHICLE ROUTING,
DAVIS COUNTY, UTAH
A THESIS PRESENTED TO
THE DEPARTMENT OF HUMANITIES AND SOCIAL SCIENCES
IN CANDIDACY FOR THE DEGREE OF
MASTER OF SCIENCE
By
MICHAEL T. WINN
NORTHWEST MISSOURI STATE UNIVERSITY
MARYVILLE, MISSOURI
JANUARY, 2014
i
A ROAD NETWORK SHORTEST PATH ANALYSIS
A Road Network Shortest Path Analysis: Applying Time-Varying
Travel-Time Costs for Emergency Response Vehicle Routing, Davis County, Utah
Michael T. Winn
Northwest Missouri State University
THESIS APPROVED
________________________________________________________________________
Thesis Advisor, Dr. Yi-Hwa Wu
Date
________________________________________________________________________
Dr. Patricia Drews
Date
________________________________________________________________________
Dr. Ming-Chih Hung
Date
________________________________________________________________________
Dean of Graduate School, Dr. Gregory Haddock
Date
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A Road Network Shortest Path Analysis
Abstract
Rapid emergency response to the scene of a traffic accident and transportation of
the injured to a medical facility is critical for saving lives. Traffic congestion is a major
problem in urban areas and Davis County, Utah is no exception. Traffic congestion can
disrupt emergency response, but dynamic network routing can offer solutions. A GIS can
be a useful tool for determining emergency vehicle response routing, and the application
of dynamic variables like historical traffic count data can help emergency response
vehicles avoid traffic congestion and improve response times.
This research examines a methodology where route solvers based on Dijkstra’s
shortest path algorithm in ArcGIS Network Analyst were utilized to identify the closest
ground emergency response unit (e.g., fire station) and hospital (e.g., trauma center) to
each incident and then solving the shortest path problem centered around emergency
response routing scenarios. Cost attributes or impedances, namely distance, free-flow
travel time and time-varying travel time originating from historical traffic data, were
applied to each routing scenario to determine the shortest, fastest, and best (optimal)
routes from an origin to a destination. The best route is defined as the route with the least
travel cost determined by the impedance applied.
Results were analyzed and compared. Findings based on these routing analyses
show that dynamic time-varying travel time derived from historical traffic count data can
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optimize emergency response routing, improve travel times and validate that dynamic
network routing can improve emergency response routing above static networks.
Although challenges and limitations existed in this research, it is believed that future
improvements through the incorporation of live traffic data using GPS technology and
traffic cams could greatly enhance this type of research and assist local public safety and
EMS agencies improve levels of service as population growth and subsequent traffic
congestion increases.
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Table of Contents
Abstract ........................................................................................................................ iii
List of Figures ............................................................................................................. vii
List of Tables ................................................................................................................. x
Acknowledgments ....................................................................................................... xii
List of Abbreviations ................................................................................................. xiii
Chapter 1: Introduction .................................................................................................. 1
1.1 Research Background ....................................................................................... 1
1.2 Research Objectives .......................................................................................... 3
1.3 Study Area ........................................................................................................ 3
Chapter 2: Literature Review ......................................................................................... 8
2.1 Network Analysis ............................................................................................. 8
2.2 Shortest Path Analysis ...................................................................................... 9
2.3 Dijkstra’s Algorithm ....................................................................................... 10
2.4 Static and Dynamic Networks ........................................................................ 10
2.5 Traffic Congestion and Dynamic Emergency Response Routing .................. 12
2.6 Historical Traffic Profiles ............................................................................... 13
Chapter 3: Conceptual Framework and Methodology ................................................. 15
3.1 Data Sources ................................................................................................... 17
3.2 Data Preparation ............................................................................................. 18
3.2.1 Road Network Centerlines ...................................................................... 18
3.2.2 Road Classifications ................................................................................ 19
3.2.3 Historical Hourly Traffic Volume Data .................................................. 21
3.2.4 Grouping Historical Traffic Volume Data .............................................. 23
3.2.5 Historical Traffic Volume Profiles ......................................................... 25
3.2.6 Modeling Historical Traffic Data ............................................................ 33
3.2.7 Incorporating Historical Traffic Data ..................................................... 35
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3.3 Developing the Road Network Model ............................................................ 37
3.3.1 One Way Restrictions ............................................................................. 39
3.3.2 Global Turn Delays ................................................................................. 41
Chapter 4: Analysis and Results .................................................................................. 45
4.1 Routing Example for IN-1 .............................................................................. 50
4.1.1 IN-1: Closest Facility Analysis ............................................................... 50
4.1.2 IN-1: Route Analysis Scenario 1 ............................................................ 58
4.1.3 IN-1: Route Analysis Scenario 2 ............................................................ 71
4.1.4 IN-1: Emergency Response Routing Review .......................................... 80
4.2 Routing Example for IN-2 .............................................................................. 84
4.2.1 IN-2: Closest Facility Analysis ............................................................... 84
4.2.2 IN-2: Route Analysis Scenario 1 ............................................................ 91
4.2.3 IN-2: Route Analysis Scenario 2 ............................................................ 98
4.2.4 IN-2: Emergency Response Routing Review ........................................ 109
4.3 Discussion of Results .................................................................................... 113
Chapter 5: Conclusion and Future Improvements ..................................................... 116
5.1 Conclusion .................................................................................................... 116
5.2 Limitations .................................................................................................... 117
5.3 Challenges and Solutions .............................................................................. 119
5.4 Future Improvements .................................................................................... 120
References .................................................................................................................. 122
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List of Figures
Figure 1. Study area, Davis County with Utah inset ....................................................... 4
Figure 2. Road network, Davis County, Utah ................................................................. 6
Figure 3. EMS facilities (ground units) and hospitals, Davis County, Utah .................. 7
Figure 4. Methodology flow chart ................................................................................. 16
Figure 5. Road network and the Urban Area Functional Classification system ............ 20
Figure 6. Geographic locations of the ATR sites ........................................................... 22
Figure 7. ATR site 0316 traffic volume profile - Tuesday average, April 2010 ............ 26
Figure 8. ATR site 0316 traffic volume profile – Saturday average, April 2010 .......... 26
Figure 9. ATR site 0316 traffic volume profile – Sunday average, April 2010 ............ 26
Figure 10. ‘DailyProfiles_Time_60min’ table: Profile 3 ............................................... 29
Figure 11. ‘DailyProfiles_Time_60min’ table: Profile 8 ............................................... 29
Figure 12. ‘DailyProfiles_Time_60min’ table: Profile 12 ............................................. 29
Figure 13. ‘DailyProfiles_Time_60min’ table: Profile 14 ............................................. 30
Figure 14. ‘DailyProfiles_Time_60min’ table: Profile 21 ............................................. 30
Figure 15. ‘DailyProfiles_Time_60min’ table: Profile 91 ............................................. 30
Figure 16. ‘DailyProfiles_Time_60min’ table: Profile 92 ............................................. 31
Figure 17. ‘DailyProfiles_Time_60min’ table: Profile 96 ............................................. 31
Figure 18. ‘DailyProfiles_Time_60min’ table: Profile 98 ............................................. 31
Figure 19. Network dataset properties associated with the historical traffic tables ....... 36
Figure 20. Assignment of network attributes ................................................................. 36
Figure 21. File geodatabase data model ......................................................................... 38
Figure 22. Correct one-way travel, from Incident 1 to Ogden Regional Medical
Center ........................................................................................................... 40
Figure 23. Incorrect one-way travel, from Incident 1 to Ogden Regional Medical
Center ........................................................................................................... 40
Figure 24. Turn categories available for various road types .......................................... 42
Figure 25. Global turn delay default settings ................................................................. 43
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Figure 26. Global turn delay customized settings .......................................................... 43
Figure 27. Example of routing scenarios S1 and S2 ...................................................... 46
Figure 28. Route analysis flowchart .............................................................................. 47
Figure 29. Analysis settings available for ‘Closest Facility’ solver .............................. 51
Figure 30. Analysis settings available settings for ‘Route’ solver ................................. 51
Figure 31. Routes from nearest ground unit to IN-1 applying DIST impedance .......... 54
Figure 32. Routes from nearest ground unit to IN-1 applying FFTT impedance .......... 55
Figure 33. Routes from nearest ground unit to IN-1 applying TVTT impedance ......... 55
Figure 34. Routes from IN-1 to nearest hospital applying DIST impedance ................ 56
Figure 35. Routes from IN-1 to nearest hospital applying FFTT impedance ................ 57
Figure 36. Routes from IN-1 to nearest hospital applying TVTT impedance ............... 58
Figure 37. IN-1, Scenario 1, Sunday travel time profile, TVTT impedance ................. 63
Figure 38. IN-1, Scenario 1, Tuesday travel time profile, TVTT impedance ................ 64
Figure 39. IN-1 Scenario 1, Route A ............................................................................. 65
Figure 40. IN-1 Scenario 1, Route B ............................................................................. 65
Figure 41. IN-1, Scenario 2, Sunday travel time profile, TVTT impedance ................. 73
Figure 42. IN-1, Scenario 2, Tuesday travel time profile, TVTT impedance ................ 74
Figure 43. IN-1 Scenario 2, Route A ............................................................................. 75
Figure 44. IN-1 Scenario 2, Route B ............................................................................. 75
Figure 45. IN-1 Scenario 2, Route C ............................................................................. 76
Figure 46. IN-1, combined scenarios, Sunday and Tuesday, DIST impedance ............ 81
Figure 47. IN-1, combined scenarios, Sunday and Tuesday, FFTT impedance ............ 81
Figure 48. IN-1, combined scenarios, Sunday, TVTT impedance ................................ 82
Figure 49. IN-1, combined scenarios, Tuesday, TVTT impedance ............................... 82
Figure 50. Routes from nearest ground unit to IN-2 applying DIST impedance ........... 85
Figure 51. Routes from nearest ground unit to IN-2 applying FFTT impedance ........... 86
Figure 52. Routes from nearest ground unit to IN-2 applying TVTT impedance .......... 87
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Figure 53. Routes from IN-2 to nearest hospital applying DIST impedance ................. 88
Figure 54. Routes from IN-2 to nearest hospital applying FFTT impedance ................. 89
Figure 55. Routes from IN-2 to nearest hospital applying TVTT impedance ................ 90
Figure 56. IN-2 Scenario 1, Sunday travel time profile, TVTT impedance ................... 93
Figure 57. IN-2 Scenario 1, Tuesday travel time profile, TVTT impedance.................. 94
Figure 58. IN-2 Scenario 1, Route A .............................................................................. 95
Figure 59. IN-2 Scenario 1, Route B .............................................................................. 95
Figure 60. IN-2 Scenario 2, Sunday travel time profile, TVTT impedance .................. 100
Figure 61. IN-2 Scenario 2, Tuesday travel time profile, TVTT impedance................. 101
Figure 62. IN-2 Scenario 2, Route A ............................................................................. 102
Figure 63. IN-2 Scenario 2, Route B ............................................................................. 102
Figure 64. IN-2 Scenario 2, Route C ............................................................................. 103
Figure 65. IN-2 Scenario 2, Route D ............................................................................. 103
Figure 66. IN-2 Scenario 2, Route E.............................................................................. 104
Figure 67. IN-2, combined scenarios, Sunday and Tuesday, DIST impedance ............ 110
Figure 68. IN-2, combined scenarios, Sunday and Tuesday, FFTT impedance ............ 110
Figure 69. IN-2, combined scenarios, Sunday, TVTT impedance ................................ 111
Figure 70. IN-2, combined scenarios, Tuesday, TVTT impedance ............................... 111
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List of Tables
Table 1. Urban Area Functional Classification system ................................................. 20
Table 2. ATR sites associated with the Functional Classification system ..................... 22
Table 3. April 2010 traffic volumes for ATR site 0316 ................................................ 23
Table 4. April 2010 traffic volumes for ATR site 0316, grouped ................................. 24
Table 5. ‘DailyProfiles_Time_60min’ file geodatabase table ....................................... 28
Table 6. Profile IDs from the ‘DailyProfiles_Time_60min’ table ................................. 28
Table 7. 'Project_Profiles' file geodatabase table ........................................................... 32
Table 8. 'ProjectArea' feature class attribute table ......................................................... 32
Table 9. ‘Global Turn Delay’ directions and penalty values in seconds ....................... 42
Table 10. Incident information from 2010 UDOT crash statistics ................................ 46
Table 11. Analysis settings for finding nearest ground unit to IN-1 ............................. 53
Table 12. Analysis settings for finding nearest hospital from IN-1 ............................... 53
Table 13. Results for finding nearest ground unit to IN-1 ............................................. 54
Table 14. Results for finding nearest hospital from IN-1 .............................................. 54
Table 15. Analysis settings used for S1 ......................................................................... 61
Table 16. Scenario 1, Sunday, Clinton FD to IN-1, DIST impedance .......................... 61
Table 17. Scenario 1, Tuesday, Clinton FD to IN-1, DIST impedance ......................... 61
Table 18. Scenario 1, Sunday, Clinton FD to IN-1, FFTT impedance .......................... 62
Table 19. Scenario 1, Tuesday, Clinton FD to IN-1, FFTT impedance ........................ 62
Table 20. Scenario 1, Sunday, Clinton FD to IN-1, TVTT impedance ......................... 63
Table 21. Scenario 1, Tuesday, Clinton FD to IN-1, TVTT impedance ........................ 64
Table 22. IN-1 Scenario 1, Sunday, comparison of cost impedance between Routes
A and B ........................................................................................................ 70
Table 23. Scenario 2, Sunday, IN-1 to Davis Hospital, DIST impedance ..................... 71
Table 24. Scenario 2, Tuesday, IN-1 to Davis Hospital, DIST impedance ................... 71
Table 25. Scenario 2, Sunday, IN-1 to Davis Hospital, FFTT impedance .................... 72
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Table 26. Scenario 2, Tuesday, IN-1 to Davis Hospital, FFTT impedance ................... 72
Table 27. Scenario 2, Sunday, IN-1 to Davis Hospital, TVTT impedance ................... 73
Table 28. Scenario 2, Tuesday, IN-1 to Davis Hospital, TVTT impedance .................. 74
Table 29. IN-1 Scenario 2, Tuesday, comparison of cost impedance between Routes
B and C ........................................................................................................ 79
Table 30. IN-1, combined scenarios, comparison of emergency response routes ......... 83
Table 31. Results for finding nearest ground unit to IN-2 .............................................. 84
Table 32. Results for finding nearest hospital from IN-2 ............................................... 84
Table 33. Scenario 1, Sunday, Kaysville FD to IN-2, DIST impedance ........................ 91
Table 34. Scenario 1, Tuesday, Kaysville FD to IN-2, DIST impedance....................... 91
Table 35. Scenario 1, Sunday, Kaysville FD to IN-2, FFTT impedance ........................ 92
Table 36. Scenario 1, Tuesday, Kaysville FD to IN-2, FFTT impedance ...................... 92
Table 37. Scenario 1, Sunday, Kaysville FD to IN-2, TVTT impedance ....................... 93
Table 38. Scenario 1, Tuesday, Kaysville FD to IN-2, TVTT impedance ..................... 94
Table 39. IN-2 Scenario 1, Tuesday, comparison of cost impedance between Routes
A and B ......................................................................................................... 97
Table 40. Scenario 2, Sunday, IN-2 to Davis Hospital, DIST impedance ...................... 98
Table 41. Scenario 2, Tuesday, IN-2 to Davis Hospital, DIST impedance .................... 98
Table 42. Scenario 2, Sunday, IN-2 to Davis Hospital, FFTT impedance ..................... 99
Table 43. Scenario 2, Tuesday, IN-2 to Davis Hospital, FFTT impedance .................... 99
Table 44. Scenario 2, Sunday, IN-2 to Davis Hospital, TVTT impedance ................... 100
Table 45. Scenario 2, Tuesday, IN-2 to Davis Hospital, TVTT impedance .................. 101
Table 46. IN-2 Scenario 2, Sunday, comparison of cost impedance between Routes
A, B, and C................................................................................................... 107
Table 47. IN-2 Scenario 2, Tuesday, summary of cost impedance between Routes
A, B, C, D, and E ......................................................................................... 108
Table 48. IN-2, combined scenarios, comparison of emergency response routes ......... 112
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Acknowledgements
I would first like to thank my thesis advisor, Dr. Yi-Hwa Wu, for her patience and
support throughout this research process. Her advice and understanding of the subject
matter was invaluable. I would like to thank my academic advisor, Dr. Patricia Drews,
who not only helped me with this research, but for over eight years guided and
encouraged me through the GIScience Master’s program. I would also like to thank Dr.
Ming-Chih Hung for his much appreciated assistance as well.
Other individuals and agencies I would like to acknowledge are Mike Price with
Entrada/San Juan, Inc. Nicolas Virgen, Scott Jones, Danielle Herrscher, and Brandi
Trujillo with the Utah Department of Transportation. Bert Granberg and his staff with
the Utah Automated Geographic Reference Center. Joshua Legler and Robert Jex with
the Utah Bureau of Emergency Medical Services. Mike King with the Hill Air Force
Base Fire Department and Patrick McDonald with the Layton City Fire Department. I
want to thank them for generously sharing information, their time, and their insight for
this research.
Lastly, I would like to thank my family for their patience and understanding over
the years. I would especially like to thank my wife Linda, for her love and support
during this long undertaking. Without her strength and encouragement, my educational
goals and this research would not have been possible.
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List of Abbreviations
AGRC: Utah Automated Geographic Reference Center
ATR: Automatic Traffic Recorder
BEMS: Utah Bureau of Emergency Medical Services
DIST: Distance cost attribute or impedance
EMS: Emergency Medical Services
Esri: Environmental Systems Research Institute
FC: Functional Classification (Urban area functional classification system)
FFTT: Free-Flow Travel Time
FGDB: File Geodatabase
GIS: Geographic Information System
GIS-T: Geographic Information Systems for Transportation
GTD: Global Turn Delays
HAFB: Hill Air Force Base
NA: Esri Network Analyst
ND: Network Dataset
NHTSA: National Highway Traffic Safety Administration
TVTT: Time-Varying Travel Time
UDOT: Utah Department of Transportation
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Chapter 1: Introduction
Emergency medical services (EMS) is a system that provides emergency medical
care. Once it is activated by an incident that causes serious illness or injury, the focus of
EMS is the emergency medical care and the patient(s). Another element of the EMS is
the ground or air transportation of the patient(s) to a hospital or trauma center (National
Highway Traffic Safety Administration Emergency Medical Services [NHTSA EMS]
2013). EMS response time is critical in emergency requests involving injury (Panahi and
Delavar 2009). Technological advances such as geographic information systems (GIS),
can allow emergency vehicles to reach patients more quickly (Wilde 2009), and
efficiency in routing emergency fire and medical vehicles to a traffic incident is critical
for saving lives (Cova 1999).
1.1 Research Background
A GIS can be used for many roles in emergency management. It is an effective
tool for determining emergency vehicle response routing and solving the emergency
vehicle shortest path routing problem (Alivand et al. 2008, Cova 1999, Panahi and
Delavar 2008). A shortest path algorithm applied to a routing problem in a transportation
network can calculate the path with minimal travel cost or least impedance from an origin
to a destination. Depending on the type of cost, the shortest path can be referred to as the
shortest, fastest, or most optimal path or route. There are several impedance factors that
can affect emergency services and vehicle response times. They include distance, travel
time, and traffic congestion as a result of variations in traffic flow related to the time of
1
day. Traffic congestion is a major problem in urban areas and can disrupt emergency
response (Panahi and Delavar 2008; 2009, Naqi et al. 2010).
In recent years, traffic congestion in Davis County, Utah has become more
problematic and widespread, thus affecting emergency response performance. Traffic
congestion will continue to be a concern as the region grows in population and
congestion increases (Utah Department of Transportation [UDOT] 2008, United States
Census Bureau 2012). East-west transportation is restricted by a narrow urban corridor
and many of the residents commute south to Salt Lake County. From 2000 to 2010,
Davis County experienced a population growth rate of 28.2% and an increase in housing
units by 31.6%, and the average population density per square mile increased by 30.7%
(United States Census Bureau 2012). With no signs of slowing population growth or
opportunities for employment, Davis County must plan for a variety of transportation
facilities such as roads and mass transit systems to accommodate the anticipated growth
(UDOT 2008).
This study selected Davis County, Utah as the case study area because of its
constricted, north/south orientated road system and traffic congestion. Using commercial
ready-to-use GIS software, a dynamic road network was created and a real-world
emergency response routing analysis was performed to determine the shortest, fastest,
and most optimal path or routes for emergency response vehicles by applying different
cost attributes or impedances. An analysis and comparison of the resulting emergency
vehicle routing scenarios was made to demonstrate how routes and travel times are
affected when these cost attributes are applied.
2
1.2 Research Objectives
The overall objective of this research was to observe if routes and response times
for emergency response vehicles change due to variations in traffic flow related to the
day (e.g., weekday or weekend) and the time of day (traffic congestion). Commonly used
shortest path algorithms were used to calculate the shortest, fastest, and the most optimal
path from an emergency response unit (e.g., fire station) to an incident (e.g., car crash)
then to a trauma center (e.g., hospital) by applying three cost attributes or impedances to
road network edges: distance, base travel time or free-flow travel time, and timedependent or time-varying travel time originating from historical traffic data. A major
component of this research was the application of historical traffic data. To perform this
analysis, traffic volume profiles based on Utah Department of Transportation (UDOT)
traffic count data were created and applied as a network cost attribute. Dynamic routing
based on cost attributes derived from historical travel-time data and applied to network
edges should help response vehicles avoid congested areas and improve travel times (Kok
et al. 2012, Panahi and Delavar 2009).
1.3 Study Area
Davis County was founded in 1850 and is situated in north central Utah (Figure
1). The Wasatch Range borders the east side of the county and the Great Salt Lake
borders the west side. Weber County is located to the north of Davis County with the
Weber River delineating part of the northern county line while Salt Lake County borders
on the south. Davis County has 15 incorporated cities and towns (Figure 1) and a total
population of 306,500 (United States Census Bureau 2012). Lands outside these
3
incorporated cities are primarily uninhabited wetlands, desert or mountainous areas. The
county seat is located in the city of Farmington which is located about mid-point in the
county. Davis County covers about 635 square miles with the Great Salt Lake occupying
more than half of this area. Hill Air Force Base (HAFB) is located entirely within the
northern part of the county and is the home of the Ogden Air Logistics Center (OALC)
which serves primarily as a repair facility for military aircraft (Davis County Emergency
Management Services 2009).
Figure 1. Study area, Davis County with Utah inset
4
An interstate highway (I-15) and a railroad system traverse the entire length of the
County and provide the only major access and egress route for the County. Davis County
contains 1,776 miles of roads mostly in the incorporated areas and includes 1,704 miles
of paved roads and 72 miles of dirt/4wd roads (Figure 2). There are 84 miles of federal
highways, 225 miles of state routes, 1,357 miles of local roads and 38 miles of access
ramps (Utah Automated Geographic Reference Center [Utah AGRC] 2012). It should be
noted that Figure 2 does not show the entire road network created for this research
project.
The study area is served by ten EMS agencies not including HAFB, four
designated emergency medical dispatch agencies and seventeen EMS facilities or ground
units not including HAFB (Utah AGRC 2012, Utah Bureau of Emergency Medical
Services [Utah BEMS] 2012a; b). There are four hospitals located in Davis County, two
of which are designated as resource hospitals that have emergency rooms staffed with
24/7 physicians (Figure 3). There are four Level I (highest level of care) trauma centers
located in the northern portion of Salt Lake County (Salt Lake City) within
approximately 8 miles of the southern border of Davis County and two Level II trauma
centers located in Ogden within 4 miles of the northern border of Davis County (Utah
AGRC 2012, Utah BEMS 2012c).
5
Figure 2. Road network, Davis County, Utah
6
Figure 3. EMS facilities (ground units) and hospitals, Davis County, Utah
7
Chapter 2: Literature Review
Geographic Information Systems for Transportation (GIS-T) represents one of the
most important application areas of GIS technology (Goodchild 2000). Shaw (2010)
referred to GIS-T as the application of information technology to the transportation
problem. Abkowitz et al. (1990) stated over two decades ago that the field of
transportation was inherently geographic and GIS was a technology with considerable
potential for achieving gains in efficiency and productivity for many transportation
applications.
2.1 Network Analysis
A background knowledge of a network can be beneficial to the understanding of
transportation network analysis. A network is essentially a set of lines known as
segments or edges connected or joined by a set of vertices known as nodes or junctions.
A GIS stores these edge and junction features with their attributes. Spatio-temporal
networks are networks whose topology and parameters change with time. These
networks are important to applications such as emergency traffic planning and route
finding (George et al. 2007).
Network analysis in GIS has its origins in the mathematical sub-disciplines of
graph theory and topology. An important association between graph theory and a
network is topology. Topological properties such as connectivity, coincidence, and
adjacency are key to network analysis. An important advantage of a GIS-based network
8
in contrast to graph theory is the geographic elements of shape or length. Length is
essential for calculating travel time (Curtin 2007).
The use of GIS for network analysis is essential for improving emergency
response routing based on travel time information (Alivand et al. 2008, Panahi and
Delavar 2008). Curtin (2007) thought network analysis was one of the most significant
research and application areas in GIScience while Sadeghi-Niarki et al. (2011) mentioned
network analysis is a powerful tool in the GIS environment for solving the optimal path
in a network.
2.2 Shortest Path Analysis
A shortest path problem is to find a path with minimum travel cost from one or
more origins to one or more destinations through a network (Lim and Kim 2005, Panahi
and Delavar 2008). Shortest path analysis is important because of its wide range of
applications in transportation (Lim and Kim 2005). Naqi et al. (2010) stated that the
shortest path helps calculate the most optimal route, and optimal routing is the process of
defining the best route to get from one location to another. The best route could be the
shortest or fastest depending on how it is defined.
The shortest path can be computed either for a given start time or to find the start
time and the path that leads to least travel time journeys. The classic shortest path
problem and finding the best route for vehicle routing in static road networks based on
Dijkstra’s algorithm has been examined extensively in the literature over the years
(Alazab et al. 2011, Alivand et al. 2008, Kim et al. 2005). George et al. (2007) claimed
that developing efficient algorithms for computing shortest paths in a time-varying spatial
network can be challenging.
9
2.3 Dijkstra’s Algorithm
Dijkstra’s algorithm or variations of it are the most commonly used route finding
algorithm for solving the shortest path (Sadeghi-Niaraki et al. 2011). Dijkstra's algorithm
is sometimes called the single-source shortest path because it solves the single-source
shortest-path problem on a weighted, directed graph (G = V, E) where
V is a set whose elements are called vertices (nodes, junctions, or intersections) and E is
a set of ordered pairs of vertices called directed edges (arcs or road segments). To find a
shortest path from a source s vertex or location to a destination location d, Dijkstra's
algorithm maintains a set S of vertices whose final shortest-path weights from the source
s have already been determined. Knowing that w is the edge weight, the edge is an
ordered pair (u, v) and assuming w (u, v) ≥ 0 for each edge (u, v) ϵ E, the algorithm
repeatedly selects the vertex u ϵ V – S with the minimum shortest-path estimate, adds u
to S, and relaxes all edges leaving u (Cormen et al. 2001, Puthuparampil 2007).
The commercial GIS software that was used to perform the route analysis for this
study is Esri ArcGIS Network Analyst. ArcGIS is suitable for this kind of research
because it is commercially available, and the Network Analyst extension is included in
the student edition of ArcGIS. The route solver in Network Analyst to determine the
shortest path is based on Dijkstra's algorithm (Karadimas et al. 2007).
2.4 Static and Dynamic Networks
A dynamic network differs from a static network in that travel time changes or
varies with respect to time. Variables used to store the cost of traversing across an edge
10
change with respect to time is a dynamic network. It is important to consider travel time
as a parameter for finding the optimal path in dynamic networks (Alivand et al. 2008).
Recent GIS data models related to GIS-T are basically static in nature. Static
information is not sufficient to estimate travel time, since it does not reflect dynamically
changing traffic conditions. Static information could lead to incorrect shortest paths;
however, if there is a way to obtain the cost in real-time and then apply a time-dependent
shortest path algorithm, it would result in a better solution for the shortest path (Panahi
and Delavar 2009). According to Nadi and Delavar (2003), most conventional GIS data
models are based on a static representation of reality and constrain GIS capabilities for
representation of dynamic information. GIS data models that can represent the dynamic
aspects of transportation challenges are needed to represent and analyze space-time
information (Shaw 2010). Static variables that could be assigned to a road edge or
junction might include distance, speed limits, free-flow travel time, number of lanes, turn
penalties, slope of the road, hierarchical classifications, etc. (Li and Lin 2003, SadeghiNiaraki et al. 2011, Thirumalaivasan and Guruswamy 1997).
In contrast, travel time is considered dynamic due to traffic volume, and historical
traffic data applied to a network can approximate traffic congestion. Dynamic variables
known as costs or weights are time-dependent or time-varying travel times derived from
historical traffic data. Dynamic variables that could be assigned to a road edge or
junction might include weather variables or time-varying travel time derived from traffic
count data (Sadeghi-Niaraki et al. 2011, Thirumalaivasan and Guruswamy 1997). The
network analysis will better reflect actual traffic conditions occurring at various times
11
during the day when time-dependent variables are incorporated (Kok et al. 2012, Panahi
and Delavar 2009).
2.5 Traffic Congestion and Dynamic Emergency Response Routing
There are several factors that can affect emergency services and vehicle response
times. Variations in traffic flow or volume related to time of day is one of them. This is
referred to as traffic congestion. Traffic congestion can have several causes. Some are
predictable such as traffic during daily peak hours and some less predictable such as
weather or accidents. Delays caused by peak hour traffic congestion constitute the
majority of traffic congestion delays (Kok et al. 2012). Delays affecting response times
in emergency services caused by traffic congestion are considered dynamic because they
spread through a network and vary over time (Panahi and Delavar 2009, Riad et al.
2012).
”The increasing ubiquity and complexity of urban congestion combined with its
severe negative impacts suggests the need for new tools to analyze and predict congestion
patterns” like a GIS (Riad et al. 2012, Wu et al. 2001). A critical component in incident
or emergency response actions is to deploy appropriate response units to the incident
scene as quickly as possible (Huang and Pan 2007). According to Panahi and Delavar
(2008; 2009), the problem of traffic congestion in urban areas can influence the travel
times of emergency vehicles, but the development of dynamic routing can offer solutions.
A more recent study (Kamga et al. 2011) showed dynamic traffic models are particularly
appropriate for modeling highway incidents because the timing of incident occurrence,
management, recovery, and the use of alternate routes is critical to roadway performance
12
and driver behaviors. Haghani et al. (2003) argued the purpose of vehicle dispatching is
to minimize the total travel time in the system and that time-dependent shortest path
analysis is useful for the calculation of travel times and can help EMS dispatching and rerouting by reducing response times and improve services. Dynamic shortest path routing
should improve emergency response times (Panahi and Delavar 2008; 2009).
2.6 Historical Traffic Profiles
Several methods are known to apply historical traffic data to a road network. One
approach is to compute travel times for each road segment, which are then stored as
attributes for each feature. Depending on the sampling rate, storage and duplication
issues can be a concern (Demiryurek et al. 2009, Esri 2012, George et al. 2007). Another
method is the use of historical traffic profiles often referred to as speed profiles that are
used to produce travel time estimates (Nannicini 2009, Park et al. 2005, TomTom 2012).
Historical traffic profiles can represent the value of travel time observed at the time
intervals of each link for a specific period of time in the past (Kim et al. 2007). The use
of traffic profiles can be useful because it is not realistic to have a road network
completely covered by traffic recorders, and they can reduce computation time and
database storage and improve data quality (Chien and Kuchipudi 2003, Shaw 2000). A
historical profile can be considered summary statistics such as mean/median travel time
for each time slice (e.g., 60 minutes) of a road segment which are observed for certain
past time periods (e.g., 30 days). For instance, if mean travel time is used as a historical
profile, it represents the average value of the observed edge travel times over certain past
time periods (Park et al. 2005).
13
Kim et al. (2005) examined the value of real-time traffic information such as
accidents, bad weather, traffic congestion, etc., to optimize vehicle routing in a dynamic
network. Real-time traffic information combined with historical traffic data can be used
to develop routing strategies that tend to improve both cost and service productivity
measures. According to Kok et al. (2012) and Panahi and Delavar (2009), historical
traffic data can realistically represent peak-hour traffic congestion and help emergency
vehicles avoid these congested areas and improve travel time.
14
Chapter 3: Conceptual Framework and Methodology
The scope of this research was to find out if time-varying travel times derived
from historical traffic data applied to road network edges would affect the response times
and routes of emergency vehicles within the study area. The use of distance and freeflow travel time as cost attributes is common in static networks but may not reflect or be
sufficient to estimate travel time for emergency vehicle routing, since they do not reflect
dynamically changing traffic conditions (Panahi and Delavar 2009).
The overall approach and objective of this study were segmented into four parts
or elements for better understanding. The first part was to successfully develop a
functioning dynamic road network for the study area. Analyses without a well-built
functioning road network would be difficult to undertake. The second part was to
successfully convert historical traffic volume into time-varying travel time profiles that
would represent realistic travel times for different times of the day and for each day of the
week. This is in contrast to traditional methods for estimating travel times that are the
same, regardless of the time and day (TomTom 2012). The third part was to effectively
incorporate these historical traffic profiles to road edges that are applied in realistic
emergency response scenarios. The fourth part was to compare travel-time costs derived
from historical traffic data to cost attributes based on distance and free-flow travel time.
This can provide a good estimation of the performance of different congestion avoidance
strategies in a realistic setting (Kok et al. 2012, Panahi and Delavar 2009). This chapter
discusses the technical aspects of the research including an explanation of the data
15
sources and how the data was acquired, prepared and used. Figure 4 shows the general
methodology used for this research.
Acquire EMS,
Hospital & Crash
Statistics
Clip to
Study Area
Acquire State
Roads Feature
Class
Clip Roads to
Study Area
Start
EMS, Hospital
& Incident
Feature
Classes
Road Feature
Class
Road Network
File GDB
Create GDB
Acquire Historical
Traffic Data
Configure Traffic
Profile Tables
Perform Route
Analysis
Scenario 1
Locate Incident,
Response Unit &
Hospital
Perform Route
Analysis
Scenario 2
Apply Analysis
Settings
Traffic Profile
Tables
Create Network
Dataset
Network
Dataset
Compare &
Analyze Results
Create Route
Analysis Layer
Build
Road ND
Created by:
Michael
Winn
Specify Attributes
and Assign
Evaluators
Road ND &
Junctions
Figure 4. Methodology flow chart
16
3.1 Data Sources
Most of the geographic datasets used for this research were obtained from the
Utah Automated Geographic Reference Center (Utah AGRC). Datasets from the Utah
AGRC included road and highway system centerline data, emergency response facilities
or units and hospital/trauma center locations. Additional data comprised state, county,
and municipal boundaries and other information to create the base maps used for this
study.
Incident data was obtained from UDOT. In accordance with the Government
Records Access Management Act (GRAMA), it was necessary to obtain written
permission to obtain this data and was received electronically (Jones 2013). Incident data
was from actual 2010 vehicle crash site locations within Davis County and included
statistical data about the crashes.
Historical traffic data was acquired from the UDOT website. Historical traffic
profile tables were available from Esri. All data was considered public domain and was
available for use at no cost. The spatial reference for all data except HAFB was UTM
Zone 12N NAD83. HAFB spatial reference was UTM Zone 12N WGS84.
17
3.2 Data Preparation
The road centerline data was obtained from the Utah AGRC. The Utah AGRC
created a functional road network called the Street Network Analysis dataset. This
dataset contained many attribute fields, some of which were not used while other fields
were added or modified to incorporate historical traffic and other functionalities.
Although the Utah AGRC continues to improve and maintain the routing capability and
connectivity of its road network centerline features, it was discovered at the beginning of
this research that additional work was needed to prepare the road network for analysis.
Edge directionality and connectivity were issues that needed to be addressed and fixed
for the network to function properly. Connectivity and directionality cannot be overemphasized and will be discussed in more detail in subsequent sections (Granberg 2011,
Utah AGRC 2012).
3.2.1 Road Network Centerlines
The road network centerline data was extracted from the statewide road dataset by
clipping to a polygon feature that encompassed the urbanized areas of Weber and Davis
counties. This area feature closely resembles the boundary represented in the OgdenLayton Urbanized Area Functional Class System map (UDOT 2012). The road network
used for this study actually covers the urbanized areas of both Davis and Weber counties.
It was necessary to extend the network into Weber County to accommodate travel to the
two Level II trauma centers situated in the Ogden area (Figure 3). The Level I hospitals
located in northern Salt Lake County are outside the scope of this study and the road
network ends at the southern border of Davis County.
18
3.2.2 Road Classifications
To include historical traffic data for this study, the classification of road segments
had to be accomplished. All road segments were classified and coded based on UDOT’s
Urban Area Functional Classification system (Figure 5). Adherence to this classification
system was closely followed except for a few modifications necessary to fit the study.
These modifications were made by disaggregating the Urban Principal Arterial
classification into several different categories (e.g., ramps and other freeways) and
aggregating urban local roads into the Urban Minor Collector classification (Federal
Highway Administration [FHWA] 1989, Nichol 2010, UDOT 2001; 2012). Table 1
shows a list of the functional classifications, their definitions and the number of road
segments associated with each classification. Functional classification (FC) codes 3, 5,
and 10 were aggregated under FC codes 11, 12, and 14, respectively.
19
Table 1. Urban Area Functional Classification system
FC Code
3
5
10
11
12
Functional Classification
Urban Principal Arterial - Interstate - Ramp
Urban Principal Arterial - Other Freeways - Ramp
Urban Principal Arterial - Other - Ramp
Urban Principal Arterial - Interstate
Urban Principal Arterial - Other Freeways
14
Urban Principal Arterial - Other
16
Urban Minor Arterial
17
Urban Collector
19
Urban Minor Collector
Basic Functional Classification Definition
Ramp feature (see FC Code 11)
Ramp feature (see FC Code 12)
Ramp feature (see FC Code 14)
Interstates (e.g., I-15)
Other Freeways (e.g., SR 67 Legacy Highway)
Serves major activity centers. Majority of trips and
through traffic.
Trips of moderate length, lower mobility than
primary arterials.
Land access and circulation within and into
residential neighborhoods, commercial and
industrial areas. Collects from local streets and
channels to arterial system.
All routes not otherwise classified as
primary/principal arterials, minor arterials, or
collectors (e.g., urban local streets and roads).
Road Segments
192
20
42
212
13
330
1,299
1,567
24,297
27,972
Figure 5. Road network and the Urban Area Functional Classification system
20
3.2.3 Historical Hourly Traffic Volume Data
Traffic volume data is commonly referred to as traffic count or historical traffic
count data. It is considered historical because it is not real time data. This data
represents the number of vehicles passing a specific point or section of roadway for each
60 minute interval during a 24 hour period (UDOT 2010).
There are ninety-three Automatic Traffic Recorder (ATR) sites situated
throughout the state of Utah (UDOT 2010). Nine of these sites were used to collect
hourly traffic volume data for April 2010. April was preferred because it was thought it
might best represent typical traffic congestion in the study area. Weather conditions are
improving and normal workday traffic patterns are not interrupted by severe winter
weather conditions. School is in session and traffic patterns due to summer vacations,
furloughs or school recess are not affecting regular traffic patterns.
Of these nine ATR sites, five were chosen and matched to the Urban Area
Functional Classification system explained in Section 3.2.2. These ATR sites are
highlighted in Table 2 (0315, 0624, 0316, 0510, and 0601) with their associated
functional classification codes and location descriptions. In Table 2, four ATR sites
(0307, 0312, 0320 and 0609) were matched to rural area functional classifications (FC
Codes 1, 2, 6, and 7); however, no profiles were created because none of the road
segments were classified as rural. No ATR was found to represent FC Code 19. All nine
ATR sites are shown in Figure 6.
21
Table 2. ATR sites associated with the Functional Classification system
FC Code
1
2
3
5
6
7
10
11
12
14
16
17
19
Functional Classification
Rural Principal Arterial - Interstate
Rural Principal Arterial - Other
Urban Principal Arterial - Interstate - Ramp
Urban Principal Arterial - Other Freeways - Ramp
Rural Minor Arterial
Rural Major Collector
Urban Principal Arterial - Other - Ramp
Urban Principal Arterial - Interstate
Urban Principal Arterial - Other Freeways
Urban Principal Arterial - Other
Urban Minor Arterial
Urban Collector
Urban Minor Collector
ATR Site Names
0307
0312
0315
0624
0320
0609
0316
0315
0624
0316
0510
0601
NA
Location
I 84 0.5 mile E of Mountain Green Int. MP 92.593
SR 6 4.5 miles SE of SR 89, Moark Jct. MP 182.390
Same as FC 11
Same as FC 12
SR 39 0.5 mile W of SR 158, Ogden Cyn. MP 13.243
SR 167 1.2 miles W of Mountain Green Int. MP 1.250
Same as FC 14
I 15 1.8 miles S of Lagoon Drive Int. MP 321.545
SR 67 Legacy Highway MP 0.944
SR 89 2 miles S of SR 193, Hillfield Road, Layton MP 402.695
SR 218 100 N 319 W, Smithfield MP 7.700
SR 92 American Fork Canyon W Toll Booth MP 7.873
Represents all unclassified and 'Local Roads'
Figure 6. Geographic locations of the ATR sites
22
County
Morgan
Utah
Weber
Morgan
Davis
Davis
Davis
Cache
Utah
3.2.4 Grouping Historical Traffic Volume Data
The April 2010 hourly traffic volume data was grouped by weekdays and
weekends and averaged (Park et al. 2005). Weekday means Monday thru Friday, a total
of twenty-two days. Weekend means Saturday and Sunday, four days for each, a total of
8 days. There were 30 days total in April. Tables 3 and 4 show hourly traffic counts for
ATR site 0316. In Table 3, the hours are displayed along the top row and weekends are
highlighted.
Table 3. April 2010 traffic volumes for ATR site 0316
ATR
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
0316
Date
4/1/2010
4/2/2010
4/3/2010
4/4/2010
4/5/2010
4/6/2010
4/7/2010
4/8/2010
4/9/2010
4/10/2010
4/11/2010
4/12/2010
4/13/2010
4/14/2010
4/15/2010
4/16/2010
4/17/2010
4/18/2010
4/19/2010
4/20/2010
4/21/2010
4/22/2010
4/23/2010
4/24/2010
4/25/2010
4/26/2010
4/27/2010
4/28/2010
4/29/2010
4/30/2010
0
238
233
400
333
183
193
187
191
233
391
339
144
184
192
237
227
352
391
142
196
177
173
224
588
433
190
178
193
207
197
1
116
129
239
213
104
114
109
131
141
225
239
95
106
104
122
128
227
269
107
115
122
117
131
246
256
83
95
118
148
140
2
82
67
144
142
73
87
73
91
84
149
137
69
65
73
87
86
122
128
60
62
81
79
110
128
204
77
70
86
84
89
3
97
94
102
89
101
88
87
109
107
114
102
84
95
84
112
95
102
109
95
104
89
108
102
103
101
103
92
94
94
107
4
221
180
118
95
201
194
181
191
193
112
91
185
191
196
190
182
138
85
185
171
199
199
181
118
99
213
195
197
178
179
5
670
499
197
152
658
627
720
702
612
275
152
670
722
688
705
592
354
147
674
706
721
677
581
258
178
687
710
714
685
573
6
1479
1252
432
278
1448
1323
1447
1438
1301
498
303
1612
1630
1682
1597
1417
524
317
1620
1656
1721
1530
1464
606
322
1642
1658
1591
1540
1339
7
2333
2117
673
397
2252
2044
2371
2400
2252
957
377
2666
2508
2692
2589
2393
988
445
2631
2576
2468
2358
2592
1059
460
2460
2465
2271
2334
2095
8
2560
2227
1108
597
2231
2150
2403
2420
2133
1263
637
2459
2538
2524
2591
2381
1588
765
2534
2467
2391
2288
2104
1586
909
2291
2344
2259
2189
2135
9
1766
1783
1144
818
1686
1576
1729
1779
1748
1530
693
1734
1755
1837
2028
1944
1716
740
1844
1816
1759
1658
1926
1827
1004
1608
1779
1601
1621
1677
10
1609
1767
1298
1066
1614
1383
1543
1669
1706
1512
1034
1655
1566
1643
1709
1740
1858
1036
1550
1741
1566
1526
1667
1806
1095
1475
1599
1370
1413
1702
11
1670
1888
1478
1169
1674
1538
1622
1711
1811
1892
989
1591
1562
1728
1869
1881
2035
1076
1705
1722
1629
1592
1823
1928
1099
1546
1721
1551
1568
1599
23
12
1668
1880
1864
1743
1652
1565
1737
1760
1865
1886
1365
1647
1659
1727
1800
1839
2093
1403
1794
1743
1703
1652
1891
2004
1497
1610
1690
1524
1602
1682
13
1776
2011
1713
1619
1755
1523
1798
1764
1869
2031
1216
1594
1733
1811
1852
2226
2216
1399
1729
1908
1783
1739
2150
2129
1303
1620
1695
1631
1564
1901
14
1886
2187
1747
1514
1778
1618
1820
1918
2057
2003
1341
1909
1890
2092
2080
2798
2123
1472
2022
2034
2065
1943
2393
2138
1435
1971
1881
1825
1910
2097
15
2401
2492
1719
1639
2127
2002
2310
2349
2465
2031
1400
2442
2512
2605
2752
3287
2132
1547
2535
2619
2563
2467
2481
2158
1735
2413
2658
2409
2519
2436
16
2914
2964
1955
2166
2677
2600
2853
2948
2960
2239
1668
2885
2844
3090
3346
3559
2527
1950
3013
3303
2896
3126
3216
2580
2138
2951
3024
2770
2841
3029
17
3379
3130
1970
1790
3181
3009
3308
3445
3228
2063
1553
3278
3413
3536
3707
3626
2126
1632
3396
3490
3314
3360
3703
2326
1746
3426
3298
3275
3316
3330
18
2281
2320
1276
1631
1974
2081
2264
2404
2158
1845
1426
2266
2307
2523
2526
2459
1928
1463
2406
2526
2324
2421
2506
1931
1688
2453
2415
2296
2118
2410
19
1424
1594
1020
1729
1270
1288
1437
1390
1487
1469
1295
1386
1457
1665
1614
1551
1583
1459
1413
1521
1433
1643
1661
1500
1358
1409
1375
1425
1414
1574
20
1328
1266
1217
1711
859
1017
1208
1252
1186
1251
1170
1088
1168
1295
1445
1301
1323
1451
1276
1262
1141
1236
1384
1307
1205
1103
1128
1226
1068
1163
21
1119
1151
1252
1184
686
864
1013
1055
1095
1083
919
893
919
940
1103
1208
1183
995
875
1011
962
1080
1065
1294
962
937
972
847
1029
1108
22
744
933
906
676
520
812
669
704
888
974
514
521
621
621
733
881
880
566
511
602
562
701
916
988
607
550
600
538
692
847
23
363
638
538
306
289
371
360
344
558
578
250
264
307
588
342
620
671
305
273
302
317
506
810
589
662
291
314
344
342
846
Table 4 shows the hourly traffic counts grouped by weekdays and the weekend.
Averages were calculated for each hourly time slice throughout the day. Because Sunday
and Tuesday will be analyzed for all routing examples and scenarios, the highlighted
rows represent the four Tuesdays in April. Tuesday averages are shown below the 22day average to show a comparison between aggregated 22-day weekday averages and the
4-day Tuesday averages. Examples of tables and profiles associated with ATR and
traffic volume data was limited to ATR site 0316 to conserve space.
Table 4. April 2010 traffic volumes for ATR Site 0316, grouped
Weekday (M-F) 22-Day and Tuesday 4-Day Average
ATR
Date
0316 4/1/2010
0316 4/2/2010
0316 4/5/2010
0316 4/6/2010
0316 4/7/2010
0316 4/8/2010
0316 4/9/2010
0316 4/12/2010
0316 4/13/2010
0316 4/14/2010
0316 4/15/2010
0316 4/16/2010
0316 4/19/2010
0316 4/20/2010
0316 4/21/2010
0316 4/22/2010
0316 4/23/2010
0316 4/26/2010
0316 4/27/2010
0316 4/28/2010
0316 4/29/2010
0316 4/30/2010
22-Day Avg
TU 4-Day Avg
1
238
233
183
193
187
191
233
144
184
192
237
227
142
196
177
173
224
190
178
193
207
197
196
188
2
116
129
104
114
109
131
141
95
106
104
122
128
107
115
122
117
131
83
95
118
148
140
117
108
3
82
67
73
87
73
91
84
69
65
73
87
86
60
62
81
79
110
77
70
86
84
89
79
71
4
97
94
101
88
87
109
107
84
95
84
112
95
95
104
89
108
102
103
92
94
94
107
97
95
5
221
180
201
194
181
191
193
185
191
196
190
182
185
171
199
199
181
213
195
197
178
179
191
188
6
670
499
658
627
720
702
612
670
722
688
705
592
674
706
721
677
581
687
710
714
685
573
663
691
7
1479
1252
1448
1323
1447
1438
1301
1612
1630
1682
1597
1417
1620
1656
1721
1530
1464
1642
1658
1591
1540
1339
1518
1567
8
2333
2117
2252
2044
2371
2400
2252
2666
2508
2692
2589
2393
2631
2576
2468
2358
2592
2460
2465
2271
2334
2095
2403
2398
9
2560
2227
2231
2150
2403
2420
2133
2459
2538
2524
2591
2381
2534
2467
2391
2288
2104
2291
2344
2259
2189
2135
2346
2375
10
1766
1783
1686
1576
1729
1779
1748
1734
1755
1837
2028
1944
1844
1816
1759
1658
1926
1608
1779
1601
1621
1677
1757
1732
11
1609
1767
1614
1383
1543
1669
1706
1655
1566
1643
1709
1740
1550
1741
1566
1526
1667
1475
1599
1370
1413
1702
1601
1572
12
1670
1888
1674
1538
1622
1711
1811
1591
1562
1728
1869
1881
1705
1722
1629
1592
1823
1546
1721
1551
1568
1599
1682
1636
13
1668
1880
1652
1565
1737
1760
1865
1647
1659
1727
1800
1839
1794
1743
1703
1652
1891
1610
1690
1524
1602
1682
1713
1664
14
1776
2011
1755
1523
1798
1764
1869
1594
1733
1811
1852
2226
1729
1908
1783
1739
2150
1620
1695
1631
1564
1901
1792
1715
15
1886
2187
1778
1618
1820
1918
2057
1909
1890
2092
2080
2798
2022
2034
2065
1943
2393
1971
1881
1825
1910
2097
2008
1856
16
2401
2492
2127
2002
2310
2349
2465
2442
2512
2605
2752
3287
2535
2619
2563
2467
2481
2413
2658
2409
2519
2436
2493
2448
17
2914
2964
2677
2600
2853
2948
2960
2885
2844
3090
3346
3559
3013
3303
2896
3126
3216
2951
3024
2770
2841
3029
2991
2943
18
3379
3130
3181
3009
3308
3445
3228
3278
3413
3536
3707
3626
3396
3490
3314
3360
3703
3426
3298
3275
3316
3330
3370
3303
19
2281
2320
1974
2081
2264
2404
2158
2266
2307
2523
2526
2459
2406
2526
2324
2421
2506
2453
2415
2296
2118
2410
2338
2332
20
1424
1594
1270
1288
1437
1390
1487
1386
1457
1665
1614
1551
1413
1521
1433
1643
1661
1409
1375
1425
1414
1574
1474
1410
21
1328
1266
859
1017
1208
1252
1186
1088
1168
1295
1445
1301
1276
1262
1141
1236
1384
1103
1128
1226
1068
1163
1200
1144
22
1119
1151
686
864
1013
1055
1095
893
919
940
1103
1208
875
1011
962
1080
1065
937
972
847
1029
1108
997
942
23
744
933
520
812
669
704
888
521
621
621
733
881
511
602
562
701
916
550
600
538
692
847
689
659
24
363
638
289
371
360
344
558
264
307
588
342
620
273
302
317
506
810
291
314
344
342
846
427
324
4
102
114
102
103
105
5
118
112
138
118
122
6
197
275
354
258
271
7
432
498
524
606
515
8
673
957
988
1059
919
9
1108
1263
1588
1586
1386
10
1144
1530
1716
1827
1554
11
1298
1512
1858
1806
1619
12
1478
1892
2035
1928
1833
13
1864
1886
2093
2004
1962
14
1713
2031
2216
2129
2022
15
1747
2003
2123
2138
2003
16
1719
2031
2132
2158
2010
17
1955
2239
2527
2580
2325
18
1970
2063
2126
2326
2121
19
1276
1845
1928
1931
1745
20
1020
1469
1583
1500
1393
21
1217
1251
1323
1307
1275
22
1252
1083
1183
1294
1203
23
906
974
880
988
937
24
538
578
671
589
594
4
89
102
109
101
100
5
95
91
85
99
93
6
152
152
147
178
157
7
278
303
317
322
305
8
397
377
445
460
420
9
597
637
765
909
727
10
818
693
740
1004
814
11
1066
1034
1036
1095
1058
12
1169
989
1076
1099
1083
13
1743
1365
1403
1497
1502
14
1619
1216
1399
1303
1384
15
1514
1341
1472
1435
1441
16
1639
1400
1547
1735
1580
17
2166
1668
1950
2138
1981
18
1790
1553
1632
1746
1680
19
1631
1426
1463
1688
1552
20
1729
1295
1459
1358
1460
21
1711
1170
1451
1205
1384
22
1184
919
995
962
1015
23
676
514
566
607
591
24
306
250
305
662
381
Saturday Average (4 days)
ATR
0316
0316
0316
0316
Date
4/3/2010
4/10/2010
4/17/2010
4/24/2010
4-Day Avg
1
400
391
352
588
433
2
239
225
227
246
234
3
144
149
122
128
136
Sunday Average (4 days)
ATR
0316
0316
0316
0316
Date
4/4/2010
4/11/2010
4/18/2010
4/25/2010
4-Day Avg
1
333
339
391
433
374
2
213
239
269
256
244
3
142
137
128
204
153
24
3.2.5 Historical Traffic Volume Profiles
The historical traffic volume profiles were created based on the weekday and
weekend averages for the five ATR sites explained in Section 3.2.3 and displayed in
Table 2. Three profiles related to ATR site 0316 are shown in Figures 7, 8, and 9.
Figure 7 represents the profile from the 4-day Tuesday averages found in Table 4. For
comparison, the red dashed line in Figure 7 represents the 22-day weekday traffic count
averages. There is little noticeable difference between the profiles. Figure 8 and Figure
9 illustrate the profile from the 4-day weekend (Saturday and Sunday, respectively)
traffic count averages.
Esri has provided a free-flow traffic profiles table for simulating time-dependent
traffic condition (Esri 2012). There were 98 records with 5 minutes intervals in the
profiles table originally created for San Francisco areas (Esri 2012). Each record has a
unique identifier or number and stores the free-flow scale factor for each time interval.
However, in dynamic network analysis, the shorter the time interval is, the more
computational power required to run a dynamic network analysis. Therefore, to reduce
the computation complexity and to accommodate UDOT traffic volume data, this study
converted the Esri 5-minutes free-flow traffic profiles into hourly free-flow traffic
profiles and created the ‘DailyProfiles_Time_60min’ table (shown in Table 5). The table
stores the free-flow scale factors or multipliers for each 60 minute time interval or time
slice during a 24 hour day. This is 24 equal time intervals represented by 24 fields. The
profile numbers are listed in the ‘ProfileID’ field. Because of the number of fields in the
‘DailyProfiles_Time_60min’ table, the field names were shortened and some fields were
omitted.
25
Figure 7. ATR site 0316 traffic volume profile - Tuesday average, April 2010
Figure 8. ATR site 0316 traffic volume profile – Saturday average, April 2010
Figure 9. ATR site 0316 traffic volume profile – Sunday average, April 2010
26
The traffic volume profiles in this study (created based on the weekday and
weekend averages for the five ATR sites) were visually matched to the free-flow traffic
profiles created from the ‘DailyProfiles_Time_60min’ table (Table 5) by comparing the
profile or graph lines and choosing the profile with the best fit. It should be noted that
the method of visually comparing profiles is subjective and can introduce bias. Of the 98
free-flow traffic profiles found in the ‘DailyProfiles_Time_60min’ table (Table 5), there
are nine free-flow traffic profiles (‘ProfileID’ 3, 8, 12, 14, 21, 91, 92, 96, and 98) as
shown in Figures 10 through 18, respectively, matched to the traffic volume profiles
created from ATR sites 0315, 0624, 0316, 0510, and 0601 (Table 2). The three free-flow
traffic profiles that matched closest to the traffic volume profiles associated with ATR
site 0316 shown in Figures 7, 8 and 9 were profiles 91, 14 and 3. These free-flow traffic
profiles can be viewed in Figures 15, 13 and 10, respectively.
Table 6 shows how the nine free-flow traffic profiles (shown in Figures 10
through 18) are arranged and correspond to the nine road functional classifications and
the days of the week. The nine ‘ProfileID’ free-flow traffic profile numbers are
organized and stored in the ‘Project_Profiles’ table (Table 7) and correspond to the daily
traffic pattern of each road segment. The fields, ‘Profile_1' through ‘Profile_7’, in the
‘Project_Profiles’ table are populated with ‘ProfileID’ numbers and match to the same
profile numbers found in the ‘DailyProfiles_Time_60min’ table. The ‘Profile_1’ field
shows the ‘ProfileID’ of Sunday free-flow traffic profile; ‘Profile_7 field represents the
‘ProfileID’ of Saturday free-flow traffic profile; ‘Profile_2’ through ‘Profile_6’ fields are
for Monday through Friday. Therefore, there is a ‘ProfileID’ for each day of the week for
27
all 27, 972 road segments or records. Table 8 represents the ‘ProjectArea’ feature class.
Each record represents a road segment.
Table 5. ‘DailyProfiles_Time_60min’ file geodatabase table
Table 6. Profile IDs from the ‘DailyProfiles_Time_60min’ table
FC Code
3
5
10
11
12
14
16
17
19
Functional Class
Urban Principal Arterial - Interstate - Ramp
Urban Principal Arterial - Other Freeways - Ramp
Urban Principal Arterial - Other - Ramp
Urban Principal Arterial - Interstate
Urban Principal Arterial - Other Freeways
Urban Principal Arterial - Other
Urban Minor Arterial
Urban Collector
Urban Minor Collector
SUN MON TUE WED THR FRI SAT Notes
8
98
98
98
98 98 92 Same as FC Code 11
12
91
91
91
91 91 12 Same as FC Code 12
3
91
91
91
91 91 14 Same as FC Code 14
8
98
98
98
98 98 92
12
91
91
91
91 91 12
3
91
91
91
91 91 14
96
21
21
21
21 21
8
12
3
3
3
3
3
3
8
98
98
98
98 98 92
28
Figure 10. ‘DailyProfiles_Time_60min’ table: Profile 3
Figure 11. ‘DailyProfiles_Time_60min’ table: Profile 8
Figure 12. ‘DailyProfiles_Time_60min’ table: Profile 12
29
Figure 13. ‘DailyProfiles_Time_60min’ table: Profile 14
Figure 14. ‘DailyProfiles_Time_60min’ table: Profile 21
Figure 15. ‘DailyProfiles_Time_60min’ table: Profile 91
30
Figure 16. ‘DailyProfiles_Time_60min’ table: Profile 92
Figure 17. ‘DailyProfiles_Time_60min’ table: Profile 96
Figure 18. ‘DailyProfiles_Time_60min’ table: Profile 98
31
Table 7. 'Project_Profiles' file geodatabase table
OBJECTID
1
LENGTH_MI FC_CODE EdgeFCID EdgeFID FreeFlowMi Profile_1 Profile_2 Profile_3 Profile_4 Profile_5 Profile_6 Profile_7
0.051704
16
53
1
0.077556
96
21
21
21
21
21
8
17
18
0.063222
0.329915
14
11
53
53
17
18
0.094832
0.304537
3
8
91
98
91
98
91
98
91
98
91
98
14
92
20
0.079990
17
53
20
0.119984
12
3
3
3
3
3
3
23
0.035119
19
53
23
0.052679
8
98
98
98
98
98
92
51
0.045459
3
53
51
0.109103
8
98
98
98
98
98
92
3493
0.107606
10
53
3493
0.161408
3
91
91
91
91
91
14
14446
0.230291
5
53
14446
0.345437
12
91
91
91
91
91
12
14449
0.453260
12
53
14449
0.494466
12
91
91
91
91
91
12
27972
Field Name
OBJECTID
LENGTH_MI
FC_CODE
FUNCTIONAL_CLASS
Shape_Length
EdgeFCID
EdgeFID
EdgeFrmPos
EdgeToPos
FreeFlowMi
Profile_1
Profile_2
Profile_3
Profile_4
Profile_5
Profile_6
Profile_7
Val_Dir
SPFREEFLOW
SPWEEKDAY
SPWEEKEND
27972
13 of 21 total fields
27, 972 total records
Data Type
Object ID
Double
Short Integer
Text
Double
Long Integer
Long Integer
Double
Double
Double
Long Integer
Long Integer
Long Integer
Long Integer
Long Integer
Long Integer
Long Integer
Short Integer
Short Integer
Short Integer
Short Integer 21 of 21 total fields
Table 8. 'ProjectArea' feature class attribute table
OBJECTID
1
2
3
4
5
SPD_LMT
40
40
40
40
40
ONE_WAY
0
0
0
1
0
MINUTES
0.077556
0.097135
0.061795
0.064878
0.031018
LENGTH_MI
0.051704
0.064757
0.041197
0.043252
0.020678
FC_CODE
16
16
16
16
16
FT_Min
0.077556
0.097135
0.061795
0.064878
0.031018
TF_Min OneWay Shape_Len
0.077556
83.209915
0.097135
104.216068
0.061795
66.300000
0.064878 FT
69.607615
0.031018
33.278655
27968
27969
27970
27971
27972
40
40
40
55
40
0
0
0
0
0
0.097976
0.099292
0.021112
0.141260
0.070704
0.065317
0.066195
0.014075
0.129488
0.047136
16
16
16
14
16
0.097976
0.099292
0.021112
0.141260
0.070704
0.097976
0.099292
0.021112
0.141260
0.070704
Field Name
OBJECTID
LABEL
SPD_LMT
ONE_WAY
MINUTES
LENGTH_MI
FC_CODE
FUNCTIONAL_CLASS
FT_Minutes
TF_Minutes
FT_WeekdayMinutes
TF_WeekdayMinutes
FT_WeekendMinutes
TF_WeekendMinutes
OneWay
Shape_Length
Data Type
Object ID
Text
Short Integer
Short Integer
Double
Double
Short Integer
Text
Double
Double
Double
Double
Double
Double
Text
Double
16 of 85 total fields
32
105.118241
106.530051
22.651280
208.391454
75.858100
10 of 85 total fields
27972 total records
3.2.6 Modeling Historical Traffic Data
Historical traffic data is at the heart of this research and is essential for creating a
dynamic road network that will represent peak-hour traffic congestion and assist first
responders to avoid these congested areas and improve travel time. The approach to
modeling historical data for this study has its origins in the private sector by industry
leaders who provide navigation products and location-based services (LBS) to the general
public and other vendors and partners (Esri 2013a, Tele Atlas 2009, TomTom 2012).
Instead of storing historical traffic data for each individual road segment, related tables
are used to store and represent the changes in travel time throughout the day (Esri 2012).
Two tables work in conjunction with the ‘ProjectArea’ feature class that stores the road
segment features (Table 8). These are the ‘DailyProfiles_Time_60min’ and
‘Project_Profiles’ tables that are discussed in Section 3.2.5 and represented in Tables 5
and 7, respectively.
Each road segment in the ‘ProjectArea’ feature class has a unique identifier. Each
record in the ‘DailyProfiles_Time_60min’ table where the free-flow multipliers are
stored, also has a unique identifier or ‘ProfileID’ for each record or traffic profile. The
‘Project_Profiles’ table stores the free-flow travel time and the ‘ProfileID’ that best
represents traffic for each day of the week and for each road segment. This table joins
the road segments in the ‘ProjectArea’ feature class to the various traffic profiles in the
‘DailyProfiles_Time_60min’ table through a unique identifier found in the ‘EdgeFID’
field that correlates to the ‘ObjectID’ field in the ‘ProjectArea’ feature class (Esri 2012).
Other values are stored in ‘ProjectArea’ and will be discussed in the following sections.
33
All these network sources are required for historical traffic data to work in the
network dataset. When a road segment in the ‘ProjectArea’ feature class is related to a
traffic profile in the ‘DailyProfiles_Time_60min’ table by the ‘Project_Profiles’ join
table, the travel time for any 60 minute time slice on a given day is calculated. This
calculation is based on the free-flow travel time value stored in the ‘Project_Profiles’
table and the free-flow multiplier value associated with the ‘ProfileID’ in the
‘DailyProfiles_Time_60min’ table.
Example: If a road segment with an ‘ObjectID’ of 20 in the ‘ProjectArea’ feature class
(not shown in Table 8) is related to a record in the ‘Project_Profiles’ table with an
‘EdgeFID’ of 20 (Table 7) and has a ‘ProfileID’ value of 3 for Tuesday, the free-flow
travel time (‘FreeFlowMi’) in minutes is 0.119984. The expected travel time at 1800
(Figure 10) for Profile 3 will be calculated by multiplying the road segment free-flow
travel time (0.119984) by the profile's free-flow multiplier or time factor value of
1.051520 (see Table 5 at 1800 for ‘ProfileID’ 3).
34
3.2.7 Incorporating Historical Traffic Data
After the historical traffic tables were configured and populated correctly, they
were incorporated into the network dataset. This is completed during the network
creation but prior to the building process. Figure 19 shows the properties associated with
the historical traffic tables and how the ‘DailyProfiles_Time_60min’ and
‘Project_Profiles’ join tables are configured. Note that the ‘First Time Slice’ is set to
4:00 am and the ‘Last Time Slice’ is set to 10:00 pm because the free-flow multiplier
value from 10:00 pm to 4:00 am is 1.
The location where network cost attributes are applied to road network edges is
shown in Figure 20. The distance cost is displayed as ‘Length’ and corresponds to the
‘LENGTH_MI’ field in the ‘Project_Profiles’ table in Table 7 and the ‘ProjectArea’
feature class in Table 8. The free-flow travel time cost is displayed as ‘MINUTES’ and
corresponds to the 'FreeFlowMi’ field in the ‘Project_Profiles’ table in Table 7 and to the
‘MINUTES’ field in the ‘ProjectArea’ feature class in Table 8. The time-varying travel
time cost is a calculated value based on historical traffic data and is displayed as
‘TravelTime’ in Figure 20. Other costs and descriptors shown in Figure 20 were
assigned values but are not used in this analysis. ‘Oneway’ restrictions will be explained
in Section 3.3.1. Global turns will be explained in Section 3.3.2.
35
Figure 19. Network Dataset properties associated with the historical traffic tables
Figure 20. Assignment of network attributes
36
3.3 Developing the Road Network Model
Esri ArcGIS Network Analyst was used to create a dynamic road network model
and spatio-temporal database for incorporating historical traffic data and performing the
shortest path analysis. The road network model is considered dynamic in the sense that
cost attributes such as travel time change with respect to time. The database is
considered spatio-temporal in the sense it has spatial, non-spatial and temporal
characteristics such as location, attribute and time (Shaw 2000). ArcGIS is suitable for
this kind of research because it is commercially available and the Network Analyst
extension is included in the student edition of ArcGIS. Network Analyst provides the
functionality to incorporate historical traffic data and model the time-dependent costs of
traveling the network.
The term Network Dataset (ND) is important to the understanding of how a road
network is modeled and functions in Network Analyst. It is defined by Esri as a
collection of topologically connected network elements (e.g., edges, junctions, and turns)
that are derived from network sources (e.g. feature classes) and used to represent a road
network. Each network element is associated with a collection of network attributes
(e.g., cost, descriptor, hierarchy, and restriction). When any analysis is performed in
Network Analyst, it is performed on a network dataset (Esri 2013b). This term is used to
when describing road network features.
Several steps were required to create the road network dataset. The first step was
to create a file geodatabase (FGDB) as a repository for all network related elements and
feature classes including the traffic profile tables. The network dataset was created in a
feature dataset to maintain topology and spatial reference. In a geodatabase-based
37
network dataset, all feature classes participating as sources in a network are stored in a
feature dataset (Esri 2013b). Figure 21 shows a view of the file geodatabase data model.
Although it is not necessary, a relationship class was created between the
‘ProjectArea’ feature class and the ‘Project_Profiles’ table. This made the process of
editing road network features faster and simpler to manage. The records and unique
identifiers in the ‘ProjectArea’ feature class and in the ‘Project_Profiles’ table should be
identical. The final step prior to performing the analysis was to build the network
dataset. Building the network dataset is the process of creating network elements,
establishing connectivity and assigning network values (Esri 2013c).
Figure 21. File geodatabase data model
38
3.3.1 One Way Restrictions
One Way restrictions are applied to limit travel on one way roads and avoid
routing irregularities. There are 184 miles of one way road segments in the road network
comprised mostly of highways and ramps. All road segments were digitized in the
‘from-to’ (FT) direction. If the ‘OneWay’ field in the ‘ProjectArea’ feature class was
populated with FT, it means travel was only allowed in the digitized direction of the road
segments. One Way restrictions can be set to ‘Prohibit’, ‘Avoid’, or ‘Prefer’ for one way
road segments (Esri 2013d). All one way roads segments are restricted and set to
‘Prohibit’. The ‘Prefer’ and ‘Avoid’ parameters were not used because they were
considered subjective and would bias the analysis.
Example: Figure 22 shows a route from Incident 1 to Ogden Regional Medical Center
with the One Way restriction on. The correct ramps and lanes were traveled for I-84.
Figure 23 shows the route from Incident 1 to Ogden Regional Medical Center with the
One Way restriction off. Notice the incorrect ramps and lanes for I-84 were traveled.
39
Figure 22. Correct one-way travel, from Incident 1 to Ogden Regional Medical Center
Figure 23. Incorrect one-way travel, from Incident 1 to Ogden Regional Medical Center
40
3.3.2 Global Turns
Global turn delays are used as a kind of cost attribute to improve travel time
estimates by delaying movements from one road segment to another. These delays are
also referred to as turn penalties. There are four types of turn directions used in the
study: straight, reverse, right and left turn. Global turn delays are not intended to be as
accurate as the turn feature class model of applying turn penalties (Esri 2013e). Global
turns were applied to the free-flow travel time and time-varying travel time cost
attributes. They are not available for use with the distance cost attribute.
If road hierarchies were applied, more turn directions would be available for use.
Because road hierarchies are not used, all roads are considered local roads and the
numbers of turn directions to choose from were reduced. This made the application of
turn delays simpler but less exact. The default Esri turn penalty values associated with
the turn directions and descriptions in Figure 24 were not considered suitable for this
study area. Averaging the default turn penalty seconds for each turn category shown in
Figure 24 produces a more representative turn penalty value for modeling emergency
response vehicle turn movements. Table 9 show the directions and penalties in seconds
used to model the turn delays. The applied values for each turn category were derived by
averaging the seconds shown in Figure 24.
Example: There are 4 left turns with the following default Esri values; 2, 10, 5 and 8
seconds. The average is 6 seconds. The default global turn delay values that are applied
in this study are shown in Figure 25. The calculated values are listed in Figure 26. The
default values for turn angles were used.
41
Table 9. Global turn delay directions and penalty values in seconds
Direction Description
Seconds (default) Seconds (applied)
Straight
From Local to Local Road Across No Roads
0
0
Straight
From Local to Local Road Across Local Road
2
4
Reverse
From Local To Local Road
3
7
Right Turn From Local To Local Road
2
3
Left Turn
2
6
From Local To Local Road
Figure 24. Turn categories available for various road types
42
Figure 25. Global turn delay default settings
Figure 26. Global turn delay customized settings
43
In general, ambulance operators are allowed some privileges when responding to
an incident; however, safety is their number one priority. Operators are responsible for
the safe operation of the response vehicle at all times, including compliance with all
traffic laws. Usually emergency vehicles are prohibited from exceeding the posted speed
limit when approaching and crossing an intersection with the right-of-way, and they must
come to a complete stop before proceeding through a controlled intersection or using the
opposing traffic lanes to approach an intersection (International Association of Fire
Chiefs [IAFC] 2013, McDonald 2013).
In addition to safety concerns, vehicle size and maneuverability were taken into
account when assigning turn penalty values. Emergency response vehicles are larger and
more challenging to drive when negotiating turns than smaller vehicles. When making
turns or negotiating curves too fast, an ambulance could be susceptible to losing control
or even overturning due to its size and box shaped design. At a minimum, equipment,
patients, and medical personnel working with patients during transport could be tossed
about or injured. Caution with or without lights and sirens is important and will take a
few seconds longer when negotiating turns. Additional factors might include weather,
road conditions, and intersection sizes. Based on these policies and other factors
mentioned, averaging turn penalty second values is thought to be a reasonable attempt to
model emergency response routing more realistically (McDonald 2013).
44
Chapter 4: Analysis and Results
This analysis comprises two routing examples centered on two discrete vehicle
accident locations selected from 2010 UDOT crash data (shown in Table 10 as IN-1 and
IN-2). Each example comprises two scenarios. The first scenario, which will be referred
to as S1, represents an ambulance on an emergency call from a ground emergency
response unit (e.g., fire station) to the scene of a traffic incident (e.g., car crash). The
second scenario, which will be referred to as S2, represents an ambulance leaving the
scene of the accident transporting the victim(s) to the nearest hospital or trauma center.
Figure 27 shows an example routing solution for scenarios 1 and 2.
The ‘Closest Facility’ solver in Network Analyst was used to locate the nearest
ground emergency response unit and hospital to each incident. The ‘Route’ solver in
Network Analyst was used to find the shortest path between two locations using a
distance-based cost attribute, the fastest route using a time-based cost attribute known as
the free-flow travel time, and the optimal route using a time-varying cost attribute based
on historical traffic data.
For both routing scenarios, similarities and differences between route directions,
distances, and travel times generated from each cost attribute are compared and analyzed.
Emergency response routing based on cost attributes derived from historical travel-time
data and applied to network edges should assist emergency response vehicles to avoid
congested areas (Kok et al. 2012, Panahi and Delavar 2009). Figure 28 shows the
general process of the routing analysis for both routing scenarios in each example.
45
Table 10. Incident data from 2010 UDOT crash statistic
Incident Crash ID Junction Type
Crash Severity
Location
IN-1
10369590 4-Leg Intersection Non-Incapacitating Injury 2000W, at 1800 N
IN-2
10364031 4-Leg Intersection Non-Incapacitating Injury Boynton at Fairfield Rd
Figure 27. Example of routing scenarios S1 and S2
46
Network
Dataset
Apply Analysis
Settings
Run 1 (R1)
DIST
Apply Analysis
Settings
Identify Incident
Location
Locate Nearest
Ground Unit with
‘Closest Facility’
Solver
Locate Nearest
Hospital with
‘Closest Facility’
Solver
Nearest
Ground Unit
Nearest
Hospital
Scenario 1
(S1)
Scenario 2
(S2)
Apply Analysis
Settings
Apply Analysis
Settings
Run 2 (R2)
FFTT
Run 3 (R3)
TVTT
Run 1 (R1)
DIST
Solve shortest path
with ‘Route’ Solver
Compare &
Analyze
Results
Run 2 (R2)
FFTT
Solve shortest path
with ‘Route’ Solver
Created by:
Michael
Winn
Figure 28. Route analysis flowchart
47
Compare &
Analyze
Results
Run 3 (R3)
TVTT
For all routing examples (IN-1, IN-2), S1 and S2 are comprised of three routing
runs. The first run (R1) uses a distance cost attribute. The distance refers to the length in
miles of each road segment or edge in the network. This cost attribute or impedance will
be referred to as DIST.
The second run (R2) uses a travel time cost attribute. This travel time cost
represents a static shortest path calculation with no major impedances or cost other than
the base travel time for each road segment or edge. The base travel time is considered
fixed and proportional to the length of a road segment (Demiryurek et al. 2010). This
impedance is also known as the free-flow travel time or FFTT which is derived from the
free-flow speed. The FFTT speed is the speed a vehicle travels when it is not impeded by
other traffic movement. This is typically the posted speed limit but can be defined as five
miles per hour greater than the posted speed limit (Esri 2012, FHWA 2013). The
equation used to calculate the FFTT in minutes for each road segment is shown in
Equation 4.1.
Road Segment Length in Miles * (60 / Speed Limit in Miles per Hour)
Equation 4.1
The third run (R3) uses historical traffic data to model time-varying costs of
traveling on the network. Time-varying or time-dependent travel time costs are used to
find the best route from an origin to a destination. For this analysis, time-varying travel
time is referred to as TVTT. TVTT is what makes the road network considered dynamic.
How historical traffic data is modeled and incorporated into this analysis was explained
in Sections 3.2.6 and 3.2.7.
48
Sunday and Tuesday are analyzed for all routing examples and scenarios. The
start times for each routing scenario were run at the top of the hour (e.g., 0700, 0800,
etc.) for a 24 hour period. Sunday was selected to best represent weekend traffic and
Tuesday was selected to best represent weekday traffic. These selections were based on
grouping days by weekdays and weekends. Niemeier et al. (2002) claimed that “It is
well accepted that temporal profiles of daily traffic volumes tend to be similar across
certain days and time periods. For instance, the typical traffic pattern seen on Tuesday is
often very similar to the traffic pattern seen on Wednesday and Thursday. Saturday and
Sunday tend to have similar traffic patterns, whereas the patterns on Monday and Friday
are usually unique”. Some liberties were taken with these selections. Two days were
selected for analysis to reduce the size of the study.
As explained in Section 3.3.2, global turn delays are only available for use with
the FFTT and TVTT impedances. When executing the ‘Route’ solver in Network
Analyst, all three cost attributes (DIST, FFTT, TVTT) run and generate results, but only
the specified impedance is used to optimize the solution. For example, when utilizing
DIST as impedance, the ‘Route’ solver will produce the best route for the specified
impedance, which is the shortest distance route. The route run results will generate three
attribute fields. The ‘DIST (mi)’ field represents the distance or total length of the route
in miles. The ‘FFTT (min)’ field represents the free-flow travel time in decimal minutes
for the specified time interval of the route without the additional travel-time costs that
would normally be added when FFTT and TVTT impedances are used to optimize the
solution. This is because global turn restrictions are not available when the DIST
impedance is used. The ‘TVTT (min)’ field represents the time-varying travel time in
49
decimal minutes for the specified time interval of the route without the additional traveltime costs for the same reasons as explained for the ‘FFTT (min)’ field.
When the ‘Closest Facility’ solver is used, no start or end time attribute fields are
generated. When the ‘Route’ solver is used, start and end time attribute fields are
generated when FFTT and TVTT impedances are applied. However, no start or end time
attribute fields are generated when the DIST impedance is used.
Figure 29 shows the analysis settings that are available for the ‘Closest Facility’
solver. Figure 30 shows the analysis settings that are available for the ‘Route’ solver.
When the DIST and FFTT impedances are applied, time settings were used but were not
necessary. These time settings are named ‘Use Time’ in ‘Closest Facility’ solver and
‘Use Start Time’ in ‘Route’ solver. For instance, if route runs were performed using the
DIST and FFTT cost attributes every hour for 24 hours, the distance and travel time
values would be the same. Changes only occur when using time setting and the TVTT
impedance. This is required in order to apply historical traffic data. Only the impedance
applied to the route run is used to optimize the solution. For instance, if the TVTT
attribute is used as the cost attribute, DIST and FFTT costs can still be accumulated and
reported to assist in the analysis but the path is actually calculated based on the TVTT
(Esri 2013f).
4.1 Route Example for IN-1
4.1.1 IN-1: Closest Facility Analysis
Incident 1 (IN-1) is located in Clinton at the intersection of 200W, at 1800N
(Table 10). After the incident location was identified, the ‘Closest Facility’ solver was
50
Figure 29. Analysis settings available for ‘Closest Facility’ solver
Figure 30. Analysis settings available for ‘Route’ solver
51
used to locate the nearest ground unit and hospital/trauma center. The analysis settings
for each cost attribute used to find the nearest ground unit are shown in Table 11. The
analysis settings for each cost attribute used to find the nearest hospital are shown in
Table 12. The only difference in the settings between Tables 11 and 12 is in the ‘Travel
From’ field. The ‘Facility to Incident’ setting was used to find the nearest ground unit to
IN-1, and the ‘Incident to Facility’ setting was used to find the nearest hospital from IN1.
The same methodology was used to determine the nearest ground unit and
hospital to IN-1. The DIST, FFTT and TVTT impedances were applied in both
instances. Although distance should determine the shortest route, it was believed that
using the FFTT and TVTT cost attributes would validate that the shortest routes were
also the routes with the least travel time. In other words, if two hospitals were close in
total distance from the same incident, TVTT could determine that during a time of heavy
traffic congestion, the travel time to the closer hospital could be greater than the travel
time to the farther hospital.
All route runs were run for Tuesday at 1700. After previously examining the
TVTT values for a 24 hour period of time, the 1700 to 1800 time slice proved to have the
greatest TVTT in both cases. Table 13 shows the results of runs applying DIST, FFTT
and TVTT impedances to determine the nearest ground unit to IN-1. Table 14 shows the
results of runs applying DIST, FFTT and TVTT impedances to determine nearest hospital
from IN-1. When observing route run results in Tables 13 and 14, the accumulated
values are shown in italicized red font and are for reference and comparison only. The
bolded values are the values based on the applied impedance. The same settings were
52
applied to all routing examples and scenarios. Changes in routes are shown in Tables 13
and 14 under the ‘Run/Route’ field, and the ‘Figure’ field indicates the corresponding
figure showing the route changes. The ‘Run/Route’ field is used to identify the route
runs. Figures 31 through 36 show the routes associated with the cost attribute used.
For Table 13, run routes R1/A, R2/A, and R3/A indicate the shortest, fastest and
optimal routes, respectively for finding the nearest ground unit to IN-1. For Table 14,
run routes R1/A, R2/B, and R3/C indicate the shortest, fastest and optimal routes,
respectively for finding the nearest hospital from IN-1. As a result of these run routes
and applying DIST, FFTT and TVTT as impedances, it was determined the closest
ground unit to IN-1 is Clinton Fire Department and the closest hospital from IN-1 is
Davis Hospital.
Table 11. Analysis settings for finding nearest ground unit to IN-1
Impedance
DIST
FFTT
TVTT
Use Time
Yes
Yes
Yes
Usage
Start time
Start time
Start time
Time of Day
1700
1700
1700
Impedance
DIST
FFTT
TVTT
Trave From
Facility to Incident
Facility to Incident
Facility to Incident
U-Turns
Allowed
Allowed
Allowed
OneWay
Prohibited
Prohibited
Prohibited
Day of Week
SUN & TUE
SUN & TUE
SUN & TUE
Facilities to Find
3
3
3
Table 12. Analysis settings for finding nearest hospital from IN-1
Impedance
DIST
FFTT
TVTT
Use Time
Yes
Yes
Yes
Usage
Start time
Start time
Start time
Time of Day
1700
1700
1700
Impedance
DIST
FFTT
TVTT
Trave From
Incident to Facility
Incident to Facility
Incident to Facility
U-Turns
Allowed
Allowed
Allowed
OneWay
Prohibited
Prohibited
Prohibited
53
Day of Week
SUN & TUE
SUN & TUE
SUN & TUE
Facilities to Find
3
3
3
Table 13. Results for finding nearest ground unit to IN-1
Cost
DIST
DIST
DIST
FFTT
FFTT
FFTT
TVTT
TVTT
TVTT
Origin-Destination
Clinton FD to IN-1
Sunset FD to IN-1
N. Davis FD West Pt to IN-1
Clinton FD to IN-1
Sunset FD to IN-1
N. Davis FD West Pt to IN-1
Clinton FD to IN-1
Sunset FD to IN-1
N. Davis FD West Pt to IN-1
Run/Route
R1/A
R1/A
R1/A
R2/A
R2/A
R2/B
R3/A
R3/A
R3/C
Day
TU
TU
TU
TU
TU
TU
TU
TU
TU
Time DIST (mi) FFTT (min) TVTT (min) Figure
1700
0.887
1.330
1.759
31
1700
1.922
2.882
3.423
31
1700
2.705
5.228
7.750
31
1700
0.887
1.747
2.176
32
1700
1.922
4.249
4.790
32
1700
2.714
5.090
6.369
32
1700
0.887
1.747
2.176
33
1700
1.922
4.249
4.790
33
1700
2.715
5.692
6.885
33
Table 14. Results for finding nearest hospital from IN-1
Cost
DIST
DIST
DIST
FFTT
FFTT
FFTT
TVTT
TVTT
TVTT
Origin-Destination
IN-1 to Davis
IN-1 to Ogden Regional
IN-1 to McKay Dee
IN-1 to Davis
IN-1 to Ogden Regional
IN-1 to McKay Dee
IN-1 to Davis
IN-1 to McKay Dee
IN-1 to Ogden Regional
Run/Route
R1/A
R1/A
R1/A
R2/B
R2/B
R2/B
R3/C
R3/B
R3/C
Day
TU
TU
TU
TU
TU
TU
TU
TU
TU
Time DIST (mi) FFTT (min) TVTT (min) Figure
1700
6.260
11.505
16.702
34
1700
8.812
16.503
28.633
34
1700
8.932
15.583
25.452
34
1700
6.362
10.579
19.310
35
1700
8.977
16.424
27.936
35
1700
8.979
18.469
24.478
35
1700
6.339
13.106
17.358
36
1700
8.979
18.469
24.478
36
1700
9.150
20.199
25.955
36
Figure 31. Routes from nearest ground unit to IN-1 applying DIST impedance
54
Figure 32. Routes from nearest ground unit to IN-1 applying FFTT impedance
Figure 33. Routes from nearest ground unit to IN-1 applying TVTT impedance
55
Figure 34. Routes from IN-1 to nearest hospital applying DIST impedance
56
Figure 35. Routes from IN-1 to nearest hospital applying FFTT impedance
57
Figure 36. Routes from IN-1 to nearest hospital applying TVTT impedance
4.1.2 IN-1: Route Analysis Scenario 1
Scenario 1 (S1) is the route run and analysis from the Clinton Fire Department to
IN-1, which illustrates an ambulance on an emergency run from Clinton Fire Department
to IN-1. The analysis settings for each cost attribute used for S1 are shown in Table 15.
58
The results from S1 are divided into three sections for examination. The first section
describes the tables and figures associated with each route analysis run. The second
section explains the findings. The third section discusses the effects of the time-varying
travel time as impedance for network analysis.
Description
Six tables and four figures were created based on these runs. Tables 16 and 17
show the results of runs from Clinton FD to IN-1 applying the DIST impedance for
Sunday and Tuesday, respectively. The DIST impedance was used to optimize the
solution. The ‘DIST (mi)’ field shows the path distance expressed as the total length of
the route in miles. The ‘FFTT (min)’ field shows the accumulated free-flow travel time
value in decimal minutes. The ‘TVTT (min)’ field shows the accumulated time-varying
travel time value in decimal minutes. The values that are italicized and highlighted in red
were used for comparison purposes only and were not used to optimize the solution.
The DIST impedance route run is considered a static network analysis since the
path distance does not change through time. Therefore, Tables 16 and 17 show one
record representing all 24 time intervals. The ‘FFTT (min)’ field represents the
accumulated free-flow travel time for the route results and the ‘TVTT (min)’ field shows
the accumulated TVTT value calculated for 1700 (5:00 pm) only. Both ‘FFTT (min)’
and ‘TVTT (min)’ fields are generated without global turns delays since the global turn
restriction is not available while applying DIST as impedance.
Tables 18 and 19 show the results of runs from Clinton FD to IN-1 applying the
FFTT impedance for Sunday and Tuesday, respectively. The FFTT impedance was used
59
to optimize the solution. The FFTT impedance is considered a static network analysis
since the free-flow travel time of each road segment does not change through time.
Therefore, Tables 18 and 19 have the same value in ‘FFTT (min)’ field throughout the
run. The ‘TVTT (min)’ field shows the accumulated TVTT value calculated for the route
in each corresponding time interval.
All tables have a ‘Route’ field that represents the path created for each impedance
analysis. Though the route results (shown in the ‘Route’ field) from both DIST and
FFTT impedance runs are the same, the values in ‘FFTT (min)’ field are different when
comparing Table 16 to Table 18 and Table 17 to Table 19. The FFTT values in Tables
18 and 19 are greater than those in Tables 16 and 17. This is because global turn delays
(Section 3.3.2) were used in the FFTT impedance runs but cannot be used in the DIST
impedance runs. Start and end times are not generated when DIST is used as the
impedance but they are generated when FFTT is used as the impedance. Global turn
delays are used and reflected in the ‘FFTT (min)’ values, but they are not reflected in the
elapsed run times found in the ‘EndTime (hms)’ field. In other words, the FFTT values
will not be the same as the end times. If global turn delays were not used, these times
would be the same.
Tables 20 and 21 show the results of runs from Clinton FD to IN-1 applying the
TVTT impedance for Sunday and Tuesday, respectively. The TVTT impedance was
used to optimize the solution. Figures 37 and 38 show the travel time profiles associated
with Tables 20 and 21, respectively. They represent the TVTT when historical traffic
data is applied. Both the FFTT and TVTT values are generated with global turn delays;
therefore, they are different from those shown in Tables 16 and 17.
60
It is important to note that when TVTT is applied as impedance, the optimal route
choice (shown in the ‘Route’ field) might be varied in different time slices. Table 20
shows that there are two optimal routes choices, Route A and Route B, in the ‘Route’
field, generated by the ‘Route’ solver based on the time, day, and impedance applied.
Route A (Figure 39) is the optimal solution for Sunday from 0000 (midnight) to 1000
(10:00 am) and from 2000 (8:00 pm) to 2400 (midnight), but Route B (Figure 40) is the
optimal solution for Sunday from 1000 (10:00 am) to 2000 (8:00 pm) when TVTT is
used for impedance. The values in the ‘TVTT (min)’ field represents the accumulated
travel time of the optimal route in each time interval. The values in the ‘DIST (mi)’ and
‘FFTT (min)’ fields are adjusted corresponding to the change of route. The values in
‘DIST (mile)’ field represents the path distance in miles of the selected optimal route
(Route A or B), and the values in ‘FFTT (min)’ field represents the free-flow travel time
of the decimal minutes of the selected optimal route (Route A or B).
Table 15. Analysis settings used for S1
Impedance
DIST
FFTT
TVTT
Use Start Time
Yes
Yes
Yes
Time of Day
0000 to 2300
0000 to 2300
0000 to 2300
Day of Week
SUN & TUE
SUN & TUE
SUN & TUE
Impedance
DIST
FFTT
TVTT
Reorder Stops
No
No
No
U-Turns
Allowed
Allowed
Allowed
OneWay
Prohibited
Prohibited
Prohibited
Use Time Windows
No
No
No
Table 16. Scenario 1, Sunday, Clinton FD to IN-1, DIST impedance
Route Origin-Destination DIST (mi) FFTT (min) TVTT (min)
A
Clinton FD to IN-1
0.887
1.330
2.242
Table 17. Scenario 1, Tuesday, Clinton FD to IN-1, DIST impedance
Route Origin-Destination DIST (mi) FFTT (min) TVTT (min)
A
Clinton FD to IN-1
0.887
1.330
1.759
61
Table 18. Scenario 1, Sunday, Clinton FD to IN-1, FFTT impedance
Route
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
Clinton FD to IN-1
0.887
1.747
1.747
0:00:00
0:01:20
Clinton FD to IN-1
0.887
1.747
1.747
1:00:00
1:01:20
Clinton FD to IN-1
0.887
1.747
1.747
2:00:00
2:01:20
Clinton FD to IN-1
0.887
1.747
1.747
3:00:00
3:01:20
Clinton FD to IN-1
0.887
1.747
1.747
4:00:00
4:01:20
Clinton FD to IN-1
0.887
1.747
1.751
5:00:00
5:01:20
Clinton FD to IN-1
0.887
1.747
1.759
6:00:00
6:01:20
Clinton FD to IN-1
0.887
1.747
1.780
7:00:00
7:01:20
Clinton FD to IN-1
0.887
1.747
1.867
8:00:00
8:01:20
Clinton FD to IN-1
0.887
1.747
2.060
9:00:00
9:01:20
Clinton FD to IN-1
0.887
1.747
2.317
10:00:00
10:01:20
Clinton FD to IN-1
0.887
1.747
2.581
11:00:00
11:01:20
Clinton FD to IN-1
0.887
1.747
2.777
12:00:00
12:01:20
Clinton FD to IN-1
0.887
1.747
2.829
13:00:00
13:01:20
Clinton FD to IN-1
0.887
1.747
2.820
14:00:00
14:01:20
Clinton FD to IN-1
0.887
1.747
2.785
15:00:00
15:01:20
Clinton FD to IN-1
0.887
1.747
2.720
16:00:00
16:01:20
Clinton FD to IN-1
0.887
1.747
2.659
17:00:00
17:01:20
Clinton FD to IN-1
0.887
1.747
2.523
18:00:00
18:01:20
Clinton FD to IN-1
0.887
1.747
2.328
19:00:00
19:01:20
Clinton FD to IN-1
0.887
1.747
2.163
20:00:00
20:01:20
Clinton FD to IN-1
0.887
1.747
1.871
21:00:00
21:01:20
Clinton FD to IN-1
0.887
1.747
1.747
22:00:00
22:01:20
Clinton FD to IN-1
0.887
1.747
1.747
23:00:00
23:01:20
Table 19. Scenario 1, Tuesday, Clinton FD to IN-1, FFTT impedance
Route
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
Clinton FD to IN-1
0.887
1.747
2.036
0:00:00
0:01:20
Clinton FD to IN-1
0.887
1.747
2.036
1:00:00
1:01:20
Clinton FD to IN-1
0.887
1.747
2.036
2:00:00
2:01:20
Clinton FD to IN-1
0.887
1.747
2.036
3:00:00
3:01:20
Clinton FD to IN-1
0.887
1.747
2.036
4:00:00
4:01:20
Clinton FD to IN-1
0.887
1.747
2.042
5:00:00
5:01:20
Clinton FD to IN-1
0.887
1.747
2.045
6:00:00
6:01:20
Clinton FD to IN-1
0.887
1.747
2.083
7:00:00
7:01:20
Clinton FD to IN-1
0.887
1.747
2.157
8:00:00
8:01:20
Clinton FD to IN-1
0.887
1.747
2.162
9:00:00
9:01:20
Clinton FD to IN-1
0.887
1.747
2.144
10:00:00
10:01:20
Clinton FD to IN-1
0.887
1.747
2.147
11:00:00
11:01:20
Clinton FD to IN-1
0.887
1.747
2.142
12:00:00
12:01:20
Clinton FD to IN-1
0.887
1.747
2.138
13:00:00
13:01:20
Clinton FD to IN-1
0.887
1.747
2.142
14:00:00
14:01:20
Clinton FD to IN-1
0.887
1.747
2.158
15:00:00
15:01:20
Clinton FD to IN-1
0.887
1.747
2.169
16:00:00
16:01:20
Clinton FD to IN-1
0.887
1.747
2.176
17:00:00
17:01:20
Clinton FD to IN-1
0.887
1.747
2.156
18:00:00
18:01:20
Clinton FD to IN-1
0.887
1.747
2.117
19:00:00
19:01:20
Clinton FD to IN-1
0.887
1.747
2.088
20:00:00
20:01:20
Clinton FD to IN-1
0.887
1.747
2.053
21:00:00
21:01:20
Clinton FD to IN-1
0.887
1.747
2.036
22:00:00
22:01:20
Clinton FD to IN-1
0.887
1.747
2.036
23:00:00
23:01:20
62
Table 20. Scenario 1, Sunday, Clinton FD to IN-1, TVTT impedance
Route
A
A
A
A
A
A
A
A
A
A
B
B
B
B
B
B
B
B
B
B
A
A
A
A
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
Clinton FD to IN-1
0.887
1.747
1.747
0:00:00
0:01:20
Clinton FD to IN-1
0.887
1.747
1.747
1:00:00
1:01:20
Clinton FD to IN-1
0.887
1.747
1.747
2:00:00
2:01:20
Clinton FD to IN-1
0.887
1.747
1.747
3:00:00
3:01:20
Clinton FD to IN-1
0.887
1.747
1.747
4:00:00
4:01:20
Clinton FD to IN-1
0.887
1.747
1.751
5:00:00
5:01:20
Clinton FD to IN-1
0.887
1.747
1.759
6:00:00
6:01:21
Clinton FD to IN-1
0.887
1.747
1.780
7:00:00
7:01:22
Clinton FD to IN-1
0.887
1.747
1.867
8:00:00
8:01:27
Clinton FD to IN-1
0.887
1.747
2.060
9:00:00
9:01:39
Clinton FD to IN-1
1.136
2.304
2.352
10:00:00
10:01:45
Clinton FD to IN-1
1.136
2.304
2.373
11:00:00
11:01:46
Clinton FD to IN-1
1.136
2.304
2.390
12:00:00
12:01:47
Clinton FD to IN-1
1.136
2.304
2.404
13:00:00
13:01:48
Clinton FD to IN-1
1.136
2.304
2.417
14:00:00
14:01:49
Clinton FD to IN-1
1.136
2.304
2.428
15:00:00
15:01:50
Clinton FD to IN-1
1.136
2.304
2.439
16:00:00
16:01:50
Clinton FD to IN-1
1.136
2.304
2.458
17:00:00
17:01:51
Clinton FD to IN-1
1.136
2.304
2.460
18:00:00
18:01:52
Clinton FD to IN-1
1.136
2.304
2.431
19:00:00
19:01:50
Clinton FD to IN-1
0.887
1.747
2.163
20:00:00
20:01:45
Clinton FD to IN-1
0.887
1.747
1.871
21:00:00
21:01:27
Clinton FD to IN-1
0.887
1.747
1.747
22:00:00
22:01:20
Clinton FD to IN-1
0.887
1.747
1.747
23:00:00
23:01:20
Figure 37. IN-1 Scenario 1, Sunday travel time profile, TVTT impedance
63
Table 21. Scenario 1, Tuesday, Clinton FD to IN-1, TVTT impedance
Route
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
Clinton FD to IN-1
0.887
1.747
2.036
0:00:00
0:01:37
Clinton FD to IN-1
0.887
1.747
2.036
1:00:00
1:01:37
Clinton FD to IN-1
0.887
1.747
2.036
2:00:00
2:01:37
Clinton FD to IN-1
0.887
1.747
2.036
3:00:00
3:01:37
Clinton FD to IN-1
0.887
1.747
2.036
4:00:00
4:01:37
Clinton FD to IN-1
0.887
1.747
2.042
5:00:00
5:01:38
Clinton FD to IN-1
0.887
1.747
2.045
6:00:00
6:01:38
Clinton FD to IN-1
0.887
1.747
2.083
7:00:00
7:01:40
Clinton FD to IN-1
0.887
1.747
2.157
8:00:00
8:01:44
Clinton FD to IN-1
0.887
1.747
2.162
9:00:00
9:01:45
Clinton FD to IN-1
0.887
1.747
2.144
10:00:00
10:01:44
Clinton FD to IN-1
0.887
1.747
2.147
11:00:00
11:01:44
Clinton FD to IN-1
0.887
1.747
2.142
12:00:00
12:01:43
Clinton FD to IN-1
0.887
1.747
2.138
13:00:00
13:01:43
Clinton FD to IN-1
0.887
1.747
2.142
14:00:00
14:01:43
Clinton FD to IN-1
0.887
1.747
2.158
15:00:00
15:01:45
Clinton FD to IN-1
0.887
1.747
2.169
16:00:00
16:01:45
Clinton FD to IN-1
0.887
1.747
2.176
17:00:00
17:01:46
Clinton FD to IN-1
0.887
1.747
2.156
18:00:00
18:01:44
Clinton FD to IN-1
0.887
1.747
2.117
19:00:00
19:01:42
Clinton FD to IN-1
0.887
1.747
2.088
20:00:00
20:01:40
Clinton FD to IN-1
0.887
1.747
2.053
21:00:00
21:01:38
Clinton FD to IN-1
0.887
1.747
2.036
22:00:00
22:01:37
Clinton FD to IN-1
0.887
1.747
2.036
23:00:00
23:01:37
Figure 38. IN-1 Scenario 1, Tuesday travel time profile, TVTT impedance
64
Figure 39. IN-1 Scenario 1, Route A
Figure 40. IN-1 Scenario 1, Route B
65
Findings
Based on the results found in Tables 16 and 17, the total distance of Route A
(Figure 39) for Sunday and Tuesday was 0.887 miles. This value is based on the DIST
impedance and represents the shortest path from Clinton FD to IN-1 for Sunday and
Tuesday. No route changes were observed based on the use of the DIST cost attribute.
When only a distance-based cost attribute is used for impedance, the result is the shortest
path between the origin and destination.
Based on the results found in Tables 18 and 19, where FFTT was used as
impedance, the total FFTT for each run was 1.747 minutes for Sunday and Tuesday. The
total distance for each run or Route A was 0.887 miles. This is the sum of all road
segments or edges associated with the route. When FFTT is used as the impedance,
historical traffic data is not used to optimize the solution; the values in the ‘TVTT (min)’
field were just calculated for comparison. No variations in DIST, FFTT, or routes were
observed based on runs for Sunday and Tuesday. Note that the DIST values are the same
as those in Tables 16 and 17 but the FFTT values are not. The difference between 1.330
value found in Tables 16 and 17 and 1.747 value found in Tables 18 and 19 is because of
the application of global turn delays (Section 3.3.2). If global turn delays were not
applied, the FFTT values in Table 18 and 19 would be 1.330, a difference of 0.417
minutes. This is a good example why accumulated values must be compared cautiously.
When only a FFTT cost attribute is used for impedance, the result is the fastest route
between the origin and the destination. In this instance, it is also the shortest route
because the total distance is the same as those distances found in Tables 16 and 17 when
the DIST impedance is applied.
66
The impedance used to create Tables 20 and 21 was the TVTT cost attribute for
Sunday and Tuesday, respectively. TVTT is derived from historical traffic data. For
Sunday (Table 20), the TVTTs for 17 of 24 time intervals are shown to vary with time.
From the time intervals 0000 (midnight) to 0400 (4:00 am) and 2200 (10:00 pm) to 2300
(11:00 pm), the travel-time values are identical (1.747 minutes). These values are exactly
the same as the free-flow travel times (shown in the ‘FFTT (min)’ field) associated with
lighter traffic patterns of late evening and early morning hours on a Sunday. TVTT
values between the time intervals 0500 (5:00 am) and 2100 (9:00 pm) vary based on
Sunday time-of-day traffic patterns. Traffic congestion is believed to be the primary
reason.
The different values in the ‘DIST (mi)’ and ‘FFTT (min)’ fields in Table 20 are
due to a route change. This change occurs between the time intervals 1000 (10:00 am)
and 1900 (7:00 pm), represented as Route B in the ‘Route’ field and highlighted in
orange. The total distance for the route associated with Route A (Figure 39) is 0.887
miles which is the same as the DIST values in Tables 16 through 19. The distance value
increased slightly (0.249 miles) to 1.136 miles due to the change from Route A to Route
B (Figure 40). It indicates that Route A has a shorter distance than Route B, but it has a
longer travel time when time-varying travel times are used for impedance. Based on
Tables 16, 18 and 20, Route A would be considered as the shortest and fastest route for
Sunday traffic patterns and the optimal route for Sunday between midnight to 10:00 am
and from 8:00 pm to midnight. Route B would be considered as the optimal route for
Sunday from 10:00 am to 8:00 pm.
67
Table 21 shows the TVTT for Tuesday; the TVTTs for 17 of 24 time intervals are
shown to vary with time. From the time intervals 0000 (midnight) to 0400 (4:00 am) and
2200 (10:00 pm) to 2300 (11:00 pm), the travel-time values are identical (2.036 minutes).
These values are close to the free-flow travel times (shown in the ‘FFTT (min)’ field)
associated with lighter traffic patterns of late evening and early morning hours on a
Tuesday. TVTT values between the time intervals 0500 (5:00 am) and 2100 (9:00 pm)
vary, however, based on Tuesday time-of-day traffic patterns. Traffic congestion is
believed to be the primary reason.
The ‘DIST (mi)’ and ‘FFTT (min)’ fields in Table 21 do not indicate a route
change. Route A shown in the ‘Route’ field is constant throughout the day. The total
distance for the path associated with Route A (Figure 39) is 0.887 miles. This distance is
the same as the DIST values in Tables 16 through 19. When Tables 19 and 21 for
Tuesday are compared, the values in the ‘DIST (mi)’, ‘FFTT (min)’ and ‘TVTT (min)’
fields are the same. Although the TVTT values in Table 21 vary with time between the
time intervals 0500 (5:00 am) and 2100 (9:00 pm), they do not change enough to generate
a new route. Based on Tables 17, 19 and 21, Route A would be considered as the
shortest, fastest and most optimal route for Tuesday traffic patterns.
Discussion
Although travel distance and travel time generated by applying TVTT impedance
sometimes increased due to traffic congestion, previous research (Alazab et al. 2011,
Chien and Kuchipudi 2003, Wu et al. 2001) has demonstrated that the travel times and
routes generated within a dynamic network are still considered as more realistic than the
68
ones in a static network environment. For instance, in Route Analysis Scenario 1 for IN1, Route B would be considered a more realistic optimal route than Route A during the
hours of 1000 (10:00am) and 2000 (8:00 pm) for Sunday traffic pattern.
Table 22 compares the travel times for Route A and Route B for Sunday during
the hours of 1000 (10:00am) to 2000 (8:00 pm) in order to validate the assumption that
applying TVTT will yield a more optimal routing solution when compared to DIST or
FFTT. Columns ‘A-I’, ‘A-II’, and ‘A-III’ are the values in the ‘DIST (mi)’, ‘FFTT
(min)’, and ‘TVTT (min)’ fields, respectively, from Table 18. Though the route choices
from Table 18 were based on FFTT as the impedance and generated Route A as the
fastest route, the values in the ‘TVTT (min)’ field were generated by applying TVTT as
impedance, which represents the accumulated time-varying travel time for Route A in
each time interval. The values in the ‘DIST (mi)’ field were generated by applying DIST
as impedance, which represents the total lengths of the road segments in Route A.
Columns ‘B-I’, ‘B-II’, and ‘B-III’ are the values in the ‘DIST (mi)’, ‘FFTT
(min)’, and ‘TVTT (min)’ fields, respectively, from Table 20 when TVTT was applied as
the impedance and generated Route B as the optimal route. The value in the ‘DIST (mi)’
represents the total lengths of Route B. The values in the ‘FFTT (min)’ field were
generated by applying FFTT as impedance, which represents the accumulated free-flow
travel time for Route B. Columns ‘A-IV’ and ‘B-IV’ are multipliers or free-flow factors
derived from Tables 18 and 20, respectively. These free-flow factors are ratios,
calculated by dividing TVTT by FFTT (TVTT/FFTT). The lower the value of the freeflow factor means the travel time is closer to the free-flow travel time with less traffic
congestion.
69
Table 22. IN-1 Scenario 1, Sunday, comparison of cost impedance between
Routes A and B
A-I
A-II
Route A
A-III
From (hrs) To (hrs) DIST (mi) FFTT (min)
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
0.887
0.887
0.887
0.887
0.887
0.887
0.887
0.887
0.887
0.887
1.747
1.747
1.747
1.747
1.747
1.747
1.747
1.747
1.747
1.747
Route B
A-IV
B-I
B-II
B-III
B-IV
Free-flow
Free-flow
TVTT (min)
DIST (mi) FFTT (min) TVTT (min)
Factor
Factor
2.317
1.326
1.136
2.304
2.352
1.021
2.581
1.478
1.136
2.304
2.373
1.030
2.777
1.590
1.136
2.304
2.390
1.037
2.829
1.619
1.136
2.304
2.404
1.043
2.820
1.614
1.136
2.304
2.417
1.049
2.785
1.594
1.136
2.304
2.428
1.054
2.720
1.557
1.136
2.304
2.439
1.059
2.659
1.552
1.136
2.304
2.458
1.067
2.523
1.444
1.136
2.304
2.460
1.068
2.328
1.333
1.136
2.304
2.431
1.055
Comparing the DIST and FFTT value between Routes A and B within a static
network environment, Route A is a better choice with shorter distance (Column ‘A-I’ vs.
Column ‘B-I’) and less free-flow travel time (Column ‘A-II’ vs. Column ‘B-II’). When
considering a dynamic network environment with time-varying travel time, Route B is a
more optimal choice with lower travel time (Column ‘B-III’ vs. Column ‘A-III’) for
Sunday during the hours of 1000 (10:00 am) and 2000 (8:00 pm). Two exceptions take
place at the time intervals 1000 (10:00 am) and 1900 (7:00 pm); Route A has less travel
time than Route B. However, when comparing Columns ‘A-IV’ and ‘B-IV’, Route B has
a lower free-flow factor than Route A, which means there is less traffic in Route B than
in Route A. Therefore, for the hours from 10:00 am to 11:00 am, and from 7:00 pm to
8:00 pm, Route B could be considered a better or more reliable route than Route A, but
not more optimal.
70
4.1.3 IN-1: Route Analysis Scenario 2
Scenario 2 is the route run and analysis from the IN-1 to Davis Hospital. S2
represents an ambulance on an emergency run from IN-1 to Davis Hospital. The analysis
settings window is shown in Figure 30. The analysis settings for each cost attribute used
for S2 are the same as those used for S1 and are shown in Table 15.
Description
Six tables and five figures were created based on these runs. Tables 23 and 24
show the results of runs from IN-1 to Davis Hospital applying the DIST impedance for
Sunday and Tuesday, respectively. Similar to Tables 16 and 17, the ‘TVTT (min)’ field
in these tables show the accumulated TVTT value calculated for 1700 (5:00 pm) only.
Tables 25 and 26 show the results of runs from IN-1 to Davis Hospital applying
the FFTT impedance for Sunday and Tuesday, respectively. Tables 27 and 28 show the
results of runs from IN-1 to Davis Hospital applying the TVTT impedance for Sunday
and Tuesday, respectively. Figures 41 and 42 show the travel time profiles associated
with Tables 27 and 28, respectively. They represent the TVTT when historical traffic
data is applied. Routes A (Figure 43), B (Figure 44) and C (Figure 45) represent the
routes generated by the ‘Route’ solver based on the time, day and impedance applied.
Table 23. Scenario 2, Sunday, IN-1 to Davis Hospital, DIST impedance
Route Origin-Destination DIST (mi) FFTT (min) TVTT (min)
A
IN-1 to Davis Hospital
6.260
11.505
15.081
Table 24. Scenario 2, Tuesday, IN-1 to Davis Hospital, DIST impedance
Route Origin-Destination DIST (mi) FFTT (min) TVTT (min)
A
IN-1 to Davis Hospital
6.260
11.505
16.702
71
Table 25. Scenario 2, Sunday, IN-1 to Davis Hospital, FFTT impedance
Route
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
IN-1 to Davis Hospital
6.362
10.579
10.579
0:00:00
0:08:23
IN-1 to Davis Hospital
6.362
10.579
10.579
1:00:00
1:08:23
IN-1 to Davis Hospital
6.362
10.579
10.579
2:00:00
2:08:23
IN-1 to Davis Hospital
6.362
10.579
10.579
3:00:00
3:08:23
IN-1 to Davis Hospital
6.362
10.579
10.579
4:00:00
4:08:23
IN-1 to Davis Hospital
6.362
10.579
10.604
5:00:00
5:08:23
IN-1 to Davis Hospital
6.362
10.579
10.624
6:00:00
6:08:23
IN-1 to Davis Hospital
6.362
10.579
10.664
7:00:00
7:08:23
IN-1 to Davis Hospital
6.362
10.579
10.775
8:00:00
8:08:23
IN-1 to Davis Hospital
6.362
10.579
10.932
9:00:00
9:08:23
IN-1 to Davis Hospital
6.362
10.579
11.119
10:00:00
10:08:23
IN-1 to Davis Hospital
6.362
10.579
11.285
11:00:00
11:08:23
IN-1 to Davis Hospital
6.362
10.579
11.373
12:00:00
12:08:23
IN-1 to Davis Hospital
6.362
10.579
11.382
13:00:00
13:08:23
IN-1 to Davis Hospital
6.362
10.579
11.379
14:00:00
14:08:23
IN-1 to Davis Hospital
6.362
10.579
11.368
15:00:00
15:08:23
IN-1 to Davis Hospital
6.362
10.579
11.325
16:00:00
16:08:23
IN-1 to Davis Hospital
6.362
10.579
11.268
17:00:00
17:08:23
IN-1 to Davis Hospital
6.362
10.579
11.157
18:00:00
18:08:23
IN-1 to Davis Hospital
6.362
10.579
11.008
19:00:00
19:08:23
IN-1 to Davis Hospital
6.362
10.579
10.911
20:00:00
20:08:23
IN-1 to Davis Hospital
6.362
10.579
10.695
21:00:00
21:08:23
IN-1 to Davis Hospital
6.362
10.579
10.579
22:00:00
22:08:23
IN-1 to Davis Hospital
6.362
10.579
10.579
23:00:00
23:08:23
Table 26. Scenario 2, Tuesday, IN-1 to Davis Hospital, FFTT impedance
Route
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
IN-1 to Davis Hospital
6.362
10.579
12.945
0:00:00
0:08:23
IN-1 to Davis Hospital
6.362
10.579
12.945
1:00:00
1:08:23
IN-1 to Davis Hospital
6.362
10.579
12.945
2:00:00
2:08:23
IN-1 to Davis Hospital
6.362
10.579
12.945
3:00:00
3:08:23
IN-1 to Davis Hospital
6.362
10.579
12.945
4:00:00
4:08:23
IN-1 to Davis Hospital
6.362
10.579
12.988
5:00:00
5:08:23
IN-1 to Davis Hospital
6.362
10.579
13.413
6:00:00
6:08:23
IN-1 to Davis Hospital
6.362
10.579
15.342
7:00:00
7:08:23
IN-1 to Davis Hospital
6.362
10.579
18.149
8:00:00
8:08:23
IN-1 to Davis Hospital
6.362
10.579
17.819
9:00:00
9:08:23
IN-1 to Davis Hospital
6.362
10.579
17.254
10:00:00
10:08:23
IN-1 to Davis Hospital
6.362
10.579
17.308
11:00:00
11:08:23
IN-1 to Davis Hospital
6.362
10.579
17.503
12:00:00
12:08:23
IN-1 to Davis Hospital
6.362
10.579
17.520
13:00:00
13:08:23
IN-1 to Davis Hospital
6.362
10.579
17.732
14:00:00
14:08:23
IN-1 to Davis Hospital
6.362
10.579
18.304
15:00:00
15:08:23
IN-1 to Davis Hospital
6.362
10.579
18.856
16:00:00
16:08:23
IN-1 to Davis Hospital
6.362
10.579
19.310
17:00:00
17:08:23
IN-1 to Davis Hospital
6.362
10.579
18.462
18:00:00
18:08:23
IN-1 to Davis Hospital
6.362
10.579
16.608
19:00:00
19:08:23
IN-1 to Davis Hospital
6.362
10.579
14.935
20:00:00
20:08:23
IN-1 to Davis Hospital
6.362
10.579
13.447
21:00:00
21:08:23
IN-1 to Davis Hospital
6.362
10.579
12.945
22:00:00
22:08:23
IN-1 to Davis Hospital
6.362
10.579
12.945
23:00:00
23:08:23
72
Table 27. Scenario 2, Sunday, IN-1 to Davis Hospital, TVTT impedance
Route
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
IN-1 to Davis Hospital
6.362
10.579
10.579
0:00:00
0:08:23
IN-1 to Davis Hospital
6.362
10.579
10.579
1:00:00
1:08:23
IN-1 to Davis Hospital
6.362
10.579
10.579
2:00:00
2:08:23
IN-1 to Davis Hospital
6.362
10.579
10.579
3:00:00
3:08:23
IN-1 to Davis Hospital
6.362
10.579
10.579
4:00:00
4:08:23
IN-1 to Davis Hospital
6.362
10.579
10.604
5:00:00
5:08:24
IN-1 to Davis Hospital
6.362
10.579
10.624
6:00:00
6:08:25
IN-1 to Davis Hospital
6.362
10.579
10.664
7:00:00
7:08:28
IN-1 to Davis Hospital
6.362
10.579
10.775
8:00:00
8:08:34
IN-1 to Davis Hospital
6.362
10.579
10.932
9:00:00
9:08:44
IN-1 to Davis Hospital
6.362
10.579
11.119
10:00:00
10:08:55
IN-1 to Davis Hospital
6.362
10.579
11.285
11:00:00
11:09:05
IN-1 to Davis Hospital
6.362
10.579
11.373
12:00:00
12:09:10
IN-1 to Davis Hospital
6.362
10.579
11.382
13:00:00
13:09:11
IN-1 to Davis Hospital
6.362
10.579
11.379
14:00:00
14:09:11
IN-1 to Davis Hospital
6.362
10.579
11.368
15:00:00
15:09:10
IN-1 to Davis Hospital
6.362
10.579
11.325
16:00:00
16:09:08
IN-1 to Davis Hospital
6.362
10.579
11.268
17:00:00
17:09:04
IN-1 to Davis Hospital
6.362
10.579
11.157
18:00:00
18:08:57
IN-1 to Davis Hospital
6.362
10.579
11.008
19:00:00
19:08:49
IN-1 to Davis Hospital
6.362
10.579
10.911
20:00:00
20:08:43
IN-1 to Davis Hospital
6.362
10.579
10.695
21:00:00
21:08:30
IN-1 to Davis Hospital
6.362
10.579
10.579
22:00:00
22:08:23
IN-1 to Davis Hospital
6.362
10.579
10.579
23:00:00
23:08:23
Figure 41. IN-1 Scenario 2, Sunday travel time profile, TVTT impedance
73
Table 28. Scenario 2, Tuesday, IN-1 to Davis Hospital, TVTT impedance
Route
B
B
B
B
B
B
B
B
C
C
C
C
C
C
C
C
C
C
C
C
B
B
B
B
Origin-Destination
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
IN-1 to Davis Hospital
DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
6.362
10.579
12.945
0:00:00
0:10:45
6.362
10.579
12.945
1:00:00
1:10:45
6.362
10.579
12.945
2:00:00
2:10:45
6.362
10.579
12.945
3:00:00
3:10:45
6.362
10.579
12.945
4:00:00
4:10:45
6.362
10.579
12.988
5:00:00
5:10:47
6.362
10.579
13.413
6:00:00
6:11:13
6.362
10.579
15.342
7:00:00
7:13:09
6.339
13.106
17.195
8:00:00
8:13:42
6.339
13.106
17.185
9:00:00
9:13:41
6.339
13.106
17.071
10:00:00
10:13:34
6.339
13.106
17.090
11:00:00
11:13:35
6.339
13.106
17.083
12:00:00
12:13:35
6.339
13.106
17.069
13:00:00
13:13:34
6.339
13.106
17.101
14:00:00
14:13:36
6.339
13.106
17.211
15:00:00
15:13:43
6.339
13.106
17.294
16:00:00
16:13:48
6.339
13.106
17.358
17:00:00
17:13:51
6.339
13.106
17.215
18:00:00
18:13:43
6.339
13.106
16.918
19:00:00
19:13:25
6.362
10.579
14.935
20:00:00
20:12:44
6.362
10.579
13.447
21:00:00
21:11:15
6.362
10.579
12.945
22:00:00
22:10:45
6.362
10.579
12.945
23:00:00
23:10:45
Figure 42. IN-1 Scenario 2, Tuesday travel time profile, TVTT impedance
74
Figure 43. IN-1 Scenario 2, Route A
Figure 44. IN-1 Scenario 2, Route B
75
Figure 45. IN-1 Scenario 2, Route C
Findings
Based on the results found in Tables 23 and 24, the total distance of Route A
(Figure 43) for Sunday and Tuesday was 6.260 miles. The value was based on the DIST
impedance and represents the shortest path from IN-1 to Davis Hospital for Sunday and
Tuesday. No route changes were observed based on the use of the DIST impedance.
Based on the results found in Tables 25 and 26, where FFTT was used as
impedance, the total FFTT for each run was 10.579 minutes for Sunday and Tuesday.
The total length for each run or Route B (Figure 44) was 6.362 miles. The difference in
length between Route A in Table 23 and Route B in Table 25 was 0.102 miles or 1.6%.
The difference in travel time between Route A and B was 0.926 minutes or 8.0%. The
use of FFTT as an impedance triggered the change from Route A in Table 23 to Route B
76
in Table 25 with relatively small differences in the path length and travel time. It was
also observed that Route B makes use of a more direct route taking advantage of
Interstate 15 (I-15) with greater speed limits when compared to Route A. No variations
in DIST or FFTT were observed based on runs for Sunday and Tuesday.
The impedance used to create Tables 27 and 28 was the TVTT cost attribute for
Sunday and Tuesday, respectively. Table 27 shows the TVTT for Sunday; the TVTTs for
17 of 24 time intervals are shown to vary with time. From the time intervals 0000
(midnight) to 0400 (4:00 am) and 2200 (10:00 pm) to 2300 (11:00 pm), the travel-time
values are identical (10.579 minutes) as free-flow travel times in the ‘FFTT (min)’ field.
These values illustrate lighter traffic patterns of late evening and early morning hours on
a Sunday. TVTT values between the time intervals 0500 (5:00 am) and 2100 (9:00 pm)
vary based on Sunday time-of-day traffic patterns.
The ‘DIST (mi)’ and ‘FFTT (min)’ fields in Table 27 do not indicate a route
change. Route B shown in the ‘Route’ field is constant throughout the day. The total
distance for Route B is 6.362 miles. This distance is the same as the DIST values in
Tables 25 and 26. When Tables 25 and 27 for Sunday are compared, the values in the
‘DIST (mi)’, ‘FFTT (min)’ and ‘TVTT (min)’ fields are the same. Although the TVTT
values in Table 27 vary with time between the time intervals 0500 (5:00 am) and 2100
(9:00 pm), they do not change enough to generate a new route. Route B, based on the
TVTT impedance for Sunday, would be considered as the optimal route. Based on
Tables 23, 25 and 27, Route A would be considered as the shortest path and Route B
would be considered as the fastest and most optimal route for Sunday traffic patterns.
77
For Tuesday (Table 28), the TTVTs for 17 of 24 time intervals are shown to vary
with time. From the time intervals 0000 (midnight) to 0400 (4:00 am) and 2200 (10:00
pm) to 2300 (11:00 pm), the travel-time values are identical (12.945 minutes). These
values are close to the free-flow travel times (shown in the ‘FFTT (min)’ field) associated
with lighter traffic patterns of late evening and early morning hours on a Tuesday. TVTT
values between the time intervals 0500 (5:00 am) and 2100 (9:00 pm) vary based on
Tuesday time-of-day traffic patterns.
The ‘DIST (mi)’ and ‘FFTT (min)’ fields in Table 28 indicate a route change.
This change occurs between the time intervals 0800 (8:00 am) and 1900 (7:00 pm)
denoted by Route B and Route C (Figure 45) in the ‘Route’ field. The total distance for
the route associated with Route B is 6.362 miles. This distance is the same as the DIST
values in Tables 25 through 27. The distance value decreased slightly (-0.023 miles) to
6.339 miles due to the change from Route B to Route C. These changes are based on
increased day time traffic congestion. Based on Tables 24, 26 and 28, Route A would be
considered as the shortest path and Route B would be considered as the fastest route for
Tuesday traffic patterns. Route B would also be considered as the most optimal route
between midnight and 8:00 am and from 8:00 pm to midnight, but Route C is the most
optimal route from 8:00 am to 8:00 pm for Tuesday.
Discussion
Table 29 compares travel times for Route B and Route C for Tuesday during the
hours between 8:00 am and 8:00 pm to validate that applying TVTT will yield a more
optimal routing solution. Columns ‘B-I’, ‘B-II’, and ‘B-III’ are the values in the ‘DIST
78
(mi)’, ‘FFTT (min)’, and ‘TVTT (min)’ fields, respectively, from Table 26. Columns ‘CI’, ‘C-II’, and ‘C-III’ are the values in the ‘DIST (mi)’, ‘FFTT (min)’, and ‘TVTT (min)’
fields, respectively, from Table 28. Columns ‘B-IV’ and ‘C-IV’ are the free-flow factors
derived from Tables 26 and 28, respectively.
Comparing the DIST and FFTT values between Routes B and C within a static
network environment, Route B is the better solution for free-flow travel times, but Route
C has shorter travel distance. When considering a dynamic network environment with
time-varying travel time, Route C is a more optimal choice with lower travel time for
Tuesday during the hours of 0800 (8:00 am) to 2000 (8:00 pm). One exception takes
place at the time interval 1900 (7:00 pm), Route B requires less travel time than Route C.
However, when compare the Columns ‘B-IV’ and ‘C-IV’, Route C has a lower free-flow
factor than Route B, which means there is less traffic in Route C than in Route B.
Therefore, for the hours between 7:00 pm and 8:00 pm, Route C could be considered a
better or more reliable route than Route B, but not more optimal.
Table 29. IN-1 Scenario 2, Tuesday, comparison of cost impedance between
Routes B and C
BI
B-II
Route B
B-III
From (hrs) To (hrs) DIST (mi) FFTT (min) TVTT (min)
0800
0900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
0900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
6.362
6.362
6.362
6.362
6.362
6.362
6.362
6.362
6.362
6.362
6.362
6.362
10.579
10.579
10.579
10.579
10.579
10.579
10.579
10.579
10.579
10.579
10.579
10.579
18.149
17.819
17.254
17.308
17.503
17.520
17.732
18.304
18.856
19.310
18.426
16.608
Route C
B-IV
C-I
C-II
C-III
C-IV
Free-flow
Free-flow
DIST (mi) FFTT (min) TVTT (min)
Factor
Factor
1.716
6.339
13.106
17.195
1.312
1.684
6.339
13.106
17.185
1.311
1.631
6.339
13.106
17.071
1.303
1.636
6.339
13.106
17.090
1.304
1.655
6.339
13.106
17.083
1.303
1.656
6.339
13.106
17.069
1.302
1.676
6.339
13.106
17.101
1.305
1.730
6.339
13.106
17.211
1.313
1.782
6.339
13.106
17.294
1.320
1.825
6.339
13.106
17.358
1.324
1.745
6.339
13.106
17.215
1.314
1.570
6.339
13.106
16.918
1.291
79
4.1.4 IN-1: Emergency Response Routing Review
In review, four maps and one table were created showing the combined results of
Scenarios 1 and 2. For each map, the dashed red line represents the emergency response
route from Clinton FD (origin) to IN-1 (destination), and the blue dashed line represents
the emergency response route from IN-1 (origin) to Davis Hospital (destination). For
comparison purposes, each route was run at 1700 (5:00 pm) for Sunday and Tuesday.
Figure 46 shows the shortest route from Clinton FD to IN-1 (S1, Route A) and
from IN-1 to Davis Hospital (S2, Route A) when the static cost attribute DIST was
applied as impedance. The results were the same for Sunday and Tuesday. No route
change was observed between Sunday and Tuesday runs. Figure 47 illustrates the fastest
route from Clinton FD to IN-1 (S1, Route A) and from IN-1 to Davis Hospital (S2, Route
B) when the static cost attribute FFTT was applied as impedance. The results were the
same for Sunday and Tuesday. No route change was observed between Sunday and
Tuesday runs. In this instance, the fastest route from Clinton FD to IN-1 (Route A) is
also the shortest route.
The optimal routes generated by the dynamic cost attribute TVTT as impedance
are shown in Figures 48 and 49. Route changes were observed between the Sunday and
Tuesday runs due to the application of historical traffic data representing traffic
congestion. Figure 48 shows the dynamic optimal route from Clinton FD to IN-1 (S1,
Route B) and from IN-1 to Davis Hospital (S2, Route B); these paths are considered as
the most optimal routes from each origin to each destination on 5:00 pm, Sunday. In this
instance, the optimal route from IN-1 to Davis Hospital (Route B) is also the fastest
route.
80
Figure 46. IN-1, combined scenarios, Sunday and Tuesday, DIST impedance
Figure 47. IN-1, combined scenarios, Sunday and Tuesday, FFTT impedance
81
Figure 48. IN-1, combined scenarios, Sunday, TVTT impedance
Figure 49. IN-1, combined scenarios, Tuesday, TVTT impedance
82
Figure 49 shows the dynamic optimal route from Clinton FD to IN-1 (S1, Route
A) and from IN-1 to Davis Hospital (S2, Route C); these paths are considered as the most
optimal routes from each origin to each destination on 5:00 pm, Sunday. In this instance,
the optimal route from Clinton FD to IN-1 (Route A) is also the shortest route.
Table 30 shows the distances and travel times associated with each route
generated for routing example IN-1, and the routes are displayed in Figures 46 through
49. This table can be used to analyze the values associated with each route. When
observing route run results, the bolded values are based on the applied impedance that
was used to optimize the solution. The accumulated values are shown in italicized red
font and are for reference and comparison only. As previously mentioned, it is important
to note that differences in travel times can occur because of the application of global turn
delays (Sections 3.3.2 and 4.1.2 IN-1).
Table 30. IN-1, combined scenarios, comparison of emergency response routes
Cost
DIST
DIST
DIST
DIST
FFTT
FFTT
FFTT
FFTT
TVTT
TVTT
TVTT
TVTT
Day StartTime (h)
SU
1700
SU
1700
TU
1700
TU
1700
SU
1700
SU
1700
TU
1700
TU
1700
SU
1700
SU
1700
TU
1700
TU
1700
Scenario
S1
S2
S1
S2
S1
S2
S1
S2
S1
S2
S1
S2
Route
A
A
A
A
A
B
A
B
B
B
A
C
Origin-Destination
Dist (mi) FFTT (min) TTVT (min) Figure
Clinton FD to IN-1
0.887
1.330
2.242 46
IN-1 to Davis Hospital
6.260
11.505
15.081 46
Clinton FD to IN-1
0.887
1.330
1.759 46
IN-1 to Davis Hospital
6.260
11.505
16.702 46
Clinton FD to IN-1
0.887
1.747
2.659 47
IN-1 to Davis Hospital
6.362
10.579
11.268 47
Clinton FD to IN-1
0.887
1.747
2.176 47
IN-1 to Davis Hospital
6.362
10.579
19.310 47
Clinton FD to IN-1
1.136
2.304
2.458 48
IN-1 to Davis Hospital
6.362
10.579
11.268 48
Clinton FD to IN-1
0.887
1.747
2.176 49
IN-1 to Davis Hospital
6.339
13.106
17.358 49
83
4.2 Route Example for IN-2
4.2.1 IN-2: Closest Facility Analysis
Incident 2 (IN-2) is located in Kaysville at the intersection of Boynton and
Fairfield Roads (Table 10). The same methodology and analysis settings used in 4.1.1
IN-1: Closest Facility Analysis were applied to this routing example. As a result of these
runs and applying DIST, FFTT and TVTT as impedances, it was determined the closest
ground unit to IN-2 is Kaysville Fire Department, and the closest hospital from IN-2 is
Davis Hospital. Tables 31 and 32 indicate runs 1A, 2A and 3A are the shortest, fastest
and optimal routes, respectively. Figures 50 through 55 show the routes associated with
the cost attribute used.
Table 31. Results for finding nearest ground unit to IN-2
Run
1A
1B
1C
2A
2B
2C
2A
2B
2C
Cost
DIST
DIST
DIST
FFTT
FFTT
FFTT
TVTT
TVTT
TVTT
Origin-Destination
Kaysville FD to IN-2
Layton FD No. 53 to IN-2
Layton FD No. 52 to IN-2
Kaysville FD to IN-2
Layton FD No. 53 to IN-2
Layton FD No. 52 to IN-2
Kaysville FD to IN-2
Layton FD No. 53 to IN-2
Layton FD No. 52 to IN-2
Route
A
A
A
A
B
A
B
B
A
Day
TU
TU
TU
TU
TU
TU
TU
TU
TU
Time DIST (mi) FFTT (min) TVTT (min) Figure
1700
1.038
1.900
3.277
50
1700
1.888
3.338
6.480
50
1700
3.985
5.978
8.639
50
1700
1.038
2.517
3.894
51
1700
1.953
4.013
4.839
51
1700
3.985
8.011
10.673
51
1700
1.277
2.879
3.431
52
1700
1.953
4.013
4.839
52
1700
3.985
8.011
10.673
52
Table 32. Results for finding nearest hospital from IN-2
Run
1A
1B
1C
2A
2B
2C
2A
2B
2C
Cost
DIST
DIST
DIST
FFTT
FFTT
FFTT
TVTT
TVTT
TVTT
Origin-Destination
IN-2 to Davis Hospital
IN-2 to McKay Dee
IN-2 to Ogden Regional
IN-2 to Davis Hospital
IN-2 to Ogden Regional
IN-2 to McKay Dee
IN-2 to Davis Hospital
IN-2 to Ogden Regional
IN-2 to McKay Dee
Route
A
A
A
B
B
B
C
C
C
Day
TU
TU
TU
TU
TU
TU
TU
TU
TU
Time DIST (mi) FFTT (min) TVTT (min) Figure
1700
5.055
7.620
15.095
53
1700
11.464
15.855
31.475
53
1700
11.551
15.509
30.022
53
1700
5.895
7.696
18.733
54
1700
12.130
17.774
28.431
54
1700
11.987
17.936
29.039
54
1700
5.338
10.538
13.485
55
1700
12.659
20.547
29.147
55
1700
12.515
20.709
29.755
55
84
Figure 50. Routes from nearest ground unit to IN-2 applying DIST impedance
85
Figure 51. Routes from nearest ground unit to IN-2 applying FFTT impedance
86
Figure 52. Routes from nearest ground unit to IN-2 applying TVTT impedance
87
Figure 53. Routes from IN-2 to nearest hospital applying DIST impedance
88
Figure 54. Routes from IN-2 to nearest hospital applying FFTT impedance
89
Figure 55. Routes from IN-2 to nearest hospital applying TVTT impedance
90
4.2.2 IN-2: Route Analysis Scenario 1
Scenario 1 is the route run and analysis from Kaysville Fire Department to IN-2.
S1 represents an ambulance on an emergency run from Kaysville Fire Department to IN2. The same methodology and analysis settings used in 4.1.2 IN-1: Route Analysis
Scenario 1 were applied to this route analysis.
Description
Six tables and four figures were created based on these runs. Tables 33 and 34
show the results of runs from Kaysville FD to IN-2 applying the DIST impedance for
Sunday and Tuesday, respectively. Similar to Tables 23 and 24, the ‘TVTT (min)’ field
in these tables shows the accumulated TVTT value calculated for 1700 (5:00 pm) only.
Tables 35 and 36 show the results of runs from Kaysville FD to IN-2 applying the
FFTT impedance for Sunday and Tuesday, respectively. Tables 37 and 38 show the
results of runs from Kaysville FD to IN-2 applying the TVTT impedance for Sunday and
Tuesday, respectively. Figures 56 and 57 show the travel time profiles associated with
Tables 37 and 38, respectively. Routes A and B are displayed in Figures 58 and 59,
respectively, and represent the routes generated by the ‘Route’ solver based on the time,
day and impedance applied.
Table 33. Scenario 1, Sunday, Kaysville FD to IN-2, DIST impedance
Route Origin-Destination DIST (mi) FFTT (min) TVTT (min)
A
Kaysville FD to IN-2
1.038
1.900
3.145
Table 34. Scenario 1, Tuesday, Kaysville FD to IN-2, DIST impedance
Route Origin-Destination DIST (mi) FFTT (min) TVTT (min)
A
Kaysville FD to IN-2
1.038
1.900
3.277
91
Table 35. Scenario 1, Sunday, Kaysville FD to IN-2, FFTT impedance
Route
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
Kaysville FD to IN-2
1.038
2.517
2.517
0:00:00
0:01:54
Kaysville FD to IN-2
1.038
2.517
2.517
1:00:00
1:01:54
Kaysville FD to IN-2
1.038
2.517
2.517
2:00:00
2:01:54
Kaysville FD to IN-2
1.038
2.517
2.517
3:00:00
3:01:54
Kaysville FD to IN-2
1.038
2.517
2.517
4:00:00
4:01:54
Kaysville FD to IN-2
1.038
2.517
2.525
5:00:00
5:01:54
Kaysville FD to IN-2
1.038
2.517
2.539
6:00:00
6:01:54
Kaysville FD to IN-2
1.038
2.517
2.571
7:00:00
7:01:54
Kaysville FD to IN-2
1.038
2.517
2.698
8:00:00
8:01:54
Kaysville FD to IN-2
1.038
2.517
2.963
9:00:00
9:01:54
Kaysville FD to IN-2
1.038
2.517
3.312
10:00:00
10:01:54
Kaysville FD to IN-2
1.038
2.517
3.668
11:00:00
11:01:54
Kaysville FD to IN-2
1.038
2.517
3.926
12:00:00
12:01:54
Kaysville FD to IN-2
1.038
2.517
3.992
13:00:00
13:01:54
Kaysville FD to IN-2
1.038
2.517
3.981
14:00:00
14:01:54
Kaysville FD to IN-2
1.038
2.517
3.936
15:00:00
15:01:54
Kaysville FD to IN-2
1.038
2.517
3.847
16:00:00
16:01:54
Kaysville FD to IN-2
1.038
2.517
3.762
17:00:00
17:01:54
Kaysville FD to IN-2
1.038
2.517
3.576
18:00:00
18:01:54
Kaysville FD to IN-2
1.038
2.517
3.309
19:00:00
19:01:54
Kaysville FD to IN-2
1.038
2.517
3.087
20:00:00
20:01:54
Kaysville FD to IN-2
1.038
2.517
2.690
21:00:00
21:01:54
Kaysville FD to IN-2
1.038
2.517
2.517
22:00:00
22:01:54
Kaysville FD to IN-2
1.038
2.517
2.517
23:00:00
23:01:54
Table 36. Scenario 1, Tuesday, Kaysville FD to IN-2, FFTT impedance
Route
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
Kaysville FD to IN-2
1.038
2.517
2.709
0:00:00
0:01:54
Kaysville FD to IN-2
1.038
2.517
2.709
1:00:00
1:01:54
Kaysville FD to IN-2
1.038
2.517
2.709
2:00:00
2:01:54
Kaysville FD to IN-2
1.038
2.517
2.709
3:00:00
3:01:54
Kaysville FD to IN-2
1.038
2.517
2.709
4:00:00
4:01:54
Kaysville FD to IN-2
1.038
2.517
2.723
5:00:00
5:01:54
Kaysville FD to IN-2
1.038
2.517
2.794
6:00:00
6:01:54
Kaysville FD to IN-2
1.038
2.517
3.148
7:00:00
7:01:54
Kaysville FD to IN-2
1.038
2.517
3.686
8:00:00
8:01:54
Kaysville FD to IN-2
1.038
2.517
3.639
9:00:00
9:01:54
Kaysville FD to IN-2
1.038
2.517
3.527
10:00:00
10:01:54
Kaysville FD to IN-2
1.038
2.517
3.540
11:00:00
11:01:54
Kaysville FD to IN-2
1.038
2.517
3.564
12:00:00
12:01:54
Kaysville FD to IN-2
1.038
2.517
3.562
13:00:00
13:01:54
Kaysville FD to IN-2
1.038
2.517
3.600
14:00:00
14:01:54
Kaysville FD to IN-2
1.038
2.517
3.712
15:00:00
15:01:54
Kaysville FD to IN-2
1.038
2.517
3.813
16:00:00
16:01:54
Kaysville FD to IN-2
1.038
2.517
3.894
17:00:00
17:01:54
Kaysville FD to IN-2
1.038
2.517
3.735
18:00:00
18:01:54
Kaysville FD to IN-2
1.038
2.517
3.391
19:00:00
19:01:54
Kaysville FD to IN-2
1.038
2.517
3.090
20:00:00
20:01:54
Kaysville FD to IN-2
1.038
2.517
2.809
21:00:00
21:01:54
Kaysville FD to IN-2
1.038
2.517
2.709
22:00:00
22:01:54
Kaysville FD to IN-2
1.038
2.517
2.709
23:00:00
23:01:54
92
Table 37. Scenario 1, Sunday, Kaysville FD to IN-2, TVTT impedance
Route
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
Kaysville FD to IN-2
1.038
2.517
2.517
0:00:00
0:01:54
Kaysville FD to IN-2
1.038
2.517
2.517
1:00:00
1:01:54
Kaysville FD to IN-2
1.038
2.517
2.517
2:00:00
2:01:54
Kaysville FD to IN-2
1.038
2.517
2.517
3:00:00
3:01:54
Kaysville FD to IN-2
1.038
2.517
2.517
4:00:00
4:01:54
Kaysville FD to IN-2
1.038
2.517
2.525
5:00:00
5:01:55
Kaysville FD to IN-2
1.038
2.517
2.539
6:00:00
6:01:55
Kaysville FD to IN-2
1.038
2.517
2.571
7:00:00
7:01:57
Kaysville FD to IN-2
1.038
2.517
2.698
8:00:00
8:02:05
Kaysville FD to IN-2
1.038
2.517
2.963
9:00:00
9:02:21
Kaysville FD to IN-2
1.038
2.517
3.312
10:00:00
10:02:42
Kaysville FD to IN-2
1.038
2.517
3.668
11:00:00
11:03:03
Kaysville FD to IN-2
1.038
2.517
3.926
12:00:00
12:03:19
Kaysville FD to IN-2
1.038
2.517
3.992
13:00:00
13:03:23
Kaysville FD to IN-2
1.038
2.517
3.981
14:00:00
14:03:22
Kaysville FD to IN-2
1.038
2.517
3.936
15:00:00
15:03:19
Kaysville FD to IN-2
1.038
2.517
3.847
16:00:00
16:03:14
Kaysville FD to IN-2
1.038
2.517
3.762
17:00:00
17:03:09
Kaysville FD to IN-2
1.038
2.517
3.576
18:00:00
18:02:58
Kaysville FD to IN-2
1.038
2.517
3.309
19:00:00
19:02:42
Kaysville FD to IN-2
1.038
2.517
3.087
20:00:00
20:02:28
Kaysville FD to IN-2
1.038
2.517
2.690
21:00:00
21:02:04
Kaysville FD to IN-2
1.038
2.517
2.517
22:00:00
22:01:54
Kaysville FD to IN-2
1.038
2.517
2.517
23:00:00
23:01:54
Figure 56. IN-2 Scenario 1, Sunday travel time profile, TVTT impedance
93
Table 38. Scenario 1, Tuesday, Kaysville FD to IN-2, TVTT impedance
Route
A
A
A
A
A
A
A
B
B
B
B
B
B
B
B
B
B
B
B
B
B
A
A
A
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
Kaysville FD to IN-2
1.038
2.517
2.709
0:00:00
0:02:06
Kaysville FD to IN-2
1.038
2.517
2.709
1:00:00
1:02:06
Kaysville FD to IN-2
1.038
2.517
2.709
2:00:00
2:02:06
Kaysville FD to IN-2
1.038
2.517
2.709
3:00:00
3:02:06
Kaysville FD to IN-2
1.038
2.517
2.709
4:00:00
4:02:06
Kaysville FD to IN-2
1.038
2.517
2.723
5:00:00
5:02:06
Kaysville FD to IN-2
1.038
2.517
2.794
6:00:00
6:02:11
Kaysville FD to IN-2
1.277
2.879
3.246
7:00:00
7:02:25
Kaysville FD to IN-2
1.277
2.879
3.394
8:00:00
8:02:34
Kaysville FD to IN-2
1.277
2.879
3.402
9:00:00
9:02:34
Kaysville FD to IN-2
1.277
2.879
3.366
10:00:00
10:02:32
Kaysville FD to IN-2
1.277
2.879
3.374
11:00:00
11:02:32
Kaysville FD to IN-2
1.277
2.879
3.362
12:00:00
12:02:32
Kaysville FD to IN-2
1.277
2.879
3.354
13:00:00
13:02:31
Kaysville FD to IN-2
1.277
2.879
3.362
14:00:00
14:02:32
Kaysville FD to IN-2
1.277
2.879
3.396
15:00:00
15:02:34
Kaysville FD to IN-2
1.277
2.879
3.416
16:00:00
16:02:35
Kaysville FD to IN-2
1.277
2.879
3.431
17:00:00
17:02:36
Kaysville FD to IN-2
1.277
2.879
3.392
18:00:00
18:02:34
Kaysville FD to IN-2
1.277
2.879
3.313
19:00:00
19:02:29
Kaysville FD to IN-2
1.277
2.879
3.256
20:00:00
20:02:25
Kaysville FD to IN-2
1.038
2.517
2.809
21:00:00
21:02:12
Kaysville FD to IN-2
1.038
2.517
2.709
22:00:00
22:02:06
Kaysville FD to IN-2
1.038
2.517
2.709
23:00:00
23:02:06
Figure 57. IN-2 Scenario 1, Tuesday travel time profile, TVTT impedance
94
Figure 58. IN-2 Scenario 1, Route A
Figure 59. IN-2 Scenario 1, Route B
95
Findings
Based on the results found in Tables 33 and 34, the total distance of Route A
(Figure 58) for Sunday and Tuesday was 1.038 miles. Based on the results found in
Tables 35 and 36, where FFTT was used as impedance, the total FFTT for each run was
the same at 2.517 minutes for Sunday and Tuesday. The total length for each run or
Route A (Figure 58) was 1.038 miles. No variations in DIST, FFTT, or routes were
observed based on runs for Sunday and Tuesday. In this instance, the fastest route is also
the shortest route from Kaysville FD to IN-2 (S1, Route A).
The impedance used to create Tables 37 and 38 was the TVTT cost attribute for
Sunday and Tuesday, respectively. For Sunday (Table 37), the TVTTs for 17 of 24 time
intervals are shown to vary with time. From the time intervals 0000 (midnight) to 0400
(4:00 am) and 2200 (10:00 pm) to 2300 (11:00 pm), the travel-time values are identical
(2.517 minutes). The ‘DIST (mi)’ and ‘FFTT (min)’ fields in Table 37 do not indicate a
route change. Based on Tables 33, 35 and 37, Route A would be considered the shortest,
fastest, and most optimal route for Sunday traffic patterns.
For Tuesday (Table 38), the TVTTs for 17 of 24 time intervals are shown to vary
with time. From the time intervals 0000 (midnight) to 0400 (4:00 am) and 2200 (10:00
pm) to 2300 (11:00 pm), the travel-time values are identical (2.709 minutes). The ‘DIST
(mi)’ and ‘FFTT (min)’ fields in Table 38 indicate a route change. This change occurs
between the time intervals 0700 (7:00 am) and 2000 (8:00 pm), represented as Route B
(Figure 59) in the ‘Route’ field and highlighted in orange. The distance value increased
slightly (0.239 miles) to 1.277 miles due to the change from Route A to Route B. Based
on Tables 34, 36 and 38, Route A would be considered the shortest and fastest route for
96
Tuesday traffic patterns. Route A would also be considered as the most optimal route
from midnight to 7:00 am and from 9:00 pm to midnight, but Route B is the most optimal
route from 7:00 am to 9:00 pm for Tuesday.
Discussion
Table 39 compares travel times for Route A and Route B for Tuesday during the
hours between 7:00 am and 9:00 pm. Route A is a better choice with shorter distance and
less free-flow travel time when comparing the static DIST and FFTT values. Route B is
a more optimal choice with lower travel time for Tuesday during the hours of 7000 (7:00
am) and 2100 (9:00 pm). Two exceptions take place at the time intervals 0700 (7:00 am)
and 2000 (8:00 pm), when Route A has less travel time than Route B, but Route B has a
lower free-flow factor with less traffic than Route A. Therefore, for the hours from 7:00
am to 8:00 am, and from 8:00 pm to 9:00 pm, Route B could be considered a better or
more reliable route than Route A, but not more optimal.
Table 39. IN-2 Scenario 1, Tuesday, comparison of cost impedance between
Routes A and B
A-I
A-II
Route A
A-III
From (hrs) To (hrs) DIST (mi) FFTT (min) TVTT (min)
0700
0800
0900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
0800
0900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
1.038
1.038
1.038
1.038
1.038
1.038
1.038
1.038
1.038
1.038
1.038
1.038
1.038
1.038
2.517
2.517
2.517
2.517
2.517
2.517
2.517
2.517
2.517
2.517
2.517
2.517
2.517
2.517
3.148
3.686
3.639
3.527
3.540
3.564
3.562
3.600
3.712
3.813
3.894
3.735
3.391
3.090
Route B
A-IV
B-I
B-II
B-III
B-IV
Free-flow
Free-flow
DIST (mi) FFTT (min) TVTT (min)
Factor
Factor
1.251
1.277
2.879
3.246
1.127
1.464
1.277
2.879
3.394
1.179
1.446
1.277
2.879
3.402
1.182
1.401
1.277
2.879
3.366
1.169
1.406
1.277
2.879
3.374
1.172
1.416
1.277
2.879
3.362
1.168
1.415
1.277
2.879
3.354
1.165
1.430
1.277
2.879
3.362
1.168
1.475
1.277
2.879
3.396
1.180
1.515
1.277
2.879
3.416
1.187
1.547
1.277
2.879
3.431
1.192
1.484
1.277
2.879
3.392
1.178
1.347
1.277
2.879
3.313
1.151
1.228
1.277
2.879
3.256
1.131
97
4.2.3 IN-2: Route Analysis Scenario 2
Scenario 2 is the route run and analysis from IN-2 to Davis Hospital. S2
represents an ambulance on an emergency run from IN-2 to Davis Hospital. The same
methodology and analysis settings used in 4.1.3 IN-1: Route Analysis Scenario 2 were
applied to this route analysis.
Description
Six tables and seven figures were created based on these runs. Tables 40 and 41
show the results of runs from IN-2 to Davis Hospital applying the DIST impedance for
Sunday and Tuesday, respectively. Similar to Tables 33 and 34, the ‘TVTT (min)’ field
in these tables show the accumulated TVTT value calculated for 1700 (5:00 pm) only.
Tables 42 and 43 show the results of runs from IN-2 to Davis Hospital applying
the FFTT impedance for Sunday and Tuesday, respectively. Tables 44 and 45 show the
results of runs from IN-2 to Davis Hospital applying the TVTT impedance for Sunday
and Tuesday, respectively. Figures 60 and 61 show the travel time profiles associated
with Tables 44 and 45, respectively. Routes A (Figures 62), B (Figures 63), C (Figures
64), D (Figures 65), and E (Figures 66) represent the routes generated by the ‘Route’
solver based on the time, day and impedance applied.
Table 40. Scenario 2, Sunday, IN-2 to Davis Hospital, DIST impedance
Route Origin-Destination
DIST (mi) FFTT (min) TVTT (min)
A
IN-2 to Davis Hospital
5.055
7.620
11.938
Table 41. Scenario 2, Tuesday, IN-2 to Davis Hospital, DIST impedance
Route Origin-Destination
DIST (mi) FFTT (min) TVTT (min)
A
IN-2 to Davis Hospital
5.055
7.620
15.095
98
Table 42. Scenario 2, Sunday, IN-2 to Davis Hospital, FFTT impedance
Route
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
IN-2 to Davis Hospital
5.895
7.696
8.288
0:00:00
0:06:46
IN-2 to Davis Hospital
5.895
7.696
8.288
1:00:00
1:06:46
IN-2 to Davis Hospital
5.895
7.696
8.288
2:00:00
2:06:46
IN-2 to Davis Hospital
5.895
7.696
8.288
3:00:00
3:06:46
IN-2 to Davis Hospital
5.895
7.696
8.288
4:00:00
4:06:46
IN-2 to Davis Hospital
5.895
7.696
8.330
5:00:00
5:06:46
IN-2 to Davis Hospital
5.895
7.696
8.368
6:00:00
6:06:46
IN-2 to Davis Hospital
5.895
7.696
8.445
7:00:00
7:06:46
IN-2 to Davis Hospital
5.895
7.696
8.685
8:00:00
8:06:46
IN-2 to Davis Hospital
5.895
7.696
9.081
9:00:00
9:06:46
IN-2 to Davis Hospital
5.895
7.696
9.574
10:00:00
10:06:46
IN-2 to Davis Hospital
5.895
7.696
10.040
11:00:00
11:06:46
IN-2 to Davis Hospital
5.895
7.696
10.333
12:00:00
12:06:46
IN-2 to Davis Hospital
5.895
7.696
10.389
13:00:00
13:06:46
IN-2 to Davis Hospital
5.895
7.696
10.376
14:00:00
14:06:46
IN-2 to Davis Hospital
5.895
7.696
10.332
15:00:00
15:06:46
IN-2 to Davis Hospital
5.895
7.696
10.213
16:00:00
16:06:46
IN-2 to Davis Hospital
5.895
7.696
10.076
17:00:00
17:06:46
IN-2 to Davis Hospital
5.895
7.696
9.798
18:00:00
18:06:46
IN-2 to Davis Hospital
5.895
7.696
9.413
19:00:00
19:06:46
IN-2 to Davis Hospital
5.895
7.696
9.131
20:00:00
20:06:46
IN-2 to Davis Hospital
5.895
7.696
8.566
21:00:00
21:06:46
IN-2 to Davis Hospital
5.895
7.696
8.288
22:00:00
22:06:46
IN-2 to Davis Hospital
5.895
7.696
8.288
23:00:00
23:06:46
Table 43. Scenario 2, Tuesday, IN-2 to Davis Hospital, FFTT impedance
Route
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
IN-2 to Davis Hospital
5.895
7.696
8.871
0:00:00
0:06:46
IN-2 to Davis Hospital
5.895
7.696
8.871
1:00:00
1:06:46
IN-2 to Davis Hospital
5.895
7.696
8.871
2:00:00
2:06:46
IN-2 to Davis Hospital
5.895
7.696
8.871
3:00:00
3:06:46
IN-2 to Davis Hospital
5.895
7.696
8.871
4:00:00
4:06:46
IN-2 to Davis Hospital
5.895
7.696
8.942
5:00:00
5:06:46
IN-2 to Davis Hospital
5.895
7.696
9.594
6:00:00
6:06:46
IN-2 to Davis Hospital
5.895
7.696
12.580
7:00:00
7:06:46
IN-2 to Davis Hospital
5.895
7.696
16.940
8:00:00
8:06:46
IN-2 to Davis Hospital
5.895
7.696
16.437
9:00:00
9:06:46
IN-2 to Davis Hospital
5.895
7.696
15.557
10:00:00
10:06:46
IN-2 to Davis Hospital
5.895
7.696
15.643
11:00:00
11:06:46
IN-2 to Davis Hospital
5.895
7.696
15.938
12:00:00
12:06:46
IN-2 to Davis Hospital
5.895
7.696
15.960
13:00:00
13:06:46
IN-2 to Davis Hospital
5.895
7.696
16.287
14:00:00
14:06:46
IN-2 to Davis Hospital
5.895
7.696
17.177
15:00:00
15:06:46
IN-2 to Davis Hospital
5.895
7.696
18.031
16:00:00
16:06:46
IN-2 to Davis Hospital
5.895
7.696
18.733
17:00:00
17:06:46
IN-2 to Davis Hospital
5.895
7.696
17.419
18:00:00
18:06:46
IN-2 to Davis Hospital
5.895
7.696
14.546
19:00:00
19:06:46
IN-2 to Davis Hospital
5.895
7.696
11.961
20:00:00
20:06:46
IN-2 to Davis Hospital
5.895
7.696
9.652
21:00:00
21:06:46
IN-2 to Davis Hospital
5.895
7.696
8.871
22:00:00
22:06:46
IN-2 to Davis Hospital
5.895
7.696
8.871
23:00:00
23:06:46
99
Table 44. Scenario 2, Sunday, IN-2 to Davis Hospital, TVTT impedance
Route
B
B
B
B
B
B
B
B
B
C
C
C
C
C
C
C
C
C
C
C
C
C
B
B
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
IN-2 to Davis Hospital
5.895
7.696
8.288
0:00:00
0:07:21
IN-2 to Davis Hospital
5.895
7.696
8.288
1:00:00
1:07:21
IN-2 to Davis Hospital
5.895
7.696
8.288
2:00:00
2:07:21
IN-2 to Davis Hospital
5.895
7.696
8.288
3:00:00
3:07:21
IN-2 to Davis Hospital
5.895
7.696
8.288
4:00:00
4:07:21
IN-2 to Davis Hospital
5.895
7.696
8.330
5:00:00
5:07:24
IN-2 to Davis Hospital
5.895
7.696
8.368
6:00:00
6:07:26
IN-2 to Davis Hospital
5.895
7.696
8.445
7:00:00
7:07:31
IN-2 to Davis Hospital
5.895
7.696
8.685
8:00:00
8:07:45
IN-2 to Davis Hospital
5.686
7.412
8.672
9:00:00
9:08:04
IN-2 to Davis Hospital
5.686
7.412
9.038
10:00:00
10:08:26
IN-2 to Davis Hospital
5.686
7.412
9.366
11:00:00
11:08:46
IN-2 to Davis Hospital
5.686
7.412
9.548
12:00:00
12:08:57
IN-2 to Davis Hospital
5.686
7.412
9.571
13:00:00
13:08:58
IN-2 to Davis Hospital
5.686
7.412
9.563
14:00:00
14:08:58
IN-2 to Davis Hospital
5.686
7.412
9.541
15:00:00
15:08:56
IN-2 to Davis Hospital
5.686
7.412
9.455
16:00:00
16:08:51
IN-2 to Davis Hospital
5.686
7.412
9.346
17:00:00
17:08:45
IN-2 to Davis Hospital
5.686
7.412
9.132
18:00:00
18:08:32
IN-2 to Davis Hospital
5.686
7.412
8.842
19:00:00
19:08:15
IN-2 to Davis Hospital
5.686
7.412
8.647
20:00:00
20:08:03
IN-2 to Davis Hospital
5.686
7.412
8.226
21:00:00
21:07:38
IN-2 to Davis Hospital
5.895
7.696
8.288
22:00:00
22:07:21
IN-2 to Davis Hospital
5.895
7.696
8.288
23:00:00
23:07:21
Figure 60. IN-2 Scenario 2, Sunday travel time profile, TVTT impedance
100
Table 45. Scenario 2, Tuesday, IN-2 to Davis Hospital, TVTT impedance
Route
C
C
C
C
C
C
C
D
E
E
E
E
E
D
E
E
E
E
E
D
D
C
C
C
Origin-Destination DIST (mi) FFTT (min) TVTT (min) StartTime (hms) EndTime (hms)
IN-2 to Davis Hospital
5.686
7.412
8.417
0:00:00
0:07:49
IN-2 to Davis Hospital
5.686
7.412
8.417
1:00:00
1:07:49
IN-2 to Davis Hospital
5.686
7.412
8.417
2:00:00
2:07:49
IN-2 to Davis Hospital
5.686
7.412
8.417
3:00:00
3:07:49
IN-2 to Davis Hospital
5.686
7.412
8.417
4:00:00
4:07:49
IN-2 to Davis Hospital
5.686
7.412
8.494
5:00:00
5:07:54
IN-2 to Davis Hospital
5.686
7.412
9.249
6:00:00
6:08:39
IN-2 to Davis Hospital
5.524
10.734
12.429
7:00:00
7:10:05
IN-2 to Davis Hospital
5.338
10.538
13.279
8:00:00
8:10:51
IN-2 to Davis Hospital
5.338
10.538
13.278
9:00:00
9:10:51
IN-2 to Davis Hospital
5.338
10.538
13.122
10:00:00
10:10:41
IN-2 to Davis Hospital
5.338
10.538
13.151
11:00:00
11:10:43
IN-2 to Davis Hospital
5.338
10.538
13.130
12:00:00
12:10:42
IN-2 to Davis Hospital
5.524
10.734
13.021
13:00:00
13:10:40
IN-2 to Davis Hospital
5.338
10.538
13.148
14:00:00
14:10:43
IN-2 to Davis Hospital
5.338
10.538
13.297
15:00:00
15:10:52
IN-2 to Davis Hospital
5.338
10.538
13.404
16:00:00
16:10:58
IN-2 to Davis Hospital
5.338
10.538
13.485
17:00:00
17:11:03
IN-2 to Davis Hospital
5.338
10.538
13.297
18:00:00
18:10:52
IN-2 to Davis Hospital
5.524
10.734
12.788
19:00:00
19:10:26
IN-2 to Davis Hospital
5.524
10.734
12.437
20:00:00
20:10:05
IN-2 to Davis Hospital
5.686
7.412
9.310
21:00:00
21:08:43
IN-2 to Davis Hospital
5.686
7.412
8.417
22:00:00
22:07:49
IN-2 to Davis Hospital
5.686
7.412
8.417
23:00:00
23:07:49
Figure 61. IN-2 Scenario 2, Tuesday travel time profile, TVTT impedance
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Figure 62. IN-2 Scenario 2, Route A
Figure 63. IN-2 Scenario 2, Route B
102
Figure 64. IN-2 Scenario 2, Route C
Figure 65. IN-2 Scenario 2, Route D
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Figure 66. IN-2 Scenario 2, Route E
Findings
Based on the results found in Tables 40 and 41, the total distance of Route A
(Figure 62) for Sunday and Tuesday was 5.055 miles. No route changes were observed
based on the use of the DIST impedance. Based on the results found in Tables 42 and 43,
where FFTT was used as impedance, the total FFTT for each run was 7.696 minutes for
Sunday and Tuesday. The total length for each run or Route B (Figure 63) was 5.895
miles. No variations in DIST, FFTT, or routes were observed based on runs for Sunday
and Tuesday. The use of FFTT as an impedance triggered the change from Route A in
Tables 40 and 41 to Route B in Table 42 and 43. It was also observed that Route B takes
more advantage of Interstate 15 (I-15) when compared to Route A.
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The impedance used to create Tables 44 and 45 was the TVTT cost attribute for
Sunday and Tuesday, respectively. Table 44 shows the TVTT for Sunday; the TVTTs for
17 of 24 time intervals are shown to vary with time. From the time intervals 0000
(midnight) to 0400 (4:00 am) and 2200 (10:00 pm) to 2300 (11:00 pm), the travel-time
values are identical (8.288 minutes) and close to the corresponding FFTT values. TVTT
values between the time intervals 0500 (5:00 am) and 2100 (9:00 pm) vary based on
Sunday time-of-day traffic patterns. The ‘DIST (mi)’ and ‘FFTT (min)’ fields in Table
44 indicate a route change. This change occurs between the time interval 0900 (9:00 am)
and 2100 (9:00 pm) denoted by Route C (Figure 64) in the ‘Route’ field. The distance
value decreased slightly (-0.209 miles) to 5.686 miles due to the change from Route B to
Route C.
For Tuesday (Table 45), the TTVTs for 17 of 24 time intervals are shown to vary
with time. From the time intervals 0000 (midnight) to 0400 (4:00 am) and 2200 (10:00
pm) to 2300 (11:00 pm), the travel-time values are identical (8.417 minutes). TVTT
values between the intervals 0500 (5:00 am) and 2100 (9:00 pm) vary based on Tuesday
time-of-day traffic patterns. The ‘DIST (mi)’ and ‘FFTT (min)’ fields in Table 45
indicate multiple route changes. Several changes occur between the time intervals 0700
(7:00 am) and 2000 (8:00 pm) denoted by Route D (Figures 65) and Route E (Figures
66) in the ‘Route’ field. The total distance for the route associated with Route C is 5.686
miles. The distance value decreased slightly (-0.162 miles) to 5.524 miles due to the
change from Route C to Route D. The distance value decreased even more (-0.348
miles) to 5.338 miles due to the change from Route C to Route E. The difference in
distance between Route D and Route E is 0.186 miles.
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Discussion
Table 46 compares travel times for Routes A, B, and C for Sunday during the
hours between 9:00 am and 10:00 pm to validate that applying TVTT will yield a more
optimal routing solution. Column ‘A-I’ is the value in the ‘DIST (mi)’ field from Table
40. Columns ‘B-I’, ‘B-II’, and ‘B-III’ are the values in the ‘DIST (mi)’, ‘FFTT (min)’,
and ‘TVTT (min)’ fields, respectively, from Table 42. Columns ‘C-I’, ‘C-II’, and ‘C-III’
are the values in the ‘DIST (mi)’, ‘FFTT (min)’, and ‘TVTT (min)’ fields, respectively,
from Table 44. Columns ‘B-IV’ and ‘C-IV’ are the free-flow factors derived from Tables
40 and 42, respectively.
Comparing the DIST and FFTT values between Routes A, B, and C within a static
network environment, Route A (Figure 62) is the best solution for the shortest distance,
and Route C (Figure 64) seems to be the best solution for free-flow travel times (7.412
minutes). However, from the route analysis applying FFTT as impedance (Table 42),
ArcGIS Network Analyst Route Solver generated Route B (Figure 63) as the fastest route
based on static free-flow travel time (7.696 minutes). According to Esri (2013g), “the
best route can be defined as the route that has the lowest impedance, where the
impedance is chosen by the users.” Therefore, Route B should be the fastest route based
on the static free-flow time (FFTT impedance) from IN-2 to Davis Hospital. There
should not be any other route with less free-flow time. Table 40 shows Route A with less
free-flow travel time (7.620 minutes) due to DIST impedance route analysis, which does
not consider the global turn restriction. Route C was generated by applying TVTT as
impedance as the optimal route during the hours between 9:00 am and 10:00 pm within a
dynamic network environment, but its FFTT value (7.412 minutes) is way less than
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Routes A and B, which raises the question of which route is actually the fastest route.
This inconsistent route analysis was re-run several times through different versions of
ArcGIS Network Analyst (9.3, 10, and 10.) to ensure no human error in parameter inputs,
but all re-runs produced the exact same results. Route C based on TVTT impedance has
less free-flow travel time than Route B generated through FFTT impedance. According
to Esri (2013f), the users “can accumulate any number of impedance attributes in a route
analysis, but accumulated attributes don’t play a role in computing the path along the
network.” The FFTT values in Table 44 is just accumulated free-flow times attributes, so
it might not be a reliable result for the fastest route. Without further investigation on
ArcGIS Network Analyst shortest path algorithm, the fastest route can’t be determined
for IN-2 Scenario 2 for Sunday traffic pattern.
Comparing TVTT and Free-flow Factor between Routes B and C with a dynamic
network environment with time-varying travel time, Route C is the optimal route during
the hours between 9:00 am and 10:00 pm. Route C requires less travel time than Route B
(TVTT values) and has lower free-flow factors in each time interval shown in Table 46.
Table 46. IN-2 Scenario 2, Sunday, comparison of cost impedance between
Routes A, B, and C
Route A
A-I
From
(hrs)
0900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
To
(hrs)
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
2200
B-I
B-II
Route B
B-III
DIST (mi) DIST (mi) FFTT (min) TVTT (min)
5.055
5.055
5.055
5.055
5.055
5.055
5.055
5.055
5.055
5.055
5.055
5.055
5.055
5.895
5.895
5.895
5.895
5.895
5.895
5.895
5.895
5.895
5.895
5.895
5.895
5.895
7.696
7.696
7.696
7.696
7.696
7.696
7.696
7.696
7.696
7.696
7.696
7.696
7.696
9.081
9.574
10.040
10.333
10.389
10.376
10.332
10.213
10.076
9.798
9.413
9.131
8.566
Route C
B-IV
C-I
C-II
C-III
C-IV
Free-flow
Free-flow
DIST (mi) FFTT (min) TVTT (min)
Factor
Factor
1.180
5.686
7.412
8.672
1.170
1.244
5.686
7.412
9.038
1.219
1.305
5.686
7.412
9.366
1.264
1.343
5.686
7.412
9.548
1.288
1.350
5.686
7.412
9.571
1.291
1.348
5.686
7.412
9.563
1.290
1.343
5.686
7.412
9.541
1.287
1.327
5.686
7.412
9.455
1.276
1.309
5.686
7.412
9.346
1.261
1.273
5.686
7.412
9.132
1.232
1.223
5.686
7.412
8.842
1.193
1.186
5.686
7.412
8.647
1.167
1.113
5.686
7.412
8.226
1.110
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Table 47 is the summary report for the shortest, fastest, and optimal route from
IN-2 to Davis Hospital for Tuesday traffic pattern. Route A (Figure 62) is the shortest
route (Table 41) with the travel distance as 5.055 miles. Route B (Figure 63) can be
considered as the fastest route (7.696 minutes) while applying FFTT as impedance (Table
43). However, Route C (Figure 64) based on TVTT as impedance (Table 45) has less
free-flow travel time (7.412 minutes) than Route B. Without further investigation, the
fastest route can’t be determined for IN-2 Scenario 2 for Tuesday traffic pattern. Route C
(Figure 64) is the optimal route during the hours from midnight to 7:00 am, and from
9:00 pm to midnight (Table 45). Route D (Figure 65) is the optimal route during the
hours from 7:00 am to 8:00 am, from 1:00 pm to 2:00 pm, and from 7:00 pm to 9:00 pm
(Table 45). Route E (Figure 66) is the optimal route during the hours from 8:00 am to
1:00 pm, and from 2:00 pm to 7:00 pm (Table 45).
Table 47. IN-2 Scenario 2, Tuesday, summary of cost impedance between Routes A, B, C,
D, and E
Routes
Route A
DIST (mi)
5.055
FFTT (min)
7.620
Route B
5.895
7.696
Route C
5.686
7.412
Route D
5.524
10.734
Route E
5.338
10.538
TVTT (min) Remarks
Shortest route
Fastest route based on FFTT
8.871-18.733
impedance
Optimal route between time intervals
8.417-9.310
0000-0600 and 2100-2300
Optimal route in time intervals 0700,
12.429-12.788
1300, 1900, and 2000
Optimal route between time intervals
13.122-13.485
0800-1200 and 1400-1800
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4.2.4 IN-2: Emergency Response Routing Review
In review, four maps and one table were created showing the combined results of
Scenarios 1 and 2. For each map, the dashed red line represents the emergency response
route from Kaysville FD (origin) to IN-2 (destination) and the blue dashed line represents
the emergency response route from IN-2 (origin) to Davis Hospital (destination). For
comparison purposes, each route was run at 1700 (5:00 pm) for Sunday and Tuesday.
Figure 67 shows the shortest route from Kaysville FD to IN-2 (S1, Route A) and
from IN-2 to Davis Hospital (S2, Route A) when the static cost attribute DIST was
applied as impedance. The results were the same for Sunday and Tuesday. No route
change was observed between Sunday and Tuesday runs. Figure 68 illustrates the fastest
route from Kaysville FD to IN-2 (S1, Route A) and from IN-2 to Davis Hospital (S2,
Route B) when the static cost attribute FFTT was applied as impedance. In this instance,
the fastest route from Kaysville FD to IN-2 (Route A) is also the shortest route.
However, the fastest route from IN-2 to Davis Hospital (Route B) might not be a reliable
result as discussed in 4.2.3.
The optimal routes generated by the dynamic cost attribute TVTT as impedance
are shown in Figures 69 and 70. Route changes were observed between and during the
Sunday and Tuesday runs due to the application of historical traffic data representing
traffic congestion. Figure 69 shows the dynamic optimal path from Kaysville FD to IN-2
(S1, Route A) and from IN-2 to Davis Hospital (S2, Route C). These paths are
considered the most optimal routes from each origin to each destination on 5:00 pm,
Sunday. In this instance, the optimal route from Kaysville FD to IN-2 (Route A) is also
the shortest and fastest route.
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Figure 67. IN-2, combined scenarios, Sunday and Tuesday, DIST impedance
Figure 68. IN-2, combined scenarios, Sunday and Tuesday, FFTT impedance
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Figure 69. IN-2, combined scenarios, Sunday, TVTT impedance
Figure 70. IN-2, combined scenarios, Tuesday, TVTT impedance
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Figure 70 shows the dynamic optimal route from the path from Kaysville FD to
IN-2 (S1, Route B) and from IN-2 to Davis Hospital (S2, Route E) on 5:00 pm, Tuesday.
S2, Route D is an additional route change that represents the optimal route on 7:00 pm,
Tuesday from IN-2 to Davis Hospital. These paths are considered the most optimal
routes from each origin to each destination on Tuesday for their specified time intervals.
Table 48 shows the distances and travel times associated with each route
generated for routing example IN-2 and are displayed in Figures 67 through 70. This
table can be used to analyze the values associated with each route. When observing route
run results, the bolded values are based on the applied impedance that was used to
optimize the solution. The accumulated values are shown in italicized red font and are
for reference and comparison only.
Table 48. IN-2, combined scenarios, comparison of emergency response routes
Cost
DIST
DIST
DIST
DIST
FFTT
FFTT
FFTT
FFTT
TVTT
TVTT
TVTT
TVTT
TVTT
Day StartTime (h)
SU
1700
SU
1700
TU
1700
TU
1700
SU
1700
SU
1700
TU
1700
TU
1700
SU
1700
SU
1700
TU
1700
TU
1300
TU
1700
Scenario
S1
S2
S1
S2
S1
S2
S1
S2
S1
S2
S1
S2
S2
Route
A
A
A
A
A
B
A
B
A
C
B
D
E
Origin-Destination
Dist (mi) FFTT (min) TTVT (min) Figure
Kaysville FD to IN-2
1.038
1.900
3.145 67
IN-2 to Davis Hospital
5.055
7.620
11.938 67
Kaysville FD to IN-2
1.038
1.900
3.277 67
IN-2 to Davis Hospital
5.055
7.620
15.095 67
Kaysville FD to IN-2
1.038
2.517
3.762 68
IN-2 to Davis Hospital
5.895
7.696
10.076 68
Kaysville FD to IN-2
1.038
2.517
3.894 68
IN-2 to Davis Hospital
5.895
7.696
18.733 68
Kaysville FD to IN-2
1.038
2.517
3.762 69
IN-2 to Davis Hospital
5.686
7.412
9.346 69
Kaysville FD to IN-2
1.277
2.879
3.431 70
IN-2 to Davis Hospital
5.524
10.734
13.021 70
IN-2 to Davis Hospital
5.338
10.538
13.485 70
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4.3 Discussion of Results
On the whole, the results seemed to agree with the expectations and meet the
objective of the study. The DIST impedance generated the shortest path with no regard
to travel time. The FFTT impedance generated the quickest or fastest path, and the
TVTT generated the best or most optimal path by applying historical traffic data.
There are three apparent inconsistent outcomes in the analysis results. First is the
travel time calculation while employing the ‘Start Time’ option in the analysis setting for
ArcGIS Network Analyst ‘Route’ solver (Figure 30). Theoretically, the results of ‘End
Time’ should be the sum of ‘Start Time’ and the travel time in the specified time interval,
but the results from this study showed different outcomes. See Table 18 (FFTT
impedance) as an example. In the time interval from 0200 (2:00 am) to 0300 (3:00 am),
the travel time is 1.747 decimal minutes or 00:01:45 (hms), therefore, the ‘End Time’
should be 2:01:45 (hms) instead of 2:01:20 (hms). This inconsistency can be observed
throughout the entire study. With further investigation, it was discovered that the ‘End
Time’ was calculated by the travel time (for both FFTT and TVTT) without global turn
delays. The ‘FFTT (min)’ field in Table 16 represents the accumulated free-flow travel
time for the same route shown in Table 18 without global turn delays. The travel time is
1.330 decimal minutes or 00:01:20 (hms), which is exactly the same elapsed time from
‘StartTime (hms)’ to ‘EndTime (hms)’ shown in Table 18.
The second inconsistent outcome is the determination of the best route while
applying TVTT as impedance. According to Esri (2013g), the best route is the result
with the lowest impedance. See Table 22 as an example. In the time intervals 1000
(10:00 am) to 1100 (11:00 am) and 1900 (7:00 pm) to 2000 (8:00 pm), Route B is the
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best route generated from TVTT impedance (Table 20), but Route A, generated from
FFTT impedance (Table 18), has a lower TVTT value than Route B. The explanation
can be made that Route B has a lower free-flow factor than Route A, but based on Esri’s
(2013g) document, the best route should be determined by the user’s specified
impedance, which is TVTT, not the free-flow factor.
The third inconsistent outcome is the accumulated impedance values generated
when a particular impedance was not used to optimize the route analysis. See Table 42
as an example. The fastest route from IN-2 to Davis Hospital, while applying FFTT
impedance, is Route B with a free-flow travel time of 7.696 minutes. However, applying
the TVTT impedance generated an optimal route, Route C, for the time intervals between
0900 (9:00 am) and 2100 (9:00 pm), (Table 44). The accumulated FFTT value for Route
C is less than Route B’s free-flow travel time. If the calculations of other accumulated
impedances through TVTT route analysis (such as DIST and FFTT from Table 44) are
correct, then Route C should be the best route results from FFTT route analysis not Route
B.
Even with these three inconsistent outcomes, this project still demonstrates that
the routes and response times for emergency response vehicles could change due to
variations in traffic flow related to the day (e.g., weekday or weekend) and the time of
day (traffic congestion). The shortest route might not be the most efficient path for
emergency vehicles. Although emergency vehicle routing can at times exceed the normal
speed limit, FFTT impedance route analysis can also serve as the surrogate of road class
(generally roads with multiple lanes have higher speed limits, which makes it easier for
emergency vehicles to pass other vehicles), which is a factor when considering traffic
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conditions and the necessity of passing other vehicles. Traffic conditions are not static;
they are dependent on the time and day. TVTT impedance route analysis could provide a
more realistic simulation than DIST and FFTT impedance route analysis. The optimal
route from IN-2 to Davis Hospital (4.2.3) changed based on the time of the day (Table
45). A decrease in travel time by a few minutes might not be significant for normal
traffic, but when considering emergency vehicle routing, it can be a matter of life and
death.
Although a fundamental aim of this study was to illustrate how a dynamic
network is preferred over a static network when applied to emergency response routing,
this research was nevertheless theoretic in nature. Regardless of how accurate the
network data is, or how many variables, restrictions, and impedances were applied to
generate the most realistic and best path, decisions made by an experienced emergency
response vehicle driver in real time under real traffic scenarios will always outweigh a
computer generated routing model. However, dynamic emergency response routing as
shown in this research can be valuable for generating preliminary routes from an origin to
a destination then modified by an experienced emergency response vehicle driver as the
situation demands.
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Chapter 5: Conclusion and Future Improvements
5.1 Conclusion
The objective of this research was to observe, record, and analyze changes to routes
and travel/response-times of emergency vehicles due to variations in traffic flow related to
traffic congestion on certain days of the week and times of day. It was believed that
dynamic routing based on cost attributes derived from historical travel-time data and
applied to network edges could help response vehicles avoid congested areas and improve
travel times (Kok et al. 2012, Panahi and Delavar 2009). As mentioned in the literature
review, because travel congestion affects the travel time of emergency vehicles and
increases response times, time-dependent variables derived from traffic count data could
realistically represent peak-hour traffic congestion and help emergency vehicles avoid
these congested areas and improve travel time (Kok et al. 2012, Panahi and Delavar
2009).
The results of this analysis indicate that when the DIST impedance was used by the
‘Route’ solver, it generated the shortest path between the origin and the destination in both
scenarios. When the FFTT impedance was applied, it generated the quickest or fastest
route. When the TVTT impedance was used, it generated the best or most optimal path
under realistic traffic conditions.
The project was overall a success and the research objectives were met. This
project was able to utilize the shortest path algorithms in Esri’s Network Analyst to
calculate the shortest, fastest, and the most optimal routes by applying various cost
attributes or impedances to practical vehicle emergency response scenarios. Differences in
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route directions, travel times, and distances were observed and analyzed based on these
impedances and the findings were discussed in detail explaining the results.
5.2 Limitations
Six noticeable limitations associated with this research are discussed in this
section. The lack of experience in the creation and application of traffic profiles was one
limitation. Scarcity of literature about the origin of and how free-flow multipliers are
generated and incorporated into a spatio-temporal database and the actual implementation
of traffic profiles was another limitation. The main source of information on the creation
and use of traffic profiles was from Esri. Other literature did not detail the making of
traffic profiles. Several inquiries to private corporations and government organizations
for clarification were not very successful. Answers to questions that would be helpful
include: What is the origin and background of historical traffic profiles? What
methodology is used to create the free-flow factors or multipliers? Is there a scientific
approach for relating traffic volume profiles created from ATR site data to free-flow
traffic profiles stored in the ‘DailyProfiles_Time_60min’ table?
Another issue that limited the study was the coarseness or resolution of the
historical traffic data. UDOT traffic volume data was only available in 60 minute time
intervals. The original Esri free-flow traffic profile (‘DailyProfiles’) table was available
in 5 minute time slices. Modifications had to be made to accommodate UDOT traffic
volume data and generate the ‘DailyProfiles_Time_60min’ table used in this research. A
loss in granularity resulted from this modification. It is believed that the precision and
correctness of travel times and routes would be improved and better represent traffic
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conditions using smaller time intervals, however, there would be a downside. For
research purposes it would increase the number of runs per 24 hour period from 24 to
288. This would impact the size and configuration of the tables and increase the work
load associated with executing the runs and the route analysis.
Road segment classification was another limitation and concern. The
methodology used to select and match ATR sites to the Urban Area Functional
Classification system was based on limited information and guidance. It is unclear if the
methodology used in this research was the most suitable approach. Questions that
surfaced were: Is one classification system preferred over another when creating a
transportation network? Is there a better or perhaps a more systematic approach to the
classification of road segments? Is there a better process to match ATR sites to a
classification system?
The study was also limited in the sense that certain dynamic variables that would
have improved the network and routing scenarios were not used due to time, availability
and the complexity of implementation. Examples include seasonal weather conditions,
road conditions, number of lanes, slope, etc.
The final limitation was the lack of transparency in Esri’s shortest path algorithm.
Esri (2013g) maintains the best route is determined based on the lowest impedance.
While applying TVTT as impedance in this study, there were several exceptions where
the new route’s TVTT was higher than the route based on FFTT, although the free-flow
factor values were lower. These results are inconsistent with Esri’s (2013g) statement.
Examples can be found in Table 22, time intervals 1000 (10:00 am) to 1100 (11:00 am)
and 1900 (7:00 pm) to 2000 (8:00 pm); Table 29, time interval 1900 (7:00 pm) to 2000
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(8:00 pm); and Table 39, time intervals 0700 (7:00 am) to 0800 (8:00 am) and 2000 (8:00
pm) to 2100 (9:00 pm). Another inconsistent result is the fastest path from IN-2 to Davis
Hospital. The TVTT route analysis generated a route (Route C, Figure 64) with a lower
free-flow travel time (Tables 44 and 45) than the solution (Route B, Figure 63) produced
from FFTT route analysis (Tables 42 and 43). These inconsistences cannot be explained
without further investigation of Esri’s shortest path algorithm. However, there is
insufficient documentation from Esri to describe how Dijkstra’s algorithm was
implemented in ArcGIS Network Analyst.
5.3 Challenges and Solutions
One challenge both in time and complexity was the preparation and maintenance
of the road network dataset. As explained in Section 3.2, additional work was needed to
prepare the road network for analysis. Preparation included directionality, connectivity
and adding one way restrictions to limit travel on one way roads and avoid routing
irregularities. Routes overshooting an expected ramp, going the wrong way on a
freeway, entering or exiting the wrong way on a ramp or overshooting an entrance into
the hospital because of junction and road segment errors were a few challenges that
needed to be addressed.
The solutions to these challenges required hours of editing road edges, junctions,
and associated attribute fields for the network to function properly. More experience
might have made this process easier and less time consuming. Identifying an error or
irregularity, repairing it through digitization or re-attribution, rebuilding the network
dataset and testing was the general pattern. For instance, after a road segment was added,
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deleted or edited in some manner such as merging or splitting segments, certain fields
had to be recalculated. Some field attributes also had to be copied to the
‘Project_Profiles’ join table so the historical traffic data would function correctly. If a
speed limit was changed in the ‘ProjectArea’ feature class, the same change had to be
made in the ‘Project_Profiles’ join table. Travel times also had to be re-calculated. After
these changes, the network dataset had to be rebuilt. To aid in the process, a relationship
class was created between the ‘ProjectArea’ feature class and the ‘Project_Profiles’ join
table and proved very useful. The relationship class is mentioned in Section 3.3 and one
way restrictions are explained in Section 3.3.1.
5.4 Future Improvements
This research has shown how a GIS was used to solve a shortest path problem
with respect to emergency vehicle response routing. Certain network attributes and
attribute values were omitted or not used to their fullest potential for this research. It was
not practical nor was this research meant to cover all aspects of network analysis.
Several future improvements could make the road network and subsequent analysis more
functional and realistic. In actuality, improvements to a road network and shortest path
are boundless. A continuation of this research might include the following
improvements:
1. Explore the feasibility of incorporating average annual daily traffic (AADT),
vehicle miles traveled (VMT), peak hourly volume (PHV), or other measures
of traffic capacity as alternatives ways to model traffic congestion.
2. Apply elevations or Z values to highway and other overpasses.
3. Incorporate slope values especially on the mountain front benches.
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4. Improve road classifications and incorporate road hierarchy.
5. Incorporate traffic lanes.
6. Incorporate more specified ‘restricted turns’ modeled from a turn feature class
versus the generalized use of global turn delays.
7. Incorporate barriers and other restrictions to resemble areas of road construction,
traffic calming measures, weather conditions, etc.
8. Fine tune the use of one way restrictions.
9. Explore and compare other route solvers available in Esri Network Analyst.
10. Compare results to real world emergency response call data.
One additional future improvement might be to expand this study and develop an
efficient low-cost web-based emergency response routing system that can incorporate
real-time or live traffic data based on using GPS technology. This system could be used
by local EMS dispatch agencies to improve response times for not only lower level
medical priority dispatches but for higher level emergency situations or disasters that can
affect large areas and cause significantly more casualties.
121
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