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Wang and Huegy
Determining the Free-Flow Speeds in a Regional Travel Demand Model Based on the
Highway Capacity Manual
Chao Wang*
Senior Research Associate
Institute for Transportation Research and Education
North Carolina State University
909 Capability Drive, Suite 3600
Research Building IV
Raleigh, NC 27606
Phone: (919) 513-7379
Fax: (919) 515-8898
Email: [email protected]
Joseph B. Huegy
Director, Travel Behavior Modeling Group
Institute for Transportation Research and Education
North Carolina State University
909 Capability Drive, Suite 3600
Research Building IV
Raleigh, NC 27606
Phone: (919) 513-7378
Fax: (919) 515-8898
Email: [email protected]
* Corresponding author
Word count 6,202 + 1,250 (1 figure + 4 tables) = 7,452
Submitted for presentation at the 93rd TRB Annual Meeting and
publication in the Transportation Research Record
January 2014, Washington, DC
Submission date: July 31, 2013
Revision date: November 15, 2013
TRB 2014 Annual Meeting
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Wang and Huegy
Abstract
This paper presents the approach to determine the free-flow speeds in the Triangle Regional
Travel Demand Model (TRM) in North Carolina. Improvements to free-flow speeds are of
particular importance in light of the need for improved network skims and accessibility measures,
and reasonable speed outputs to support air quality analyses. Directly using formulas in the
Highway Capacity Manual (HCM) has several advantages including: saving additional studies,
the consistency of free-flow speeds and capacities, and the consistency of travel demand
modeling with traffic operations analysis. With the publication of the HCM 2010, it is of great
interest to learn if the new HCM can generate reasonable free-flow speeds in the framework of a
regional travel demand model. One of the key challenges is that the HCM requires many link
attributes, some of which are not usually available to a regional travel demand model. For such
link attributes, default values are used by facility type and area type. As a result, when a link’s
area type is changed for a future year model run, a different set of default values will be used,
which results in different free-flow speeds without manually changing the coded link attributes.
The resulting free-flow speeds are validated based on a floating car survey conducted in 2011.
The result indicates that the HCM is able to yield reasonable free-flow speeds in a regional travel
demand model with adjustments based on local data.
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In recent years interest has been growing in estimating reasonable speeds in travel demand
models. More and more regions have started to validate the highway assignment results by
comparing the speed outputs with the observed speeds, whereas historically validation only
focused on the comparison of assigned link trips with traffic counts. This change is prompted by
several new demands on the travel demand modeling process such as: air quality analyses, the
consistency of accessibility measures in model feedback loops, and nontraditional travel demand
management strategies (1).
In a travel demand model, speeds are estimated in the highway trip assignment stage
based on volume-delay functions (VDFs), which use link capacity, free-flow speed, and trip
volume to calculate the speeds under congested conditions. Many studies have been focused on
the VDFs, including the development of new functional forms (2) and how to calibrate these
functions (3). VDFs account for the effects of congestion on the travel speed, and they are
critical to reasonable speed outputs from travel demand models. On the other hand, free-flow
speed is the theoretical speed of traffic as density approaches zero, so it is the basis for speed
estimation and should also be determined carefully. In addition, free-flow speed is usually the
initial speed for the model feedback loops for the peak period, and the initial speed for highway
trip assignment in the off-peak period. It is also usually used in practice to calculate the network
skims for the off-peak period, which affects trip distribution and mode choice in the off-peak
period.
The Highway Capacity Manual (HCM) presents the procedures for evaluating the
operational characteristics of roadways, including the formulas to determine free-flow speeds.
Although the HCM has been used in the determination of free-flow speeds in many regional
travel demand models, few of them directly adopt the formulas or procedures in the HCM.
However, there are several obvious advantages to directly using the formulas in the HCM:
•
The formulas are readily available and they are the product of substantial research
efforts. There are more than six decades of research behind the HCM since its first
edition was published in 1950. The latest edition, HCM 2010 (4), is the result of a multiagency effort (including TRB, AASHTO, and FHWA) over many years to meet changing
analytic needs, and to provide contemporary evaluation tools. So the HCM is a good
choice if local data or studies are not available.
•
The HCM is widely used in the determination of capacities in travel demand
models. Using formulas for free-flow speeds in the HCM ensures consistency of the freeflow speeds and capacities.
•
The HCM is also widely used for the analysis of traffic operations, which
sometimes uses the output from a travel demand model, or its highway network.
Therefore, using formulas in the HCM ensures consistency of the travel demand
modeling with traffic operations analysis.
With the publication of a new version of the HCM in 2010, it is of great interest to learn
if the new HCM can generate reasonable free-flow speeds in the framework of a regional travel
demand model. This paper shares the experience of using the free-flow speed formulas in the
HCM 2010 for the Triangle Regional Travel Demand Model (TRM), which covers Raleigh,
Durham and Chapel Hill in North Carolina.
This paper first reviews the current practices in determining free-flow speeds in travel
demand models in the United States. Then it summarizes the formulas that calculate the freeflow speeds. These formulas are originally taken from the HCM, but some of them are simplified
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to fit the free-flow condition. This paper then discusses how to implement these formulas,
followed by the validation of the free-flow speeds based on a floating car survey. The result
indicates that the HCM 2010 is able to yield reasonable free-flow speeds in a regional travel
demand model with adjustments based on local data.
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Many regions in the United States determine free-flow speeds based on lookup tables, which are
typically stratified by link facility type, area type and other strata. For example, the free-flow
speed lookup table used in the Atlanta Regional Commission (ARC) model is stratified by link
facility type and area type (5). The values in the table were reviewed by a model panel and
validated with two speed studies. Another example is the Southern California Association of
Governments (SCAG) Regional Model, whose free-flow lookup table is stratified by facility type,
area type and posted speed (6). In the New York Best Practice Model (BPM), Physical Link
Type (PLT) and area type are used to look up the free-flow speed for each link (7). Several
sources were used to determine the free-flow speed values. For uninterrupted facilities, free-flow
speed was basically computed as capacity divided by critical density, which is the density when
capacity occurs. For other roadways, free-flow speed was defined in a manner consistent with
other similar models and was adjusted based on local knowledge. Due to the unique PLT and
area type values being used in the BPM, there were many cells in the speed lookup table that
cannot be derived from the literature or from other models. In these cases, judgments were made
to apply changes between adjacent rows or columns of the table, based on logical relationships.
The lookup table approach is easy to implement, but it has some limitations. The values
in the tables are averages that might or might not reflect actual speed conditions for specific links
(1). For example, if free-flow speeds are determined from a lookup table stratified by area type
and facility type, the underlying assumption is that the free-flow speeds for all links of a specific
area type and facility type are the same, even if they have different posted speeds, median types,
signal timings or parking restrictions. To address this issue, some regions post-process the values
from the lookup table based on link attributes. For example, in the BPM Model, the values in the
lookup tables need to be reduced by 5% if on-street parking is allowed, and in the SCAG model,
the values should be increased by 4% for divided arterials or collectors. However, such simple
post-processing might not be applicable when more link attributes need to be considered.
Another approach to determine free-flow speeds for travel demand models is based on
formulas that use link attributes as inputs to calculate free-flow speeds. For example, the Florida
Southeast Regional Planning Model VI (SERPM6) uses two types of formulas to calculate freeflow speeds: one for uninterrupted facilities, and another for interrupted facilities (8). The
formula for uninterrupted facilities is a revision of the equation presented in NCHRP 387 (9).
The formula for interrupted facilities is a function of posted speed and signal information, such
as signal locations, the ratio of effective green time and cycle length, and the cycle length. The
basic idea is to add the intersection delay to a link’s free-flow travel time to obtain the total travel
time, and distance divided by the total travel time yields the free-flow speeds. Similar formulas
are used for interrupted facilities in the Dallas-Fort Worth Regional Travel Model (DFWRTM)
(10) and the Indiana Statewide Travel Demand Model (ISTDM) (11).There are two major
differences among these three models. First, SERPM6 and ISTDM use a function of posted
speed as a link’s free-flow speed. In detail, SERPM6 uses the linear function from NCHRP 387
and ISTDM develops non-linear regression models based on speed surveys. However,
DFWRTM uses a link’s posted speed directly as a link’s free flow speed. Second, SERPM6 and
CURRENT PRACTICES
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ISTDM use formulas in the Highway Capacity Manual 2000 (12) to calculate the delay at
signalized intersections, and the delay used in DFWRTM is the sum of intervening control delay
and end-node control delay. Intervening control delay is the delay experienced at the intersection
of a coded link with streets that have not been coded in the travel demand model network. It is
assumed to be 12 seconds for each intervening control. End-node control delay is the delay
experienced at the downstream intersection (i.e., end node) of a link. It is determined based on a
set of lookup tables that consider end node traffic control types, functional classifications and
area types.
Compared to the lookup table approach, the formula approach is more flexible in
incorporating different factors in the determination of free-flow speeds. It can yield more
reasonable free-flow speed for a link since it is calculated based on the characteristics of that
specific link. However, it requires more input data and the formulas need to be carefully
determined.
The six models reviewed above indicate that free-flow speed lookup tables and formulas
are developed based on different methods, including speed surveys (ISTDM), previous studies
(SERPM6), other models (BPM), and professional judgment (ARC). However, the HCM is
involved in most models. The SERPM6 model starts with the formulas in NCHRP 387, which
results in the HCM 2000. The BPM model develops free-flow speeds based on capacities, which
are obtained following the HCM procedures. Both the ISTDM and the SERPM6 models use the
formulas in the HCM 2000 to calculate the signalized intersection delay. But none of the models
directly use the formulas in the HCM.
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The formulas to calculate the free-flow speeds based on the HCM 2010 are summarized below.
These formulas are originally taken from the HCM, but some of them are simplified to fit the
free-flow condition.
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Chapter 11 of the HCM 2010 describes the procedures to analyze basic freeway segments. The
formula to estimate the free-flow speed on a basic freeway segment is shown below (Equation
11-1 from the HCM 2010).
DETERMINING THE FREE-FLOW SPEEDS BASED ON THE HIGHWAY CAPACITY
MANUAL
Free-flow Speeds for Freeways
75.4 3.22.
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Where,
(1)
is the free-flow speed (mph);
is the adjustment for lane width (mph);
is the adjustment for right-side lateral clearance (mph); and
is the total ramp density (ramps/mile).
Adjustment for lane width (
) can be found in Exhibit 11-8 from the HCM 2010, and
adjustment for right-side lateral clearance (
) is in Exhibit 11-9. Lane width, right-side lateral
clearance and the number of lanes are needed for these two adjustments. The first two terms are
not usually collected for a regional travel demand model. When they are not available, default
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values of 12 feet and 6 feet can be used for lane width and right-side lateral clearance,
respectively. With these two default values, 0.
Total ramp density is defined as the average number of ramps (including on-ramps, offramps, major merges, and major diverge junctions) per mile over a 6-mile freeway segment, 3mile upstream and 3-mile downstream of the midpoint of the study segment.
Posted speed is not included in Equation 1 as a factor to affect free-flow speeds on
freeways. A possible reason is that posted speed is highly correlated with total ramp density.
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Chapter 14 of the HCM 2010 describes the procedures to analyze multilane highways. In general,
uninterrupted flow exists on a multilane highway since there are two miles or more between
traffic signals. Where signals are more closely spaced, the facility should be analyzed as an
urban street. The formula to estimate the free-flow speed on a multilane highway is shown below
(Equation 14-1 from the HCM 2010).
Free-flow Speeds for Multilane Highways
Where,
(2)
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Free-flow Speeds for Two-Lane Highways
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Chapter 15 of the HCM 2010 describes the procedures to analyze two-lane highways. The
principal characteristic that separates two-lane and multilane highways is that passing maneuvers
have to take place in the opposing lane of traffic for two-lane highways. The formula to estimate
the free-flow speed on a two-lane highway is shown below (Equation 15-2 from the HCM 2010).
is the free-flow speed (mph);
is the base free-flow speed (mph);
is the adjustment for lane width (mph);
is the adjustment for total lateral clearance (mph);
is the adjustment for median type (mph); and
is the adjustment for access point density (mph).
The base free-flow speed () is like the design speed – it represents the potential
free-flow speed based only upon the horizontal and vertical alignment of the highway. While
speed limits are not always uniformly set, the base free-flow speed may be estimated as the
posted speed plus 5 mph for posted speed of 50 mph and higher, and the posted speed plus 7 mph
for posted speed less than 50 mph.
The adjustment for lane width (
) and total lateral clearance (
) are shown in
Exhibits 14-8 and 14-9 of the HCM 2010, respectively. The adjustment for median type ( ) is
-1.6 mph for undivided multilane highways, and 0 mph if the median is divided or is a two-way
left-turn lane. The adjustment for access point density ( ) is -0.25 mph for each access point per
mile. The number of access points per mile is determined by dividing the total number of access
points (i.e., driveways and unsignalized intersections) on the right side of the highway in the
direction of travel, by the length of the segment in miles. An intersection or driveway should
only be included in the count if it influences traffic flow. Access points that go unnoticed by
drivers, or with little activity, should not be used to determine access-point density.
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Where,
(3)
is the free-flow speed (mph);
is the base free-flow speed (mph);
is the adjustment for lane and shoulder width (mph); and
is the adjustment for access point density (mph).
The design speed might be an acceptable estimator of base free-flow speed (), as it
is based primarily on horizontal and vertical alignment. Posted speed may not reflect current
conditions or driver desires. A very rough estimate of might be taken as the posted speed
plus 10 mph.
The adjustment for lane and shoulder width (
) is shown in Exhibit 15-7 of the HCM
2010. The adjustment for access point density ( ) is -0.25 mph for each access point per mile.
The access-point density is computed by dividing the total number of unsignalized intersections
and driveways on both sides of the roadway segment by the length of the segment in miles.
Free-flow Speeds for Urban Streets
Traffic flow on urban streets is interrupted flow, because of the existence of traffic signals or
other traffic control devices. Therefore, free-flow speeds on urban streets depend on two
principal factors: running time over urban street segments, and control delay at signalized
intersections. The formula is shown below (Equation 17-12 from the HCM 2010). This formula
is the same as the formulas used in the SERPM6, DFWRTM, and ISTDM models.
3600
5280 !"
(4)
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Where,
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In Equation 4, the running time ( ) can be calculated based on the formula shown below (a
revision of Equation 17-1 from the HCM 2010).
is the free-flow speed that includes the impact of intersection delay (mph);
is the segment length (feet);
is the segment running time (seconds), that is, the time to traverse a segment; and
! is the control delay at the downstream intersection (seconds/veh).
Running Time on Urban Streets
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Where,
6.0 $%
0.0025
3600
5280
(5)
$% is the start-up lost time, which is 2.0 for signalized intersections (seconds); and
is the segment free-flow speed, which does not include the impact of intersection
delay (mph).
Equation 5 is a revision of Equation 17-1 in the HCM 2010 to fit the free-flow condition
when the traffic volume is low. It assumes that the impact of traffic density on travel speed can
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be ignored, therefore the vehicle proximity adjustment factor (& ) is equal to one. It also assumes
the delay due to turning vehicles or other factors is zero. The first term in Equation 5 accounts
for the time required to accelerate to the running speed, less the start-up lost time used to
compute the through movement delay. The divisor in this term is an empirical adjustment that
minimizes the contribution of this term for longer segments. in Equation 5 is calculated
based on the formula shown below (a consolidation of Equations 17-2 and 17-3 from the HCM
2010).
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Where,
below.
"
(6)
is the speed constant (mph);
is the adjustment for cross section, that is, median and curb (mph);
is the adjustment for access point (mph); and
is the signal spacing adjustment factor.
The speed constant ( ) in Equation 6 is a linear function of posted speed, as shown
25.6
0.47 ' ()*+!,++!
(7)
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The adjustment for cross section ( ) in Equation 6 reflects the impact of median type
and presence of curb, and the formula is shown below.
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Where,
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1.5,./ 0.47,01.2 3.7,./ ,01.2
(8)
,./ is the proportion of link length with restrictive median (decimal); and
,01.2 is the proportion of segment with curb on the right-hand side (decimal).
The adjustment for access point ( ) in Equation 6 is a function of access point density
and the number of through lanes, as shown below.
Where,
0.0783 /567
(9)
3 5280538,:
(10)
538,; "/ <= "
3 is the access point density on segment (points/mile);
567 is the number of through lanes in the subject direction of travel;
538,: is the number of access points on the right side in the subject direction of travel;
538,; is the number of access points on the right side in the opposing direction of travel;
is the segment length (feet); and
<= is the width of signalized intersection (feet).
The signal spacing adjustment factor (
) in Equation 6 accounts for the observation that
drivers tend to choose slower free-flow speed on shorter segments, all other factors being the
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same. The formula is shown below. If in Equation 11 is less than 400 feet, it should be set to
400 feet.
1.02 4.7
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19.5
? 1.0
(11)
Control Delay at Signalized Intersections
Chapter 18 of the HCM 2010 describes the procedures to analyze signalized intersections, which
can be used to determine the control delay (!) in Equation 4. Equations 18-19 from the HCM
2010 show that the control delay is the sum of uniform delay, incremental delay and initial queue
delay. Uniform delay is the delay when arrivals are random throughout the cycle (uniform
arrivals). Incremental delay accounts for the delays caused by random or sustained
oversaturation. Initial queue delay accounts for the additional delay incurred due to an initial
queue. For the purpose of calculating delays in free-flow conditions, incremental delay and
initial queue delay can be assumed to be zero.
Compared to the HCM 2000, the HCM 2010 adopted a new procedure to calculate
uniform delay. This new procedure is called “incremental queue accumulation.” It requires
detailed data that are difficult for a travel demand model to collect, such as saturation flow rate
and arrival rate, and no formulas are available for this procedure. Therefore, it was decided to
continue using the procedure described in the HCM 2000, which was also adopted in the
SERPM6 and ISTDM models. The formula is shown below (a compilation of Equations 16-9 to
16-11 in the HCM 2000).
Where,
B D
! 0.5@ A1 C ' (
@
(12)
@ is the cycle length (seconds);
B is the effective green time (seconds); and
( is the progression adjustment factor.
Progression adjustment factor (() in Equation 12 is used to account for the quality of
signal progression, and can be calculated using the formula shown below (Equation 16-10 from
the HCM 2000).
Where,
B
1 ("E A1 8 ∙ @ C E
( B B
1 A@ C
1 A@ C
(13)
( is the proportion of vehicles arriving on green;
E is the supplemental adjustment factor for a platoon arriving during green, and its
default value for each arrival type is listed in Exhibit 16-12 in the HCM 2000; and
8 is the platoon ratio, and its default value for each arrival type is listed in Exhibit 16-12
in the HCM 2000.
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IMPLEMENTATION
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How to Get the Link Attributes Required by the Formulas
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As shown in the above section, the free-flow speed formulas in the HCM 2010 require many link
attributes as inputs. Some of them are not typically available to a regional travel demand model.
According to how difficult it is to collect them, these link attributes are classified into two groups
in the TRM, as shown in Table 1.
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TABLE 1 Classification of Link Attributes in the TRM
Link Attributes that are Easier to Collect
Link Attributes that are More Difficult to Collect
1) Number of lanes
1) Access point density (for freeways, it is called
2) Median/left turn lane
total ramp density)
3) Posted speed
2) Signal spacing (distance between two adjacent
4) Lane width
signals, used as the segment length )
5) Shoulder width
3) Signal cycle length
6) Lateral clearance
4) G/C ratio (the ratio of green time and cycle
length)
5) Vehicle arrival type at intersections
Link attributes in the first column of Table 1 are easier to collect for the model base year.
Most of them are links’ physical attributes. They are also usually specified for new projects in
future plans, such as the Metropolitan Transportation Plan (MTP), therefore they are available
for future year model runs.
Compared to the link attributes in the first column of Table 1, the attributes in the second
column are more difficult to collect, especially for future year model runs. They are mostly
attributes related to traffic operations, and could change frequently. For example, signal timing at
intersections (“Signal cycle length” and “G/C ratio”) is usually adjusted frequently to
accommodate new traffic patterns. Different signal timings could even be set up at the same
intersection for different time periods during a day. It is even more difficult to obtain these link
attributes for future years.
Most of the attributes in the second column of Table 1 have strong correlations with area
type. For example, when an urban street’s area type changes from rural in the base year to urban
in a future year, usually more access points will be created to access this urban street and the
access point density will increase. At the same time, signal timing will usually be adjusted to
accommodate new traffic patterns. In a travel demand model, economic development will induce
the change of area type, and therefore some of the link attributes in the second column of Table 1.
Unfortunately, these link attributes are not usually specified in future plans.
Based on the characteristics of the link attributes in the second column of Table 1, lookup
tables are used to determine their values in the TRM. In detail, default values for these link
attributes are developed by facility type and area type, and all links with the same facility type
and area type use the same default values. As a result, when a link’s area type is changed due to
future economic development, its free-flow speeds could change even if its link attributes in the
first column of Table 1 remain the same. Obviously, using default value lookup tables yield less
accurate free-flow speeds for each specific link in the highway network. However, it should have
limited negative impacts on the performance of a regional model, and it makes it possible to
change free-flow speeds automatically when a link’s area type is changed.
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In summary, the link attributes in the first column of Table 1 should be collected for the
model base year and coded in the network. For a future year model run, they should be updated
manually if any future year project changes their values. On the other hand, the link attributes in
the second column of Table 1 use default values by facility type and area type, and there is no
need to collect these link attributes for the model base year or future years. When a link’s area
type is changed for a future year model run, a different set of default values will be used, which
results in different free-flow speeds without manually changing the coded link attributes.
The classification of link attributes shown in Table 1 is used by the TRM. If the same
method is used in other regions, link attributes can be classified differently to fit their own data
availability. For example, lane width, shoulder width and lateral clearance can be classified into
the second column if they are not available.
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In order to make it easier to use the free-flow speed formulas from the HCM, the facility type
defined in the TRM follows the chapters in the HCM, as shown in Table 2.
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Major Facility Types
TABLE 2 Major Facility Types in the TRM
Facility Type
Description
Freeway
Uninterrupted facility with full control of access
Multilane
Uninterrupted facility without full control of
Highway
access, more than one lane in each direction
Two-lane
Uninterrupted facility without full control of
Highway
access, only one lane in each direction
Interrupted facility whose major function is to
Major Arterial
provide high-speed movement
Interrupted facility that is not a major arterial or
Minor Arterial
collector/local street
Collector/Local Interrupted facility whose major function is to
Street
provide accessibility
HCM 2010
Chapter 11
Equation
Equation 1
Chapter 14
Equation 2
Chapter 15
Equation 3
Chapters
17, 18
Equations 4
to 13
Table 2 shows that three facility types are defined for urban streets. The motivation is to
provide appropriate default values. The link attributes could be quite different for different urban
streets with the same area type. For example, two intersecting urban streets could have different
signal timings: one has much longer green time or much better progression than the other.
Therefore it is not appropriate to use the same default values for these two urban streets. If they
are defined as two different facility types, different default values can then be applied.
How to Develop the Default Values
Several sources are used to develop the default values. The HCM 2010 suggests some default
values, such as access point density, which are directly used in the TRM. A study on the Level of
Service (LOS) in North Carolina (13) is used to develop the default signal cycle length, G/C ratio,
and vehicle arrival type at intersections. Default signal spacing is determined based on the
average of samples by facility type and area type collected from the field.
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RESULTS AND VALIDATION
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Free-flow speeds in the TRM were calculated based on the approach described in this paper.
Only free-flow speeds on freeways were calibrated due to the limitations of available speed data.
The free-flow speeds were then validated based on the travel time data from a floating car survey.
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There are many ways to collect free-flow speeds on freeways, such as using sensors installed on
freeways, GPS-based devices, and cell phones or probe vehicles. In the TRM, a cell phone
location based data set is selected to calibrate the free-flow speeds on freeways.
TRM sampled several freeway segments in the model area and calculated their average
observed speeds in the off-peak time period by area type and posted speed. The results indicate
that the observed free-flow speeds are significantly different for freeway segments with the same
area type but with different posted speeds.
The modeled free-flow speeds on freeways are calculated based on Equation 1. This
equation shows that the free-flow speeds on freeways are only affected by lane width, right-side
lateral clearance, and total ramp density, but not by posted speed. Since all freeway segments in
the TRM use the same lane width and right-side lateral clearance, and use the default value for
total ramp density based on area type, all freeway segments with the same area type have the
same free-flow speeds, despite their posted speeds. This is not consistent with the observed freeflow speeds.
One of the reasons for this inconsistency is that default total ramp density, instead of the
real total ramp density, is used. However, it is difficult to collect the total ramp density for each
highway link in a regional travel demand model. To address this inconsistency issue, an additive
term is developed based on a regression analysis. The basic idea is to take the free-flow speed
from Equation 1 as the free-flow speed for freeway segments with posted speed of 65 mph,
which is the most popular posted speed for freeways in the TRM model area. If a freeway
segment has a posted speed different from 65 mph, a term is added to Equation 1 to adjust its
free-flow speed. In this regression analysis, the dependent variable is calculated as the observed
free-flow speed by area type and posted speed minus the observed free-flow speed for freeway
segments with the same area type and posted speed of 65 mph. The independent variable is the
posted speed minus 65 mph. This term is shown below.
Calibration of Free-flow Speeds on Freeways
G 0.0086H I
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Where,
0.051H D
0.5223H
(14)
G is the additive term to reflect the impact of posted speeds on free-flow speeds; and
H is the posted speed minus 65 mph, and H should not be greater than 5 mph or smaller
than -10 mph.
Equation 14 is added to Equation 1 to calculate the free-flow speeds on freeways. Since
the posted speed for freeways in the TRM model area is in the range of 55 mph to 70 mph, H in
Equation 14 should be in the range of -10 mph and 5 mph. The calculated free-flow speed based
on Equations 1 and 14 is further calibrated using a multiplicative factor to match the observed
speeds.
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Paper revised from original submittal.
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Validation
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The free-flow speeds are validated based on the speed data from a floating car survey. The major
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reason to select a floating car survey is that it can provide reasonable free-flow speeds on urban
streets. Intersection delay is an important component of free-flow speeds on urban streets.
Therefore, the observed free-flow speeds for an urban street should come from a long urban
street segment that includes several signals. In a floating car survey, a GPS-quipped probe
vehicle is driven along a preselected route and the elapsed time and distance traversed are
measured. Therefore, intersection delay is a part of the probe vehicle’s travel time.
The floating car survey was conducted in 2011. It selected 48 routes in Durham, Chapel
Hill and Hillsborough. There are two directions for each route, and nine vehicle runs for each
direction. Table 3 summarizes the surveyed roadway length by facility type and area type. The
length of a two-way roadway is counted twice in Table 3, and the length of a one-way roadway
is counted only once.
TABLE 3 Surveyed Roadway Length by Facility Type and Area Type (miles)
Facility Type
CBD
Urban
Suburb
Freeway
3
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44
Multilane Highway
0
7
2
Two-lane Highway
0
0
22
Major Arterial
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49
Minor Arterial
3
75
42
Collector/Local Street
1
3
0
Rural
24
0
9
0
0
0
Table 3 shows that the 48 routes in the floating car survey cover almost 480 miles of
roadways in the model area. They provide good coverage of major facility types, such as freeway,
major arterial and minor arterial. Unfortunately, not enough multilane highways, two-lane
highways and collector/local streets were surveyed.
For each route and direction, the vehicle runs that were conducted when the traffic was
light are selected, and their average travel time is used as the observed free-flow travel time. The
observed free-flow speeds are then calculated as route length divided by observed free-flow
travel time. They are compared to the modeled free-flow speeds. Since the roadway segments in
a route could have different facility types and area types, therefore different free-flow speeds, the
modeled free-flow speed is the average speed over a route, calculated as route length divided by
the sum of modeled free-flow travel times over each of the roadway segments. Table 4 shows
samples of the observed and modeled free-flow speeds.
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Table 4 Samples of Observed and Modeled Free-flow Speeds from the Floating Car Survey
Major
Route
Observed
Modeled
Area
Length
Free-flow
Free-flow
Route (direction)
Major Facility Type
Type
(miles) Speed (mph) Speed (mph)
I-85 (EB)
Freeway
Suburb
21.2
65.4
68.7
I-40 (EB)
Freeway
Suburb
24.1
67.2
68.0
NC 147 (WB)
Freeway
Urban
13.0
61.6
61.1
Eubanks Rd. (EB)
Two-lane Highway Suburb
2.6
37.3
42.8
Multilane Highway,
Fordham Blvd. (EB)
Urban
7.3
41.0
36.6
Major Arterial
MLK Blvd. (EB)
Major Arterial
Urban
5.3
30.0
32.5
Davis Dr. (NB)
Major Arterial
Urban
2.8
33.1
32.2
Erwin Rd. (EB)
Major Arterial
CBD
2.3
23.0
21.9
US 70 (NB)
Minor Arterial
Suburb
3.1
28.8
35.1
Jones Ferry Rd.
Minor Arterial
Urban
1.0
31.8
28.7
(WB)
Estes Dr. (NB)
Minor Arterial
Urban
1.7
26.6
28.3
Horton Rd. (WB)
Minor Arterial
Urban
1.9
29.2
28.3
The samples in Table 4 are selected because most of their roadway segments have the
same facility type and area type. However, please notice that each route in Table 4 still could
consist of roadway segments with different facility types and area types, and Table 4 only shows
the major facility type and area type.
Table 4 shows that the observed and the modeled free-flow speeds are close for the
sampled routes. To consider all 48 routes in the floating car survey, the observed travel times are
compared with the modeled travel times. The results are shown in Figure 1.
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y = 0.9801x
R² = 0.9736
Modeled Travel Time (s)
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0
0
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1000
Observed Travel Time (s)
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1400
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SUMMARY
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Free-flow speed is important to a travel demand model. It is the basis for speed estimation. The
speed estimation determines the network skims and accessibility measures, which affect almost
all steps in a traditional four-step model. Reasonable speed estimation is also needed to validate a
travel demand model and support air quality analyses.
A review of the current practices in other regions reveals that free-flow speeds are usually
determined using lookup tables or formulas. Directly using formulas in the HCM has several
advantages, including saving additional studies, the consistency of free-flow speeds and
capacities, and the consistency of travel demand modeling with traffic operations analysis. This
paper shares the experience in using the formulas in the newest version of the HCM (the HCM
2010) to determine the free-flow speeds in a regional travel demand model.
The formulas to calculate the free-flow speeds based on the HCM 2010 are summarized
in this paper. They are either directly taken from the HCM 2010 or are modified to fit the freeflow condition. These formulas require many link attributes as inputs, but some of them are not
FIGURE 1 Comparison of the observed travel time and the modeled travel time.
There are 48 routes and each has two directions, so 96 data points are plotted in Figure 1.
The thin black line is the regression line, and the thick red line is the reference line of G H. The
regression equation is G 0.9801H, which implies that the modeled travel time is very close to
(slightly smaller than) the observed value, or in other words, the modeled free-flow speed is very
close to (slightly higher than) the observed value. The R-squared value is as high as 0.9736. So,
the modeled travel time matches the observed travel time very well.
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typically available to a regional travel demand model. So the link attributes are classified into
two groups. In the first group, the link attributes should be collected for the model base year and
coded in the network. For a future year model run, they should be updated manually if any future
year project changes their values. In the second group, the link attributes use default values by
facility type and area type, and there is no need to collect these link attributes for the model base
year or future years. When a link’s area type is changed for a future year model run, a different
set of default values will be used, which results in different free-flow speeds without manually
changing the coded link attributes.
The free-flow speeds on freeways are calibrated based on a cell phone location based
speed data set. An additive term is introduced to consider the impact of posted speed. The freeflow speeds on other facilities are not calibrated due to the limitations of available speed data. A
floating car survey is used to validate the free-flow speeds. The observed travel time for each
route direction in the floating car survey is compared with the modeled travel time calculated
from the modeled free-flow speed. The comparison indicates that the modeled free-flow speeds
are reasonable.
Appropriate default values are important to the performance of these free-flow speed
formulas. They should be carefully determined based on local studies or field data whenever
possible. It is also suggested to validate the free-flow speeds based on observed speed data, and
to make adjustments to the default values if necessary.
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The author would like to thank the North Carolina Department of Transportation, the Capital
Area Metropolitan Planning Organization, the Durham-Chapel Hill-Carrboro Metropolitan
Planning Organization, and Triangle Transit for funding this project.
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ACKNOWLEDGEMENTS
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D.C., 1996, pp. 27-36.
2. Spiess, H. Conical Volume-Delay Functions. Transportation Science, Vol. 24, No. 2,
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3. Huntsinger, L. F. and N. M. Rouphail. Bottleneck and Queuing Analysis: Calibrating
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13. Fain, S. J., C. M. Cunningham, R. S. Foyle, and N. M. Rouphail, NCDOT Level of
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North Carolina Department of Transportation, Raleigh, N.C., 2006.
TRB 2014 Annual Meeting
Paper revised from original submittal.