Systems Engineering for the
Transportation Critical
Infrastructure
The Development of a Methodology and
Mathematical Model for Assessing the Impacts of K
Links Disconnects have on Defined Links of the
Network
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Terms and Definitions
•
•
•
•
•
•
•
4
Critical Infrastructure (CI)
System
Transportation CI
System of Systems (SoS)
Major Cities
City Boundary
Network
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Terms and Definitions
•
•
•
•
•
•
5
Movement of Goods
Trucks
Peak Traffic
Normal Traffic
Other Traffic
Days of Operation
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Terms and Definitions
•
•
•
•
•
•
•
•
6
Node
Arc  Link
Disconnect
Steady State
Highway
Defined Links
Worst Link
Best Link
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Objective
• The objective of this dissertation is to develop
a methodology, using a SE approach, and
apply the methodology to develop a
mathematical model, using performance
metrics such as travel time and flow, to
simulate the impacts K Links disconnects
have on highway networks of major
metropolitan cities
7
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Objective
– Two Objective Steps
1. Systems Engineering Approach
2. K Links with Highest Affect on Network
8
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Research Significance
• Contribution: This dissertation provides
officials a decision-making methodology and
tool for resource allocation and risk mitigation
– Metrics that measure the performance of the
network given disconnects occurring
– Ranking of K Links affecting the network the most
9
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Research Significance
• Decision Making Methodology and Tool
i, j
10
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Research Significance
• Algorithm for finding efficiently the K Links
with the greatest impact on the network
Accuracy
Accuracy Vs. Time
11
Minutes
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Brief Literature Review
• SE
– Osmundson et al, The Journal of The International Council on Systems
Engineering (INCOSE), 2004
– Tahan et al, The Journal of The INCOSE, 2005
– Bahill et al, The Journal of The INCOSE, 2005
– Blanchard et al, “Stems Engineering and Analysis”, 1990
– INCOSE, “Systems Engineering Handbook”, 2004
– Hazelrigg, “Sys. Eng.: An Approach to Information-Based Design” 1996
– Miller et al, “Systems Engineering Management”, 2002
– Stock et al, “Strategic Logistics Management”, 1993
– Ibarra et al, Conference for Systems Engineering, 2005
– Blanchard, “Logistics Engineering and Management”, 2004
– US Department of Homeland Security, “Budget in Brief, Fiscal Year 2005”
12
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Brief Literature Review
• Modeling
– Osmundson et al, The Journal of The International Council on Systems
Engineering (INCOSE), 2004
– Bahill et al, The Journal of The INCOSE, 2005
– Sathe et al, Transportation Research Board, 2005
– Jain et al, Transportation Science, 1997
– Arroyo et al, Transportation Research Board, 2005
– Rardin, “Optimizations in Operations Research”, 1998
– Rinaldi et al, IEEE Control System Magazine. 2001
– Murray-Tuite, Dissertation, 2003
13
SMU School of Engineering
Department of EMIS
Leadership in Engineering
The Systems Engineering Process
• Defining the System – System of Systems
Food
Agriculture
Banking and
Finance
Water
Public Health
Postal and
Shipping
Emergency
Services
Chemical and
HazMat
Defense
Industrial
Base
Government
Transportation
14
Telecom.
Energy
SMU School of Engineering
Department of EMIS
Leadership in Engineering
The Systems Engineering Process
• Need Analysis
• Stakeholders
•
•
•
•
15
City
State and Federal
Business
Society (Indirectly)
SMU School of Engineering
Department of EMIS
Leadership in Engineering
The Systems Engineering Process
• Requirements
– Mission Definition
– Performance and Physical Parameters
– Use Requirements
16
SMU School of Engineering
Department of EMIS
Leadership in Engineering
The Systems Engineering Process
Components
• Transportation CI SoS
INPUT
•Disconnects
•Hrs of Op.
Attributes
Relationships
17
•Flow
•Distance
PROCESS
•Mathematical
model
Movement
of Goods
•Links
•Nodes
•Efficiency
of model
OUTPUT
•Performance
Perf. of
Defined
Links
Efficiently
Finding
K Links
•Disconnects
•Hours of
operation
SMU School of Engineering
Department of EMIS
Leadership in Engineering
The Systems Engineering Process
• Ground Rules and Assumptions
– Highway
– Major Cities
– Steady State
• Non-Event Days
• Construction established and on-going
• Mon – Fri
– Disconnect
18
SMU School of Engineering
Department of EMIS
Leadership in Engineering
The Systems Engineering Process
• Metrics
– Performance of Network
• Travel Time
• Throughput
– Solution – Processing Time of Model (as a
function of OD table and network topology)
(OD)
Links
19
Model /
Algorithm
Time
Accuracy
SMU School of Engineering
Department of EMIS
Leadership in Engineering
The Systems Engineering Process
System
Solution
System
Requirements
Functional Analysis
System Objective
Validate &
Verify
Enumeration
Processing Time
City Boundary
Enumeration
Processing Time
Section of City
Small Network
Enumeration
Actual
Model
20
SMU School of Engineering
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Model
• Most naive process
–
–
–
–
21
Disconnect Link (Li,j) subject to Time (tn)
Simulate Network Performance
Connect Link (Li,j)
Repeat until all links tested
SMU School of Engineering
Department of EMIS
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Model
• Objective
– Performance of Network based on Defined Links
• Constraints
– Mathematical model of how the system responds
to changes in variables
• Variables
– Time of Day
– Disconnected Links
22
SMU School of Engineering
Department of EMIS
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Example of Model
1
i
6
3
a
2
3
4
8
4
b
6
c
3
5
O D Matrix
3
4
1
200 100
2
200 200
4
Time
Number of Vehicles traveling from Origin to Destination
during Off-Peak Period
23
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Example of Model: Routing
Assignment
1
i
6, 300
3
3, 450
a
4, 400
8, 450
b
4, 250
6, 700
c
3, 300
5, 400
2
4
Time, Flow
q
1
2
a
i
b
c
24
a
300
400
Flow = Veh / Hr
i
b
c
3
450
t
4
250
450
700
400
300
1
2
a
i
b
c
a
6
5
Travel Time = Minutes
i
b
c
3
3
4
4
8
6
4
3
SMU School of Engineering
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Example of Model: Effects of
Disconnect on Link (a,b)
1
i
6, 300
3
3, 700
a
q
1
2
a
i
b
c
25
b
5, 400
2
a
300
400
D Avg. T = 2.5
Min/Veh
Flow = Veh / Hr
i
b
c
3
700
4, 400
8, 700
4
0
700
700
400
300
6, 700
c
3, 300
4
Time, Flow
1,3 = {1,a a,i i,b b,c c,3} = 27
1,3 = {1,a a,b b,c c,3} = 20
1,4 = {1,a a,i i,b b,c c,4} = 26
1,4 = {1,a a,b b,c c,4} = 19
2,4 = {1,a a,i i,b b,c c,3} = 26
2,3 = {1,a a,b b,c c,3} = 19
2,4 = {1,a a,i i,b b,c c,4} = 25
2,4 = {1,a a,b b,c c,4} = 18
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Example of Model
3
i
1
4, 400
6, 300
a
2
b
4, 700
6, 700
c
3, 300
5, 400
3
i
1
4, 400
6, 300
a
2
6, 700
c
3, 300
5, 400
5, 400
8, 450
3, 450
a
4
3
i
6, 300
26
b
4, 700
1
2
4
4, 250
b
c
4
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Example of Model: Performance for a
General Metric
Defined
Links
Link 1
Link 2
Link 3
Link 4
Link 5
Link 6
Link 7
Link 8
Link 9
System
Link a
17.2
74.0
22.2
37.1
90.7
28.9
75.1
43.1
23.9
412.2
Links in Network
Link b
Link c
Link d
25.1
35.0
72.0
36.3
93.4
19.8
17.4
28.8
0.5
74.2
32.0
29.7
9.3
95.5
98.1
32.9
82.7
61.7
23.1
1.2
14.9
33.8
64.5
18.4
16.0
46.4
68.9
268.0
479.6
383.8
, …,
Link e
19.1
15.6
97.4
28.0
60.7
54.8
13.2
60.3
53.4
402.5
OUTPUTS
System
500.0
400.0
300.0
Sum of Performance
200.0
100.0
0.0
System
27
Link a
Link b
Link c
Link d
Link e
412.2
268.0
479.6
383.8
402.5
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Example of Model
OUTPUTS
Worst
Performance
K Links = {2,11}, …, {1,12}
affecting the Transportation
CI the most
Best
Links
28
0 is threshold
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Network
L1
Input
Single Disconnect; 1/0
I=1
I35W
L2
L3
I35E
Hwy 75
L9 I20
Output
Performance:
•Travel Time/Throughput
I30
L4
I20
L5
I=1
I35W
Variables
•Temporal
Time of Day: I =1, 2, 3 (peak, norm, other)
•Links: l =(i,j), [(i+1), (j+1)],…, (i+n, j+n)
29
L8
I35E
L7
I45
Information Flow
L6
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Ideas for Improving Algorithmic
Model Efficiencies
1
i
6, 300
3, 450
a
2
3
4, 400
8, 450
4, 250
5, 400
b
6, 700
c
3, 300
4
• Restricting the Search Space
– Find least reliable links
– Find largest/lightest flow
• Approximation Methods
– “Quickly” find “Good” solution
30
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Validation and Verification
• SE Approach
– Integrations Process
– V-Chart
• Model
– Small Network
– Enumeration
– Efficiency of Model
31
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Conclusion
• Transportation CI is important
– To individuals’ way of life
– To companies’ way of doing business
• Proposed a Methodology and Mathematical
Model to Determine Impact of K Links
Disconnects have on the Defined Links of a
Network
32
SMU School of Engineering
Department of EMIS
Leadership in Engineering
Conclusion
• Research Significance
– Society: A Methodology and Tool for Officials to
use in the Decision Making Process
– Engineering: A New Algorithm for Solving
Complex Systems Efficiently
33
SMU School of Engineering
Department of EMIS
Leadership in Engineering