Terms and Definitions

Department of EMISSMU School of Engineering

Leadership in Engineering

Systems Engineering for the Transportation Critical

InfrastructureThe Development of a Methodology and

Mathematical Model for Assessing the Impacts of K Links Disconnects have on Defined Links of the

Network

4Department of EMIS

SMU School of Engineering


• Critical Infrastructure (CI)

• System

• Transportation CI

• System of Systems (SoS)

• Major Cities

• City Boundary

• Network

Terms and Definitions

5Department of EMIS



• Movement of Goods

• Trucks

• Peak Traffic

• Normal Traffic

• Other Traffic

• Days of Operation


6Department of EMIS



• Node• Arc Link• Disconnect• Steady State• Highway • Defined Links• Worst Link• Best Link


7Department of EMIS



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

8Department of EMIS



Objective

– Two Objective Steps

1. Systems Engineering Approach

2. K Links with Highest Affect on Network

9Department of EMIS



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

10Department of EMIS




• Decision Making Methodology and Tool

i, j





• Algorithm for finding efficiently the K Links with the greatest impact on the network

Minutes

Acc

urac

y

Accuracy Vs. Time




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”




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




The Systems Engineering Process• Defining the System – System of Systems

AgricultureWater

Public Health

EmergencyServices

DefenseIndustrial

Base

Telecom.

EnergyTransportation

Government

Chemical andHazMat

Postal andShipping

Banking andFinance

FoodAgriculture

Water

Public Health

EmergencyServices

DefenseIndustrial

Base

Telecom.

EnergyTransportation

Government

Chemical andHazMat

Postal andShipping

Banking andFinance

Food




The Systems Engineering Process

• Need Analysis

• Stakeholders• City• State and Federal• Business• Society (Indirectly)





• Requirements– Mission Definition– Performance and Physical Parameters– Use Requirements




The Systems Engineering ProcessC

ompo

nent

s

• Transportation CI SoS

INPUT•Disconnects•Hrs of Op.

PROCESS•Mathematical model

Att

ribu

tes

•Flow•Distance

•Links •Nodes•Efficiency of model

RelationshipsMovement of Goods

Efficiently Finding K Links

Perf. of Defined

Links

OUTPUT•Performance

•Disconnects•Hours of operation





• Ground Rules and Assumptions – Highway– Major Cities– Steady State

• Non-Event Days

• Construction established and on-going

• Mon – Fri

– Disconnect





• Metrics– Performance of Network

• Travel Time

• Throughput

– Solution – Processing Time of Model (as a function of OD table and network topology)

(OD)

Links

Model /Algorithm

Time

Accuracy




The Systems Engineering ProcessSystem

Requirements

SystemSolution

Validate &Verify

Actual Model

System Objective

City Boundary

Section of City

Small Network Enumeration

EnumerationProcessing Time

Functional Analysis

EnumerationProcessing Time




Model

• Most naive process– Disconnect Link (Li,j) subject to Time (tn)

– Simulate Network Performance

– Connect Link (Li,j)

– Repeat until all links tested




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




Example of Model

Time

1

2

a

i

b c

3

4

6

5

3

4

8

6

4

3

O D Matrix3 4

1 200 1002 200 200

Number of Vehicles traveling from Origin to Destination during Off-Peak Period




1

2

a

i

b c

3

4

6, 300

5, 4004, 250

8, 450

6, 700

4, 400

3, 300

3, 450

Example of Model: Routing Assignment

Time, Flow

a i b c 3 4 a i b c 3 41 300 1 62 400 2 5a 450 250 a 3 4i 450 i 8b 700 b 6c 400 300 c 4 3

Flow = Veh / Hr Travel Time = Minutesq t




1

2

a

i

b c

3

4

6, 300

5, 400

8, 700

6, 700

4, 400

3, 300

3, 700

Example of Model: Effects of Disconnect on Link (a,b)

Time, Flow

qa i b c 3 4

1 3002 400a 700 0i 700b 700c 400 300

Flow = Veh / Hr 1,3 = {1,a a,i i,b b,c c,3} = 271,3 = {1,a a,b b,c c,3} = 201,4 = {1,a a,i i,b b,c c,4} = 261,4 = {1,a a,b b,c c,4} = 192,4 = {1,a a,i i,b b,c c,3} = 262,3 = {1,a a,b b,c c,3} = 192,4 = {1,a a,i i,b b,c c,4} = 252,4 = {1,a a,b b,c c,4} = 18

Avg. T = 2.5Min/Veh




Example of Model

1

2

a

i

b c

3

4

6, 300

5, 4006, 700

4, 400

3, 300

1

2

a

i

b c

3

4

6, 300

5, 400

8, 4503, 450

4, 700

1

2

a

i

b c

3

4

6, 300

5, 4006, 700

4, 400

3, 3004, 700

4, 250




0.0

100.0

200.0

300.0

400.0

500.0

System

System 412.2 268.0 479.6 383.8 402.5

Link a Link b Link c Link d Link e

DefinedLinks Link a Link b Link c Link d Link eLink 1 17.2 25.1 35.0 72.0 19.1Link 2 74.0 36.3 93.4 19.8 15.6Link 3 22.2 17.4 28.8 0.5 97.4Link 4 37.1 74.2 32.0 29.7 28.0Link 5 90.7 9.3 95.5 98.1 60.7Link 6 28.9 32.9 82.7 61.7 54.8Link 7 75.1 23.1 1.2 14.9 13.2Link 8 43.1 33.8 64.5 18.4 60.3Link 9 23.9 16.0 46.4 68.9 53.4System 412.2 268.0 479.6 383.8 402.5

Links in Network

Example of Model: Performance for a General Metric

OUTPUTS

Sum of Performance

, …,




0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

500.0

(2, 11) (1, 11) (2, 12) (3, 14) (1, 12) (4, 7) (5, 6) (3, 8) (4, 8) (2, 5) (3, 8) (1, 2) (3, 5) (2, 4) (4, 5) (5, 8)

Example of Model

Links

Perf

orm

ance

Worst

Best

OUTPUTS

0 is threshold

K Links = {2,11}, …, {1,12}affecting the TransportationCI the most




OutputPerformance:•Travel Time/Throughput

I35W I35E I45

I35W I35E Hwy 75

I20

I30

I20

InputSingle Disconnect; 1/0

Variables•Temporal Time of Day: I =1, 2, 3 (peak, norm, other)•Links: l =(i,j), [(i+1), (j+1)],…, (i+n, j+n)

L1 L2 L3

L8 L7 L6

L5

L4

L9

Information Flow

I=1

I=1

Network




• Restricting the Search Space– Find least reliable links

– Find largest/lightest flow

• Approximation Methods– “Quickly” find “Good” solution

Ideas for Improving Algorithmic Model Efficiencies

1

2

a

i

b c

3

4

6, 300

5, 4004, 250

8, 450

6, 700

4, 400

3, 300

3, 450




Validation and Verification

• SE Approach– Integrations Process– V-Chart

• Model– Small Network– Enumeration– Efficiency of Model




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




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

Documents

Terms and Definitions