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the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD Candidate Committee Update: April 5, 2006

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Page 1: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

A Systems’ Approach to the Design of a Methodology and

Mathematical Model for Determining the Most Critical

Links of a Highway Network

Gerard Ibarra

PhD Candidate

Committee Update: April 5, 2006

Page 2: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

Sys

tem

s E

ng

inee

rin

g P

roce

ssFe

ed B

ack

Loo

p

Develop the InitialRequirements

Perform theFeasibility Analysis

Compose OperationalReq. from the Needs

Evaluate the Maintenance and Support

Develop TechnicalPerformance Measures

Initiate theFunctional Analysis

Perform theDesign Synthesis

Perform theTrade-off Analysis

INPUT

OUTPUTSelection of Perferred

Candidates

Define the Problem and Identify the Needs

1

2

3

5

4

6

7

8

9

10

Continuous

Verification Process

Page 3: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

Systems Engineering Process

Define the Problem and Identify the Needs Critical Infrastructure Protection is an important

topic to every major city in the US Homeland Security funding being more scrutinize For the transportation sector, need help with

identifying the k-critical links of a highway network

Page 4: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

Systems Engineering Process

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

Define the Problem

Page 5: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

Systems Engineering Process

Initial Requirements To develop a process and mathematical model to

help determine the k-critical links of a highway network

Feasibility Analysis No current simulation model capable of feasibly

performing k-critical links of a highway network Models that look at CIP do not include

geographical interdependencies – a systems view of the links

Page 6: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

Systems Engineering Process

Operational Requirements Mission Definition Performance and Physical Parameters Operational Deployment Operational Life Cycle Utilization Requirements Effectiveness Factor Environment

Page 7: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

Systems Engineering Process

Maintenance and Support Specific to the process and mathematical model

Technical Performance Parameters Accuracy of k-critical links Model’s information processing time Maintainability and Supportability of system

Functional Analysis Details of the Process and Model

Page 8: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

Systems Engineering Process

Design Synthesis Trade-off Analysis Selection of Preferred Candidate

Page 9: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

Systems Engineering Process

DHSResource

Allocation

k-Critical LinksNetworkAnalysis

The bottom line:

Page 10: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

A System’s Prospective View

K-criticalLinks

RailLines

PowerLines

Population

HazardousCargo

System’sView

System’sView

Mo

del

Page 11: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

A System’s Prospective View

Houston

Page 12: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

A System’s Prospective View

K-Critical Links The link with the most flow under normal

conditions is the most critical The link with the most cuts is the most critical The link with maximum sensitivity is the most

critical

Page 13: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

A System’s Prospective View

Geographical Interdependencies (GI) Rail and Power Lines (Heuristic: Transportation)

Proximity Parallel Transverse

Population (Bureau of Statistics: Public Health) Proximity

Hazardous Cargo (DOT: Chem. & HazMat) Developed a methodology

Page 14: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

A System’s Prospective View

Transportation

PublicHealth

Chem. &HazMat

CriticalInfrastructures

Page 15: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

Rail Lines Intersecting Highways – I610 and Inside

1 – 24 Intersections I610 and Inside, 25 – 35 outside I610 up to Beltway 8

1 2

3

18

20

13

45

7

14

915

8

12

11

16 1710

6

19

24

232221

6A

16

17

18

19

2021

22

23

24

29 26

27

28

25

Page 16: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

A System’s Prospective View

Mathematical Model Utility Theory: Additive Function Simulation: Monte Carlo Statistics: Weighted Averages and Variances

Decision Maker’s Input Professional/Expert’s Input

Page 17: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

A System’s Prospective View

Mathematical Model

otherwise 0

selectedif h and k

and Ah cargo hazardoush

Ap populationp

Ae line powere

Ar line railr

Ak link critical k where

WVhWVp

WVe WVrWVkl

i.jji,

ji,i.j

ji,i.j

ji,i.j

ji,i.j

ji,ji,

hhjippji

eejirrjikkjiji

jiji

jijiji

10

,

,,

,,,

,,

,,,,

Page 18: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

A System’s Prospective View

Mathematical Model (Continued)

h

p

e

r

k

m

1im

Wh of Weight

Wp of Weight

We of Weight

Wr of Weight

Wk of Weight

and

(items) n ..., 2, 1, m where

W

,00.1

ji,

ji,

ji,

ji

ji,

hji,

pji,

eji,

rji,

kji,

q

Vh of Value

Vp of Value

Ve of Value

Vr of Value

Vk of Value

and

(items) n ..., 2, 1, q where

V and

,

],100[

Page 19: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

A System’s Prospective View

Mathematical Model

30% 15% 10% 25% 20%K-critical Rail Power Haz

Link Links Lines Lines Pop. Cargo(16, 17) 10 8 7 8 0(17, 18) 10 3 3 5 0(18, 19) 0 0 0 3 10

Weights

Val

ues

K-critical Rail Power HazLink Links Lines Lines Pop. Cargo Total

(16, 17) 3.00 1.20 0.70 2.00 0.00 6.90(17, 18) 3.00 0.45 0.30 1.25 0.00 5.00(18, 19) 0.00 0.00 0.00 0.75 2.00 2.75

Page 20: A Systems’ Approach to the Design of a Methodology and Mathematical Model for Determining the Most Critical Links of a Highway Network Gerard Ibarra PhD

Conclusion

Applied the SE process for the design of a system solution for the most critical links of a highway network Developed a methodology for determining those

most critical links Constructed a mathematical model for evaluating

those links based on the network’s GI Provided maintainability and supportability design

criteria in the methodology and model