a systems’ approach to the design of a methodology and mathematical model for determining the most...
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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
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
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
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
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
Systems Engineering Process
Operational Requirements Mission Definition Performance and Physical Parameters Operational Deployment Operational Life Cycle Utilization Requirements Effectiveness Factor Environment
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
Systems Engineering Process
Design Synthesis Trade-off Analysis Selection of Preferred Candidate
Systems Engineering Process
DHSResource
Allocation
k-Critical LinksNetworkAnalysis
The bottom line:
A System’s Prospective View
K-criticalLinks
RailLines
PowerLines
Population
HazardousCargo
System’sView
System’sView
Mo
del
A System’s Prospective View
Houston
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
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
A System’s Prospective View
Transportation
PublicHealth
Chem. &HazMat
CriticalInfrastructures
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
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
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
,
,,
,,,
,,
,,,,
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[
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
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