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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. Terms and Definitions. Critical Infrastructure (CI) System Transportation CI

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Terms and Definitions

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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

### Terms and Definitions

• Critical Infrastructure (CI)

• System

• Transportation CI

• System of Systems (SoS)

• Major Cities

• City Boundary

• Network

### Terms and Definitions

• Movement of Goods

• Trucks

• Peak Traffic

• Normal Traffic

• Other Traffic

• Days of Operation

• Node

• Disconnect

• Highway

### 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

### Objective

• Two Objective Steps

1. Systems Engineering Approach

2. K Links with Highest Affect on Network

### 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

i, j

### Research Significance

• Decision Making Methodology and Tool

### Research Significance

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

Accuracy Vs. Time

Accuracy

Minutes

### 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

### The Systems Engineering Process

• Need Analysis

• Stakeholders

• City

• State and Federal

• Society (Indirectly)

### The Systems Engineering Process

• Requirements

• Mission Definition

• Performance and Physical Parameters

• Use Requirements

### The Systems Engineering Process

• Transportation CI SoS

• INPUT

• Disconnects

• Hrs of Op.

• PROCESS

• Mathematical

• model

• OUTPUT

• Performance

Components

Perf. of

Defined

Efficiently

Finding

Movement

of Goods

Relationships

• Flow

• Distance

• Nodes

• Efficiency

• of model

• Disconnects

• Hours of

• operation

Attributes

### The Systems Engineering Process

• Ground Rules and Assumptions

• Highway

• Major Cities

• Non-Event Days

• Construction established and on-going

• Mon – Fri

• Disconnect

### 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)

Model /

Algorithm

(OD)

Time

Accuracy

### The Systems Engineering Process

System

Solution

System

Requirements

Functional Analysis

V

System Objective

Validate &

Verify

Enumeration

Processing Time

City Boundary

Enumeration

Processing Time

Section of City

Small Network

Enumeration

Actual

Model

### Model

• Most naive process

• Disconnect Link (Li,j) subject to Time (tn)

• Simulate Network Performance

• 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

### Example of Model

Time

Number of Vehicles traveling from Origin to Destination

during Off-Peak Period

Time, Flow

q

t

Time, Flow

D Avg. T = 2.5

Min/Veh

q

### Example of Model: Performance for a General Metric

OUTPUTS

, …,

Sum of Performance

### Example of Model

OUTPUTS

Worst

K Links = {2,11}, …, {1,12}

affecting the Transportation

CI the most

Performance

Best

0 is threshold

Information Flow

### Network

L1

L2

L3

• Output

• Performance:

• Travel Time/Throughput

Input

Single Disconnect; 1/0

I35W

I35E

Hwy 75

I30

L4

I=1

I20

I20

L9

L5

I=1

I35W

I35E

I45

• Variables

• Temporal

• Time of Day: I =1, 2, 3 (peak, norm, other)

• Links: l =(i,j), [(i+1), (j+1)],…, (i+n, j+n)

L8

L7

L6

### Ideas for Improving Algorithmic Model Efficiencies

• Restricting the Search Space

• Find largest/lightest flow

• Approximation Methods

• “Quickly” find “Good” solution

### Validation and Verification

• SE Approach

• Integrations Process

• V-Chart

• Model

• Small Network

• Enumeration

• Efficiency of Model

V

### 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