A Systems’ Approach to Formulating a Methodology and Mathematical Model for Determining the Most Critical Flow Links of a Network Gerard Ibarra PhD Candidate Committee Update: April 5, 2006

2 Dissertation Outline Introduction Literature Review Developing A New Methodology for Identifying Critical Links Utilizing Systems Engineering Illustration of Methodology for Finding the K-Critical Links Analysis of Findings Conclusion Today’s Objective Show what I have accomplished Significance of accomplishment Agreement on completion of dissertation: format and content

3 Accomplishment Overview Identified parameters of dissertation and methodological approach for studying large network systems Original contribution development of a generic model for capacitated networks for identifying critical links of a network Systems Engineering approach to flow patterns for large networks Versatility of methodology – applicability to various modes of transportation networks

4 Introduction Introducing a new methodology for identifying critical disconnects and their impact on the flow of a network

5 Literature Review Ford-Fulkerson Algorithm: Ford, L. R. Jr, and D. R. Fulkerson Gomory-Hu Algorithm: Gomory, R. E. and Hu, T. C. “Recent Developments in Maximum Flow Algorithms,” Goldberg A. V. “Understanding, and Analyzing Critical Infrastructure Interdependencies,”: Steven M. Rinaldi, James P. Peerenboom, and Terrence K. Kelly “Network control by normalized cut fuzzy clustering strategy for critical infrastructures,”: Michaela D Quirk, Adriana Climescu-Haulica, and Kevin J. Saeger Abdelghany, Khaled F. and Mahmassani, Hani S.

6 Systems Engineering Methodology

7 Systems Engineering Process Overview of the Problem

8 Systems Engineering Process Define the Problem Identify the Needs Critical Infrastructure Protection (CIP) is an important topic to every major city in the US For the transportation sector, it has significant social and economic consequences Identifying Deficiencies in Critical Infrastructures

9 Systems Engineering Process Initial Requirements To develop a methodology and mathematical model to help determine the most critical links of a network Feasibility Analysis No current simulation model capable of feasibly finding the most critical links of a highway network Models that look at CIP do not include the most critical links of highway networks – mostly generic

10 I llustration of Methodology capacity

11 I llustration of Methodology 15 Node / 28 Arc Network

12 I llustration of Methodology 15 Node / 28 Arc Network Hours Demand Processing Time

13 I llustration of Methodology

14 K-Critical Links The link in the most cuts is the most critical The link with the most flow under normal conditions is the most critical The link giving maximum sensitivity is the most critical I llustration of Methodology (Cont.)

15 Mathematical Model k-Critical Links for flow based on disconnects Network Cuts

16 K-Critical Links for Flow and Other Potential Applications Other elements potentially affecting the k- critical links beyond flow

17 Systems Engineering Approach Potential Application

18 Conclusion Applied the SE process for the design of a system solution for the most critical links of a network Developed a methodology for determining the most critical links Used a proven mathematical model for evaluating the flow on networks such as highways Provided a more effective and efficient flow model for large, highly connected networks

19 Agreement on Dissertation Committee guidance and input: Dr. Vacante: Looks good. I have a guideline to help me finish in two months. Dr. Olinick: Looks good. Make sure I finish the sensitivity analysis on links. Dr. Stracener: Looks good. Dr. Hinderer: Looks good. Dr. Szygenda: All looks good. Make sure I include in the conclusion future work on my dissertation topic.