Gerard Ibarra PhD Candidate Committee Update: April 5, 2006

1. 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 Today’s Objective • Show what I have accomplished • Significance of accomplishment • Agreement on completion of dissertation: format and content • 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

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. Methodology Systems Engineering

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. Illustration of Methodology capacity

11. Illustration of Methodology • 15 Node / 28 Arc Network

12. Processing Time Hours Demand Illustration of Methodology • 15 Node / 28 Arc Network

13. Illustration of Methodology

14. Illustration of Methodology (Cont.) • 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

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.