Terms and Definitions

1. 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

2. Terms and Definitions • Critical Infrastructure (CI) • System • Transportation CI • System of Systems (SoS) • Major Cities • City Boundary • Network

3. Terms and Definitions • Movement of Goods • Trucks • Peak Traffic • Normal Traffic • Other Traffic • Days of Operation

4. Terms and Definitions • Node • Arc  Link • Disconnect • Steady State • Highway • Defined Links • Worst Link • Best Link

5. 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

6. Objective • Two Objective Steps 1. Systems Engineering Approach 2. K Links with Highest Affect on Network

7. 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

8. i, j Research Significance • Decision Making Methodology and Tool

9. Research Significance • Algorithm for finding efficiently the K Links with the greatest impact on the network Accuracy Vs. Time Accuracy Minutes

10. 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”

11. 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

12. The Systems Engineering Process • Defining the System – System of Systems

13. The Systems Engineering Process • Need Analysis • Stakeholders • City • State and Federal • Business • Society (Indirectly)

14. The Systems Engineering Process • Requirements • Mission Definition • Performance and Physical Parameters • Use Requirements

15. The Systems Engineering Process • Transportation CI SoS • INPUT • Disconnects • Hrs of Op. • PROCESS • Mathematical • model • OUTPUT • Performance Components Perf. of Defined Links Efficiently Finding K Links Movement of Goods Relationships • Flow • Distance • Links • Nodes • Efficiency • of model • Disconnects • Hours of • operation Attributes

16. The Systems Engineering Process • Ground Rules and Assumptions • Highway • Major Cities • Steady State • Non-Event Days • Construction established and on-going • Mon – Fri • Disconnect

17. 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 Links Accuracy

18. 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

19. Model • Most naive process • Disconnect Link (Li,j) subject to Time (tn) • Simulate Network Performance • Connect Link (Li,j) • Repeat until all links tested

20. 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 • Disconnected Links

21. Example of Model Time Number of Vehicles traveling from Origin to Destination during Off-Peak Period

22. Time, Flow Example of Model: Routing Assignment q t

23. Time, Flow Example of Model: Effects of Disconnect on Link (a,b) D Avg. T = 2.5 Min/Veh q

24. Example of Model

25. Example of Model: Performance for a General Metric OUTPUTS , …, Sum of Performance

26. Example of Model OUTPUTS Worst K Links = {2,11}, …, {1,12} affecting the Transportation CI the most Performance Best Links 0 is threshold

27. 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

28. Ideas for Improving Algorithmic Model Efficiencies • Restricting the Search Space • Find least reliable links • Find largest/lightest flow • Approximation Methods • “Quickly” find “Good” solution

29. Validation and Verification • SE Approach • Integrations Process • V-Chart • Model • Small Network • Enumeration • Efficiency of Model V

30. 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

31. 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