1. Critical Infrastructure Protection In the Transportation Network A Mathematical Model and Methodology for Determining and Analyzing The k-Critical Links of a Highway Network

2. 2 Objective The objective of this dissertation is to develop a methodology, using a SE approach, and apply the methodology to 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 for risk mitigation and resource allocation

3. 3 The Systems Engineering Process Problem Definition and Need Identification Feasibility Study Operational Requirements Maintenance Support Concept Technical Performance Measures Functional Analysis and Allocation

4. 4 The Systems Engineering Process Trade-Off Analyses System Specification

5. 5 Problem Definition and Need Analysis Defining the System – System of Systems

6. 6 Example of Model Problem Definition and Need Analysis

7. 7 Feasibility Study What tools are available to perform analysis? What methods have been developed in this area?

8. 8 Operational Requirements Requirements Operating Environment Operational Life Cycle Utilization Requirements Prime Definition Of Mission Performance Parameters Operational Deployment Effectiveness Factors

9. 9 Maintenance Concept Levels of Maintenance Repair Policies Organizational Responsibilities Maintenance Support Elements Effectiveness Requirements Environment

10. 10 Technical Performance Parameters Efficiency Of Model Accuracy Of Model Simulation

11. 11 Functional Analysis Components Transportation CI SoS INPUT Disconnects Hrs of Op. PROCESS Mathematical model Attributes Flow Distance Links Nodes Efficiency of model Relationships Movement of Goods Efficiently Finding K Links Perf. of Defined Links OUTPUT Performance Disconnects Hours of operation

12. 12 Functional Analysis System Requirements System Solution Validate & Verify Actual Model System Objective City Boundary Section of City Small NetworkEnumeration Simulation Processing Time Functional Analysis Simulation Processing Time

13. 13 Output Performance: Travel Time/Throughput I35WI35E I45 I35WI35E Hwy 75 I20 I30 I20 Input Single Disconnect; 1/0 Variables Temporal Time of Day: I =1, 2, 3 (peak, norm, other) Links: l =(i,j), [(i+1), (j+1)],…, (i+n, j+n) L1L2L3 L8L7L6 L5 L4 L9 Information Flow I=1 Network Trade-Off Analysis

14. 14 Trade-Off Analysis: Link (a,b) Time, Flow

15. 15 Trade-Off Analysis: Link (a,b)  Avg. T = 2.5 Min/Veh

16. 16 Trade-Off Analysis: All Links

17. 17 Trade-Off Analysis Geographical Interdependencies

18. 18 Example of Model: Performance for a General Metric OUTPUTS Sum of Performance, …, Trade-Off Analysis

19. 19 Example of Model Links Performance Worst Best OUTPUTS 0 is threshold k Links = {2,11}, …, {1,12} affecting the Transportation CI the most Trade-Off Analysis

20. 20 Validation and Verification SE Approach –Integrations Process –Verify and Validate Requirements Model –Small Network –Enumeration –Efficiency of Model System Specification

21. 21 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

22. 22 Research Significance Decision Making Methodology and Tool

23. 23 Conclusion Transportation CI is important –To individuals’ way of life –To companies’ way of doing business Proposed a Methodology using a Mathematical Model to Determine Impact of k Links Disconnects have on the Defined Links of a Network for risk mitigation and resource allocation

24. 24 Conclusion Research Significance –Society: A Methodology and Tool for Officials to use in the Decision Making Process –Engineering: Systems Engineering Approach for Solving Complex Systems Efficient and Accurate Network Modeling for Large and Complex Systems

25. 25 Critical Infrastructure (CI) System Transportation CI System of Systems (SoS) Major Cities City Boundary Network Terms and Definitions

26. 26 Movement of Goods Trucks Peak Traffic Normal Traffic Other Traffic Days of Operation Terms and Definitions

27. 27 Node Arc  Link Disconnect Shortest Path Steady State Snapshot of System Terms and Definitions Highway Defined Links Worst Link Best Link

28. 28 The Systems Engineering Process Need Analysis Stakeholders City State and Federal Business Society

29. 29 The Systems Engineering Process Requirements –Mission Definition –Performance and Physical Parameters –Use Requirements

30. 30 The Systems Engineering Process Ground Rules and Assumptions –Highway –Major Cities –Steady State –Disconnect –Shortest Path –Snapshot of System

31. 31 The Systems Engineering Process Metrics –Performance of Network Travel Time Throughput

32. 32 The Systems Engineering Process Model –Most naive process Disconnect Link (A i,j ) subject to Time (t n ) Simulate Network Performance Connect Link (A i,j ) Repeat until all links tested

33. 33 The Systems Engineering Process Model (Continued) –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

34. 34 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”

35. 35 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 –Yan et al, IEEE/ACM, 2000 –Orda et al, IEEE/AMC, 2003

36. 36 Questions What is cost of truck if delayed by 15 minutes Airplanes at $1,000 per minute – 2002 (Vacante) Show how it has practical implication Convert time to cost Tell city fathers what they need to fix and where do you beef up security and resources If you cannot go straight, then which way? Time to fix link? Minimize time to fix Suggestions to repair

37. 37 Questions Minimize risk Which rout to take Link – Reliability of the system given a terrorist attack How much more time is it going to take to get to destination Minimize the time, increase throughput Value of dissertation: –This will tell you how to get around accidents in time and efficient manner Create fluid –Create situation where they do not get stuck in other jams Probability of accident increases on new route

38. 38 Questions Focus on mitigation –How to mitigate time loss and improve throughput Alternate routes for final destination is least amount of time

39. 39 Outline Terms and Definitions Objective Brief Literature Review Research Significance The Systems Engineering (SE) Process

40. 40 Outline Network Ideas for Improving Algorithmic Model Efficiencies Validation and Verification Conclusion

41. 41 Non-Eventful Days Construction established and on-going Mon – Fri

42. 42 Example of Model Time Number of Vehicles traveling from Origin to Destination during Off-Peak Period

43. 43 Example of Model: Routing Assignment Time, Flow qt City Boundary

44. 44 Example of Model: Effects of Disconnect on Link (a,b) Time, Flow  Avg. T = 2.5 Min/Veh

45. 45 Research Significance Algorithm for finding efficiently the K Links with the greatest impact on the network Minutes Accuracy Accuracy Vs. Time

46. 46 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) (OD) Links Model / Algorithm Time Accuracy

47. 47 Restricting the Search Space –Find least reliable links –Find largest/lightest flow Approximation Methods –“Quickly” find “Good” solution Ideas for Improving Algorithmic Model Efficiencies

48. 48 Objective –Two Objective Steps 1. Systems Engineering Approach 2. K Links with Highest Affect on Network

49. 49 EMG a b f e cd Defined Links

50. 50 Agriculture Water Public Health Emergency Services Defense Industrial Base Telecom Energy

51. 51 Example of Model: Effects of Disconnect on Link (a,b) Time, Flow  Avg. T = 2.5 Min/Veh

52. 52 Trade-Off Analysis Geographical Interdependencies –Rail lines –Power plants –Reliability of link –Pipe lines –Population –Water –Bridge Rail Lines Power Plants Reliability Of Link Population Water Bridges Population