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

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

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

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

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

6 Node Arc  Link Disconnect Steady State Highway Defined Links Worst Link Best Link Terms and Definitions

7 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

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

9 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

10 Research Significance Decision Making Methodology and Tool i, j

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

12 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”

13 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 –Murray-Tuite, Dissertation, 2003

14 The Systems Engineering Process Defining the System – System of Systems

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

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

17 The Systems Engineering Process 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

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

19 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

20 The Systems Engineering Process System Requirements System Solution Validate & Verify Actual Model System Objective City Boundary Section of City Small NetworkEnumeration Processing Time Functional Analysis Enumeration Processing Time

21 Model Most naive process –Disconnect Link (L i,j ) subject to Time (t n ) –Simulate Network Performance –Connect Link (L i,j ) –Repeat until all links tested

22 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

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

24 Example of Model: Routing Assignment Time, Flow qt

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

26 Example of Model

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

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

29 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

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

31 Validation and Verification SE Approach –Integrations Process –V-Chart Model –Small Network –Enumeration –Efficiency of Model

32 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

33 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