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

2

3 Systems Engineering Process Define the Problem and Identify the Needs Critical Infrastructure Protection is an important topic to every major city in the US Homeland Security funding being more scrutinized For the transportation sector, need help with identifying the k-critical links of a highway network

4 Systems Engineering Process Define the Problem

5 Systems Engineering Process Initial Requirements To develop a process and mathematical model to help determine the k-critical links of a highway network Feasibility Analysis No current simulation model capable of feasibly finding the k-critical links of a highway network Models that look at CIP do not include geographical interdependencies – a systems view of the links

6 Systems Engineering Process Operational Requirements Mission Definition Performance and Physical Parameters Operational Deployment Operational Life Cycle Utilization Requirements Effectiveness Factor Environment

7 Systems Engineering Process Maintenance and Support Specific to the process and mathematical model Technical Performance Parameters Accuracy of k-critical links Model’s information processing time Maintainability and Supportability of system Functional Analysis Details of the Process and Model

8 Systems Engineering Process Design Synthesis Trade-off Analysis Selection of Preferred Candidate

9 Systems Engineering Process The bottom line:

10 A System’s View K'-critical Links Rail Lines Power Lines Population Hazardous Cargo System’s View Model Water

11 A System’s View Houston

12 A System’s View K-Critical Links The link with the most flow under normal conditions is the most critical The link in the most cuts is the most critical The link giving maximum sensitivity is the most critical

13 A System’s View Geographical Interdependencies (GI) Rail and Power Lines (Heuristic: Transportation and Energy) Proximity Parallel Transverse Population (Bureau of Statistics: Public Health) Proximity

14 A System’s View Geographical Interdependencies (GI) Hazardous Cargo (DOT: Chem. & HazMat) Routes Bodies of Water (Map: Water) Lakes Rivers Streams

15 A System’s View Transportation & Energy Public Health Water Chem. & HazMat Critical Infrastructures

16 Rail Lines Intersecting Highways – I610 and Inside 1 – 24 Intersections I610 and Inside, 25 – 35 outside I610 up to Beltway A

17 Mathematical Model Utility Theory: Additive Function Simulation: Monte Carlo Statistics: Weighted Averages and Variances Decision Maker’s Input Professional/Expert’s Input

18 Mathematical Model

19 Mathematical Model

20 Conclusion Applied the SE process for the design of a system solution for the most critical links of a highway network Developed a methodology for determining those most critical links Constructed a mathematical model for evaluating those links based on the network’s GI Provided maintainability and supportability design criteria in the methodology and model

21 What is Next? Abstract 1.0 Introduction 2.0 Literature Review 3.0 Application of the Systems Engineering Process 4.0 Finding the K-Critical Links 4.1 Validation of Methodology 4.2 Pros and Cons of the Models