Internship Report Erin Kersh July 27, 2009 Nextrans Center A Strategic Planning Framework to Enhance Infrastructure Network Survivability and Functionality under Disasters Srinivas Peeta and Lili Du
Outline Background Related Literature Problem Description Related Methodologies Bi-level Stochastic Problem Knapsack Problem Maximum Flow Shortest Path Model Network Data Analysis
Background Man made and natural disasters both represent randomness Disasters disrupt the connectivity and functionality of transportation networks Pre-Disaster Planning Post-Disaster Management Previous work shows that upgrading the network would negate this effect Subject to budget limitations Need to optimize which links to upgrade Network Survivability Network Connectivity
Related Literature Page and Perry (1994) Soni, Gupta and Pirkul (1999) Werner, Taylor, Moore, Mander, Jernigan, and Hwang Liu and Fan (2006) Murray-Tuite and Mahmassani (2004) Matisziw and Murray (2007)
Problem Description First Stage - Investment Decisions Link importance is measured in the first level in terms of: Network connectivity - W c Improvement of survivability rate - W p Expected traffic flow – W f Second Stage - Network Performance Expected travel time
Related Methodologies Bi-level stochastic problem Knapsack Problem Determine the best use of the budget to improve connectivity Maximum Flow Requires paths to take into account the maximum allowable capacity Shortest Path Used to determine functional routes in the surviving network after a disaster
Bi-Level Stochastic Network Model
Two-Stage Stochastic Model
Sioux Fall City Network 24 Nodes 38 Two-Way Links (76 Total Links) Liu and Fan (2006)
Input Data for The Algorithm Travel Time Upgrade Cost Probability of Disaster Probability of Link Failure Capacity Randomly assigned using service volumes of multilane highways in LOS C
My Work Test the sensitivity of O-D Pairs Number Configuration For the given network, determined 4 O-D pair scenarios: OD2 OD5 ODcenter ODspread
Chart Flow of O-D Pair Sensitivity Analysis
First Set of O-D Pairs Used for Sensitivity Analysis: Importance of the Number of O-D Pairs 2 O-D Pairs 5 O-D Pairs
Results for Sensitivity Analysis of the Number of O-D Pairs Used in the Algorithm Network With 5 O-D Pairs Using Y2 vs Y5 Expected Travel Time for the Shortest 835 830 825 Path Across ODs 820 815 810 805 800 Y_MSA_OD2 Y_MSA_OD5
Results for Sensitivity Analysis of the Number of O-D Pairs Used in the Algorithm Network With 5 O-D Pairs Using Y2 vs Y5 Average Expected OD Survivability 0.415 0.41 0.405 0.4 0.395 0.39 Y_MSA_OD2 Y_MSA_OD5
Results for Sensitivity Analysis of the Number of O-D Pairs Used in the Algorithm Network With 2 O-D Pairs Using Y2 vs Y5 385 Expected Travel Time for the Shortest Path Across ODs 380 375 370 365 360 355 Y_MSA_OD2 Y_MSA_OD5
Results for Sensitivity Analysis of the Number of O-D Pairs Used in the Algorithm Network With 2 O-D Pairs Using Y2 vs Y5 0.35 Average Expected OD Survivability 0.34 0.33 0.32 0.31 0.3 0.29 Y_MSA_OD2 Y_MSA_OD5
Second Set of O-D Pairs Used For Sensitivity Analysis: Importance of O-D Pair Configuration Centralized O-D Pairs Spread Out O-D Pairs
Results for the Sensitivity Analysis of the Configuration of O-D Pairs Used in the Algorithm Network With Centered O-D Pairs Using YCenter vs. YSpread 1050 Expected Travel Time for the Shortest 1000 Path Across ODs 950 900 850 800 Y_MSA_ODSpread Y_MSA_ODCenter
Results for the Sensitivity Analysis of the Configuration of O-D Pairs Used in the Algorithm Network With Centered O-D Pairs Using YCenter vs. YSpread 0.55 Average Expected OD Survivability 0.54 0.53 0.52 0.51 0.5 0.49 0.48 0.47 0.46 0.45 Y_MSA_ODSpread Y_MSA_ODCenter
Results for the Sensitivity Analysis of the Configuration of O-D Pairs Used in the Algorithm Network With Spread Out O-D Pairs Using YCenter vs. YSpread 1380 Expected Travel Time for the Shortest 1360 1340 Path Across ODs 1320 1300 1280 1260 1240 1220 Y_MSA_ODSpread Y_MSA_ODCenter
Results for the Sensitivity Analysis of the Configuration of O-D Pairs Used in the Algorithm Network With Spread Out O-D Pairs Using YCenter vs. YSpread 0.36 Average Expected OD Survivability 0.35 0.34 0.33 0.32 0.31 0.3 0.29 0.28 Y_MSA_ODSpread Y_MSA_ODCenter
Third Set of O-D Pairs Used For Sensitivity Analysis: Importance of O-D Pair Configuration Spread Out O-D Pairs Centralized O-D Pairs “In Between” O-D Pairs
Results for the Sensitivity Analysis of the Configuration of O-D Pairs Used in the Algorithm Centered O-D Pairs Network Using YCenter2 vs. YMiddle vs. YSpread2 800 Expected Travel Time for the Shortest Path Across ODs 750 700 650 600 550 Y_MSA_ODSpread2 Y_MSA_ODCenter2 Y_MSA_ODMiddle
Results for the Sensitivity Analysis of the Configuration of O-D Pairs Used in the Algorithm Centered O-D Pairs Network Using YCenter2 vs. YMiddle vs. YSpread2 0.64 0.62 Average Expected OD 0.6 Survivability 0.58 0.56 0.54 0.52 0.5 Y_MSA_ODSpread2 Y_MSA_ODCenter2 Y_MSA_ODMiddle
Results for the Sensitivity Analysis of the Configuration of O-D Pairs Used in the Algorithm Spread Out O-D Pairs Network Using YCenter2 vs. YMiddle vs. YSpread2 1180 Expected Travel Time for the Shortest Path Across ODs 1160 1140 1120 1100 1080 1060 Y_MSA_ODSpread2 Y_MSA_ODCenter2 Y_MSA_ODMiddle
Results for the Sensitivity Analysis of the Configuration of O-D Pairs Used in the Algorithm Spread Out O-D Pairs Network Using YCenter2 vs. YMiddle vs. YSpread2 0.35 Average Expected OD 0.34 0.33 Survivability 0.32 0.31 0.3 0.29 0.28 Y_MSA_ODSpread2 Y_MSA_ODCenter2 Y_MSA_ODMiddle
Results for the Sensitivity Analysis of the Configuration of O-D Pairs Used in the Algorithm Middle O-D Pairs Network Using YCenter2 vs. YMiddle vs. YSpread2 1080 Expected Travel Time for the Shortest Path Across ODs 1070 1060 1050 1040 1030 1020 1010 Y_MSA_ODSpread2 Y_MSA_ODCenter2 Y_MSA_ODMiddle
Results for the Sensitivity Analysis of the Configuration of O-D Pairs Used in the Algorithm Middle O-D Pairs Network Using YCenter2 vs. YMiddle vs. YSpread2 0.385 0.38 Average Expected OD 0.375 Survivability 0.37 0.365 0.36 0.355 0.35 Y_MSA_ODSpread2 Y_MSA_ODCenter2 Y_MSA_ODMiddle
Conclusion Fewer O-D Pairs can be used to determine network survivability Centered network out-performed other investment strategies
Questions or Comments?
Knapsack Problem Any IP that has only one constraint Branch-and-Bound Method Each variable (x i ) must equal 0 or 1: c i /a i = benefit item i earns for each unit of resource used by item i (larger value = better item) To Solve: Compute all c i /a i values, put best item in knapsack, put the second-best item in knapsack, continue until the best remaining item will fill the knapsack
Maximum Flow Problem in which the arcs have a capacity which limits the quantity of a product that can be shipped through that arc 0 ≤ flow through each arc ≤ capacity Flow into node i = flow out of node i (conservation-of-flow constraint) Ford-Fulkerson Method – is it optimal flow or can it be modified to have a larger flow?
Shortest Path Problem of finding the shortest path (path of min length) from node 1 to another node Dijkstra’s Algorithm – find shortest path from one node to all others Add what we used
Recommend
More recommend
