Internship Report Erin Kersh July 27, 2009 Nextrans Center A - - PowerPoint PPT Presentation
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
A Strategic Planning Framework to Enhance Infrastructure Network Survivability and Functionality under Disasters Srinivas Peeta and Lili Du
Background Related Literature Problem Description Related Methodologies Bi-level Stochastic Problem Knapsack Problem Maximum Flow Shortest Path Model Network Data Analysis
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
Page and Perry (1994) Soni, Gupta and Pirkul (1999) Werner, Taylor, Moore, Mander, Jernigan,
Liu and Fan (2006) Murray-Tuite and Mahmassani (2004) Matisziw and Murray (2007)
First Stage - Investment Decisions Link importance is measured in the first
Network connectivity - Wc Improvement of survivability rate - Wp Expected traffic flow – Wf
Second Stage - Network Performance
Expected travel time
Bi-level stochastic problem Knapsack Problem
Determine the best use of the budget to
Maximum Flow
Requires paths to take into account the
Shortest Path
Used to determine functional routes in the
Liu and Fan (2006)
Travel Time Upgrade Cost Probability of Disaster Probability of Link Failure Capacity
Randomly assigned using service volumes of
Test the sensitivity of O-D Pairs
Number Configuration
For the given network, determined 4 O-D
OD2 OD5 ODcenter ODspread
2 O-D Pairs 5 O-D Pairs
800 805 810 815 820 825 830 835 Expected Travel Time for the Shortest Path Across ODs Y_MSA_OD2 Y_MSA_OD5
0.39 0.395 0.4 0.405 0.41 0.415 Average Expected OD Survivability Y_MSA_OD2 Y_MSA_OD5
355 360 365 370 375 380 385 Expected Travel Time for the Shortest Path Across ODs Y_MSA_OD2 Y_MSA_OD5
0.29 0.3 0.31 0.32 0.33 0.34 0.35 Average Expected OD Survivability Y_MSA_OD2 Y_MSA_OD5
Centralized O-D Pairs Spread Out O-D Pairs
Network With Centered O-D Pairs Using YCenter vs. YSpread 800 850 900 950 1000 1050 Expected Travel Time for the Shortest Path Across ODs Y_MSA_ODSpread Y_MSA_ODCenter
Network With Centered O-D Pairs Using YCenter vs. YSpread 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 Average Expected OD Survivability Y_MSA_ODSpread Y_MSA_ODCenter
Network With Spread Out O-D Pairs Using YCenter vs. YSpread 1220 1240 1260 1280 1300 1320 1340 1360 1380 Expected Travel Time for the Shortest Path Across ODs Y_MSA_ODSpread Y_MSA_ODCenter
Network With Spread Out O-D Pairs Using YCenter vs. YSpread 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 Average Expected OD Survivability Y_MSA_ODSpread Y_MSA_ODCenter
Centralized O-D Pairs Spread Out O-D Pairs “In Between” O-D Pairs
550 600 650 700 750 800 Expected Travel Time for the Shortest Path Across ODs Y_MSA_ODSpread2 Y_MSA_ODCenter2 Y_MSA_ODMiddle
0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 Average Expected OD Survivability Y_MSA_ODSpread2 Y_MSA_ODCenter2 Y_MSA_ODMiddle
1060 1080 1100 1120 1140 1160 1180 Expected Travel Time for the Shortest Path Across ODs Y_MSA_ODSpread2 Y_MSA_ODCenter2 Y_MSA_ODMiddle
0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 Average Expected OD Survivability Y_MSA_ODSpread2 Y_MSA_ODCenter2 Y_MSA_ODMiddle
1010 1020 1030 1040 1050 1060 1070 1080 Expected Travel Time for the Shortest Path Across ODs Y_MSA_ODSpread2 Y_MSA_ODCenter2 Y_MSA_ODMiddle
0.35 0.355 0.36 0.365 0.37 0.375 0.38 0.385 Average Expected OD Survivability Y_MSA_ODSpread2 Y_MSA_ODCenter2 Y_MSA_ODMiddle
Fewer O-D Pairs can be used to
Centered network out-performed other
Any IP that has only one constraint Branch-and-Bound Method
Each variable (xi) must equal 0 or 1: ci/ai = benefit item i earns for each unit of resource
used by item i (larger value = better item)
To Solve: Compute all ci/ai values, put best item in
knapsack, put the second-best item in knapsack, continue until the best remaining item will fill the knapsack
Problem in which the arcs have a capacity
0 ≤ flow through each arc ≤ capacity Flow into node i = flow out of node i
Ford-Fulkerson Method – is it optimal flow