new findings from the application of accelerated ue traffic assignments
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New Findings from the Application of Accelerated UE Traffic Assignments. Howard Slavin Jonathan Brandon Andres Rabinowicz Paul Ricotta Srini Sundaram Caliper Corporation May 2011. Accelerated UE Assignment Methods. Multi-threaded Frank-Wolfe (FW) - PowerPoint PPT PresentationTRANSCRIPT
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New Findings from the Application of Accelerated UE Traffic AssignmentsHoward SlavinJonathan BrandonAndres RabinowiczPaul RicottaSrini Sundaram
Caliper CorporationMay 2011
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Accelerated UE Assignment Methods • Multi-threaded Frank-Wolfe (FW)
• Multi-threaded Bi-conjugate FW – BFW (Daneeva and Lindberg)
• Origin User Equilibrium (OUE), Dial’s Algorithm B on which OUE is based, Bar-Gera’s OBA and TAPAS, and other Origin and Path-based Methods
• To varying degrees, all provide faster and tighter convergence
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Previous Empirical Testing of Faster Algorithms & Convergence Impacts• Established the achievability of
unprecedented convergence levels
• Demonstrated speed enhancements through distributed processing and multi-threading
• Illustrated the practicality of OUE and warm start efficiency
• Indicated some of the benefits of tighter convergence
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New Empirical Tests
• Use of More Threads from newer hardware
• Further testing of BFW and OUE• Warm start tests emphasizing Feedback
Loop Cases• Investigation of very large test problems
using 64-bit implementations• Examination of Irrelevant, Small, and
Major Project Impacts• Select Link Analysis with OUE and Most
Likely Route Flow Estimates
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Test Cases- From Small to Large
• Victoria BC Regional Model-550 zones, 8500 links, 2 classes
• A regional model for greater Washington metro area DC that Caliper developed for MNCPPC-Prince George’s County with 2,500 zones, 6 purposes, 3 time periods, 5 assignment classes, 57,000+ links
• NYMTC Updated 2011 BPM-3586 zones, 4 time periods, 6 assignment classes, 88,000+ links
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FW Convergence with 1, 2, 4 & 8 CoresDC Regional Network
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Comparison of FW, BFW, & OUEDC Regional Net with 8 Cores
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0:00:00 0:30:00 1:00:00 1:30:00 2:00:00 2:30:00 3:00:00 3:30:00 4:00:00
Rela
tive
Gap
Time (hr)
FW
Bi-Conjugate
OUE
OUE - Warm Start with 10% Random Perturbation of OD Matrix
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Convergence Graphs for Victoria BC
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Bi-conjugate NYMTC runs-8 cores
Model StepsLoop
1Loop 2 Loop 3 Loop 4
AM Assignment 26.0 25.0 26.5 25.0
MD Assignment 29.0 25.0 27.0 24.0
PM Assignment 22.0 21.0 23.0 22.0
NT Assignment 8.0 9.0 9.0 9.0
Total Time (min)
85.0 80.0 85.5 80.0
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NYMTC Feedback Loop OUE Assignments with and without a Warm Start (Rg=)
Warm Start RunModel Steps Loop 1 Loop 2 Loop 3 Loop 4
AM Assignment 38 17.5 10.5 11
MD Assignment 33 17 10 10.5
PM Assignment 43 19.5 13.5 10
NT Assignment 12 9.5 9 9
Total Time (Min.) 126 63.5 43 40.5
Cold Start RunModel Steps Loop 1 Loop 2 Loop 3 Loop 4
AM Assignment 38 51.5 52 52.5
MD Assignment 33 43.5 42 43
PM Assignment 43 54 55 55.5
NT Assignment 12 14 14 14
Total Time (Min.) 126 163 163 165
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NYMTC OUE Warm Start Savings
Run Time SavingsModel Steps Loop 1 Loop 2 Loop 3 Loop 4AM Assignment 0 34 41.5 41.5MD Assignment 0 26.5 32 32.5PM Assignment 0 34.5 41.5 45.5NT Assignment 0 4.5 5 5Total Saving (min) 0 99.5 120 124.5
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Convergence Levels & Project Impacts• Three Examples Examined
• An Irrelevant network change-eliminating a remote minor link
• A capacity expansion in a central location in Victoria
• A Transit Improvement –DC Metro
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INSIGNIFICANT CHANGE
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INSIGNIFICANT CHANGE
Relative Gap of 0.01 Relative Gap of 0.001
Non-localized effects present through Relative Gap of 0.001 –
need to go lower!
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INSIGNIFICANT CHANGE
OUE at Relative Gap of Only localized effects remain
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PROJECT DIFFERENCES
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PROJECT DIFFERENCES
Frank-Wolfe at 0.001 Relative Gap
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PROJECT DIFFERENCES
TransCAD – OUE at 8.2 E-08 Relative Gap
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Hypothetical DC Rail Improvement
• Improvement to the Blue Line• Peak and Off-peak headway and run-time
improvements• 2600 Riders diverted to transit from driving• Examination of resulting highway impacts
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Flow Differences from FW at RG=.001
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Flow Differences (OUE) at RG=.000001
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Highway Travel Time Savings from Transit Improvement
Assignment Gap
VHT_Base VHT_Build VHT_Benefits
1e-6 2,461,243 2,460,597 646
1e-3 2,462,616 2,462,084 532
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Select Link Analysis
• Only the total link flows from a UE assignment are uniquely determined
• Select link analysis may be biased especially when derived from order dependent assignment methods
• Most likely route flows or “proportional” route flows can be computed for OUE to provide more dependable estimates
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Proportionality Example
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SELECT LINK ANALYSIS
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Select Link Analysis with OUE and Proportionality
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Conclusions
• Static UE assignments no longer need be a computing bottleneck
• Orders of magnitude greater convergence can be achieved quickly
• BFW dominates FW• OUE is superior for very small gaps• Warm starts make OUE very
attractive • Greater convergence can reduce
errors in models and estimated project impacts
• Most likely route flow estimates from OUE appear to make select link analysis more reliable
• There is little risk in taking advantage of these developments