2009 SATURN User Group - ITS Leeds

29 April 2020

SATURN OBA-MUC

Friday 11 th September 2009

Dirck Van Vliet

What is OBA?

Origin-Base Assignment

● An algorithm developed by Dr Hillel Bar-Gera ● A major breakthrough in both theory and practice for equilibrium traffic assignment

Mathematical Properties

● Wardrop equilibrium solution is guaranteed (for buffer networks) ● Restriction to solutions that are a-cyclic by origin ● Store link flows by origin ● Effective in eliminating residual flows

Advantages & Disadvantages: OBA v Frank-Wolfe

Advantages

● Exact solutions to Wardrop Equilibrium Assignment ● ● Accurate in assessing small schemes Eliminate “noise” that exists in Frank-Wolfe ● Natural algorithm for Warm Start ● Exact solutions for standard post-assignment analysis: – Trees/Forests/Selected Link Analysis ● No approximation to previous results – Required under FW with default DIDDLE option (ie SAVEIT=T)

Disadvantages:

● RAM Intensive as route flows are stored ● Slower than FW (especially FW Multi-Core) ● Sensitive to poor network coding

History of SATURN-OBA

… more protracted than we would have preferred Single User Class (SUC OBA)

● First available in SATURN 10.5 ● Low cost add-on module ● Few applications

Multiple User Class (MUC OBA)

● An extended version of Hillel Bar Gera’s SUC OBA ● Implemented by Dr Yanling Xiang, Atkins (2006-9) ● Previously released in Beta with v10.8.xx on request ● Now bundled with v10.9 for free Beta evaluation ● Intention to embed within core product

SATURN OBA MUC: Performance

●

Reported in 2009 European Transport Conference Paper

● Benchmarked for Five Real-life applications – Frank-Wolfe – OBA-MUC ● Some optimisation of SATURN network coding undertaken ● Comments: – Typically higher levels of convergence with OBA MUC – Slower than FW Leads to: – Development of Hybrid FW-OBA MUC algorithm – Initial FW assignment before switching to OBA MUC – Looks promising … but very experimental

Benchmarks: FW v OBA-MUC (Model 2)

1.0

0 0.1

10 20 30 40 50 60

453 zones, 9 User Classes

70 0.01

0.001

0.0001

CPU Time (minutes) FW OBA

Benchmarks: + Hybrid (Model 3)

1.0

0 0.1

5 10 15 20 25 30 Switch from FW to OBA for Hybrid

321 zones, 9 User Classes 453 zones, 9 User Classes

35 0.01

FW OBA Hybrid 0.001

0.0001

0.00001

CPU Time (minutes) Target %GAP <0.001 for four consecutive loops

Benchmarks: + Hybrid (Model 4)

10.0

1.0

0 0.1

0.01

0.001

0.0001

Switch from FW to OBA for Hybrid 50 100

510 zones, 5 User Classes

150 200 250

Under-investigation

CPU Time (minutes) Target %GAP <0.001 for four consecutive loops FW OBA Hybrid

SATURN OBA MUC: Next Steps

●

Further testing work:

– – –

Warm Start Embed within GBMF / DIADEM Optimisation (20+ years for FW!)

●

Secondary Analysis

– Further checks on procedures ●

Feedback from Users

●

Longer term for Hybrid FW-OBA Algorithm

– – – –

FW Multi-Core already added Clear potential More development required Optimisation strategies