Delft University of Technology
Improving convergence of quasi dynamic assignment models - poster
Brederode, Luuk; Pel, Adam; Wismans, L.J.J.; de Romph, Erik
Publication date 2016
Citation (APA)
Brederode, L., Pel, A., Wismans, L. J. J., & de Romph, E. (2016). Improving convergence of quasi dynamic assignment models - poster. Poster session presented at 6th International Symposium on Dynamic Traffic Assignment, Sydney, Australia.
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Improving convergence of
quasi dynamic assignment models
Results
For application in a strategic context, assignment models need to converge to a stable state. Besides poor convergence, dynamic models lack the tractability, scalability and low input and computational requirements that are needed in this context. Therefore, in this research we use the quasi dynamic assignment model STAQ, that combines tractability, scalability and low input and computational requirements of static with the realism of dynamic models and try to improve its rate of convergence.
Capacity and storage constraints may cause route cost functions to become: 1. over-sensitive causing an ‘instable phase’ during the first iterations;
2. strongly inseparable when sharing (spillback from) a bottleneck.
Both properties are also existent in pure DTA models and lead to poor convergence.
Ad 1: SRA outperforms MSA, but only when higher precision user equilibrium is needed. For lower precision the ‘instable phase’ needs to be shortened, which can be done by normalizing the scale factor of the route choice model to the largest routecost. Ad 2: SRA-ODspecific outperforms SRA, but only when inseparability of routes is taken into account: OD pairs should be clustered based on level of inseparability.
High precision (DG<1E-05) is not needed for strategic application (finding is in line with literature on static traffic assignment models, i.e.: Boyce, Ralevic and Bar Gera 2004).
Network Loading Model: STAQ
Static STAQ 1st order DTA
Link model: Travel time function Fundamental diagram
Node model: None Explicit node model
Demand: Stationary Time varying
Time periods: Single Multiple
Route Choice Model: Multinomial Logit
Convergence Metric: Stochastic Duality Gap
Straightforward extension of deterministic
duality gap, but will go to 0 when using MNL route choice model
MSA: method of successive averages (1/i)
SRA: Self regulating average (Liu et al 2009)
Spillback network: D1 D2 O Dependent network: D1 D2 O Independent network: D1 D2 O Test networks:
Tested averaging schemes:
Convergence:
SRA od specific
SRA normalize mu based on maxcost:
Proposed enhancements:
Luuk Brederode
* 1, 2
, Adam Pel
1
, Luc Wismans
2,3
, Erik de Romph
1
1Delft University of Technology, Department of Transport & Planning - 2DAT.mobility - 3University of Twente, Centre for Transport Studies Corresponding author: lbrederode@dat.nl
Research objective
Methods used
Conclusions
Den Bosch / Oss region (PM peak)
Gaps MSA vs SRA (test networks)
Gaps enhanced methods (test networks)
Gaps all methods (real network)
Realistic Network: 148 zones, 7005 nodes, 15200 links, 25000 routes Diverging iterations: decrease stepsize Converging iterations:
maintain stepsize MSA
SRA
Stepsizes: MSA vs SRA
1E-02 1E-04 1E-15
Legend
Bandwith: flow
Color: relative speed (% of free flow speed) 100%
0% 65% (critical)
Presented at the 6th international symposium on
