Watling, DP (2002) A second order stochastic network equilibrium model. I: theoretical foundation. Transportation Science, 36 (2). 149 - 166. ISSN 0041-1655
Abstract
Existing models of stochastic network equilibrium route choice in transport networks are able to represent exogenously specified variations in drivers' actual or perceived travel costs, but assume throughout that flows are deterministic. In this paper, a new notion of equilibrium is presented based on stochastic flow variables, in which the impact of variable flows on the variability in travel costs is endogenously handled. Firstly, a very general notion of equilibrium is deduced as a fixed point condition on the joint probability distribution of network flows. Then, an approximation to this condition is derived, which operates by equilibrating moments of order n and below of the joint flow probability distribution, and is termed a Generalized Stochastic User Equilibrium of order n, being denoted GSUE(n). The GSUE(1) model is seen to be a conventional Stochastic User Equilibrium. The paper goes on to focus on the second order model, GSUE(2). Conditions are presented to guarantee the existence of GSUE(2) solutions. Conditions are deduced to guarantee (a) uniqueness of solutions in networks with a single interzonal movement, and (b) proximity of solutions in networks with multiple interzonal movements. Finally, a simple example is presented.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2002, INFORMS. This is an author produced version of a paper published in Transportation Science. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | stochastic |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Environment (Leeds) > Institute for Transport Studies (Leeds) > ITS: Spatial Modelling and Dynamics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 08 Jun 2015 12:13 |
Last Modified: | 17 Jan 2018 19:45 |
Published Version: | http://dx.doi.org/10.1287/trsc.36.2.149.560 |
Status: | Published |
Publisher: | INFORMS |
Identification Number: | 10.1287/trsc.36.2.149.560 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:84666 |