Sumalee, A, Connors, R orcid.org/0000-0002-1696-0175 and Watling, D orcid.org/0000-0002-6193-9121 (2006) An Optimal Toll Design Problem with Improved Behavioural Equilibrium Model: The Case of the Probit Model. In: Lawphongpanich, S, Hearn, DW and Smith, MJ, (eds.) Mathematical and Computational Models for Congestion Charging. Applied Optimisation, 101 . Springer , pp. 219-240. ISBN 978-0-387-29644-9
Abstract
This paper considers the optimal toll design problem that uses the Probit model to determine travellers’ route-choices. Under probit, the route flow solution to the resulting stochastic user equilibrium (SUE) is unique and can be stated implicitly as a function of tolls. This reduces the toll design problem to an optimization problem with only nonnegativity constraints. Additionally, the gradient of the objective function can be approximated using the chain rule and the first order Taylor approximation of the equilibrium condition. To determine SUE, this paper considers two techniques. One uses Monte-Carlo simulation to estimate route choice probabilities and the method of successive averages with its prescribed step length. The other relies on the Clark approximation and computes an optimal step length. Although both are effective at solving the toll design problem, numerical experiments show that the technique with the Clark approximation is more robust on a small network.
Metadata
Item Type: | Book Section |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2006 Springer Science and Business Media, Inc. This is an author produced version of a book chapter published in Mathematical and Computational Models for Congestion Charging. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Network Design Problem; Probit SUE; Optimal toll; Sensitivity Analysis |
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: | 01 Aug 2022 15:42 |
Last Modified: | 02 Aug 2022 10:17 |
Published Version: | http://www.springer.com/mathematics/book/978-0-387... |
Status: | Published |
Publisher: | Springer |
Series Name: | Applied Optimisation |
Identification Number: | 10.1007/0-387-29645-X_10 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:189607 |