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Applications of sensitivity analysis for probit stochastic network equilibrium

Clark, S.D. and Watling, D.P. (2006) Applications of sensitivity analysis for probit stochastic network equilibrium. European Journal of Operational Research, 175 (2). pp. 894-911. ISSN 0377-2217

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Abstract

Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported.

Item Type: Article
Copyright, Publisher and Additional Information: © 2006 Elsevier. This is an author produced version of a paper published in European Journal of Operational Research. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: Traffic, equilibrium network flows, robustness and sensitivity analysis, probit choice model.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Environment (Leeds) > Institute for Transport Studies (Leeds)
Depositing User: Adrian May
Date Deposited: 02 Aug 2007
Last Modified: 10 Jun 2014 06:11
Published Version: http://www.sciencedirect.com/science/journal/03772...
Status: Published
Publisher: Elsevier Science
Refereed: Yes
Identification Number: 10.1016/j.ejor.2005.06.012
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/2556

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