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User equilibrium traffic network assignment with stochastic travel times and late arrival penalty

Watling, D.P. (2006) User equilibrium traffic network assignment with stochastic travel times and late arrival penalty. European Journal of Operational Research, 175 (3). pp. 1539-1556. ISSN 0377-2217

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Abstract

The classical Wardrop user equilibrium (UE) assignment model assumes traveller choices are based on fixed, known travel times, yet these times are known to be rather variable between trips, both within and between days; typically, then, only mean travel times are represented. Classical stochastic user equilibrium (SUE) methods allow the mean travel times to be differentially perceived across the population, yet in a conventional application neither the UE or SUE approach recognises the travel times to be inherently variable. That is to say, there is no recognition that drivers risk arriving late at their destinations, and that this risk may vary across different paths of the network and according to the arrival time flexibility of the traveller. Recent work on incorporating risky elements into the choice process is seen either to neglect the link to the arrival constraints of the traveller, or to apply only to restricted problems with parallel alternatives and inflexible travel time distributions. In the paper, an alternative approach is described based on the ‘schedule delay’ paradigm, penalising late arrival under fixed departure times. The approach allows flexible travel time densities, which can be fitted to actual surveillance data, to be incorporated. A generalised formulation of UE is proposed, termed a Late Arrival Penalised UE (LAPUE). Conditions for the existence and uniqueness of LAPUE solutions are considered, as well as methods for their computation. Two specific travel time models are then considered, one based on multivariate Normal arc travel times, and an extended model to represent arc incidents, based on mixture distributions of multivariate Normals. Several illustrative examples are used to examine the sensitivity of LAPUE solutions to various input parameters, and in particular its comparison with UE predictions. Finally, paths for further research are discussed, including the extension of the model to include elements such as distributed arrival time constraints and penalties.

Item Type: Article
Copyright, Publisher and Additional Information: © 2006 Elsevier B.V. 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; Transportation; Equilibrium; Assignment; Network; Uncertainty
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: 08 Feb 2013 17:04
Published Version: http://www.sciencedirect.com/science/journal/03772...
Status: Published
Publisher: Elsevier Science
Refereed: Yes
Identification Number: 10.1016/j.ejor.2005.02.039
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/2557

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