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Beyond normality: A cross moment-stochastic user equilibrium mode

Beyond normality: A cross moment-stochastic user equilibrium mode
Beyond normality: A cross moment-stochastic user equilibrium mode
The Stochastic User Equilibrium (SUE) model predicts traffic equilibrium flow assuming that users choose their perceived maximum utility paths (or perceived shortest paths) while accounting for the effects of congestion that arise due to users sharing links. Inspired by recent work on distributionally robust optimization, specifically a Cross Moment (CMM) choice model, we develop a new SUE model that uses the mean and covariance information on path utilities but does not assume the particular form of the distribution. Robustness to distributional assumptions is obtained in this model by minimizing the worst-case expected cost over all distributions with fixed two moments. We show that under mild conditions, the CMM-SUE (Cross Moment-Stochastic User Equilibrium) exists and is unique. By combining a simple projected gradient ascent method to evaluate path choice probabilities with a gradient descent method to find flows, we show that the CMM-SUE is efficiently computable. CMM-SUE provides both modeling flexibility and computational advantages over approaches such as the well-known MNP-SUE (Multinomial Probit-Stochastic User Equilibrium) model that require distributional (normality) assumptions to model correlation effects from overlapping paths. In particular, it avoids the use of simulation methods employed in computations for the distribution-based MNP-SUE model. Preliminary computational results indicate that CMM-SUE provides a practical distributionally robust alternative to MNP-SUE.
0191-2615
333-354
Ahipasaoglu, Selin D.
55e05cd4-636e-424e-a98d-2421b605f2fb
Meskarian, Rudabeh
932d1dac-784b-4f24-bdda-5ea34a16d8a2
Magnanti, Thomas L.
3ab852da-2f2f-4b88-95db-28dd58c0062b
Natarajan, Karthik
5045c362-74e5-417c-95b9-4556fc9f9c7e
Ahipasaoglu, Selin D.
55e05cd4-636e-424e-a98d-2421b605f2fb
Meskarian, Rudabeh
932d1dac-784b-4f24-bdda-5ea34a16d8a2
Magnanti, Thomas L.
3ab852da-2f2f-4b88-95db-28dd58c0062b
Natarajan, Karthik
5045c362-74e5-417c-95b9-4556fc9f9c7e

Ahipasaoglu, Selin D., Meskarian, Rudabeh, Magnanti, Thomas L. and Natarajan, Karthik (2015) Beyond normality: A cross moment-stochastic user equilibrium mode. Transportation Research Part B: Methodological, 81 (Part 2), 333-354. (doi:10.1016/j.trb.2015.01.005).

Record type: Article

Abstract

The Stochastic User Equilibrium (SUE) model predicts traffic equilibrium flow assuming that users choose their perceived maximum utility paths (or perceived shortest paths) while accounting for the effects of congestion that arise due to users sharing links. Inspired by recent work on distributionally robust optimization, specifically a Cross Moment (CMM) choice model, we develop a new SUE model that uses the mean and covariance information on path utilities but does not assume the particular form of the distribution. Robustness to distributional assumptions is obtained in this model by minimizing the worst-case expected cost over all distributions with fixed two moments. We show that under mild conditions, the CMM-SUE (Cross Moment-Stochastic User Equilibrium) exists and is unique. By combining a simple projected gradient ascent method to evaluate path choice probabilities with a gradient descent method to find flows, we show that the CMM-SUE is efficiently computable. CMM-SUE provides both modeling flexibility and computational advantages over approaches such as the well-known MNP-SUE (Multinomial Probit-Stochastic User Equilibrium) model that require distributional (normality) assumptions to model correlation effects from overlapping paths. In particular, it avoids the use of simulation methods employed in computations for the distribution-based MNP-SUE model. Preliminary computational results indicate that CMM-SUE provides a practical distributionally robust alternative to MNP-SUE.

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Accepted/In Press date: 17 January 2015
e-pub ahead of print date: 26 March 2015
Published date: November 2015

Identifiers

Local EPrints ID: 413266
URI: https://eprints.soton.ac.uk/id/eprint/413266
ISSN: 0191-2615
PURE UUID: 0d0880b7-5b93-4435-9844-96153a01bfac

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Date deposited: 18 Aug 2017 16:31
Last modified: 13 Mar 2019 19:32

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Contributors

Author: Selin D. Ahipasaoglu
Author: Thomas L. Magnanti
Author: Karthik Natarajan

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