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Distributionally Robust Markovian Traffic Equilibrium

Selin Damla Ahipasaoglu(ahipasaoglu***at***sutd.edu.sg)
Ugur Arikan(ugur arikan***at***sutd.edu.sg)
Karthik Natarajan(karthik natarajan***at***sutd.edu.sg)

Abstract: Stochastic user equilibrium models are fundamental to the analysis of transportation systems. Such models are typically developed under the assumption of route based choice models for the users. A class of link based models under a Markovian assumption on the route choice behavior of the users has been proposed to deal with the drawbacks of route based choice models. However, the application of this model has been thus far mainly restricted to the multinomial logit model. Furthermore, the complete distribution of the random utilities in such a model is rarely known to a system planner. In this paper, we propose a distributionally robust Markovian traffic equilibrium model and a corresponding choice model under the assumption that the marginal distributions of the link utilities are known but the joint distribution is unknown. By using a distributionally robust approach, we develop a new convex optimization formulation and propose an efficient algorithm to compute equilibrium flows. In the special case of exponential marginals, our formulation reduces to the entropy formulation of the Markovian multinomial logit model. Importantly, our formulation is completely link based and relaxes the assumption of independence and identical distributions in the link utilities. Our numerical experiments indicate that this provides modeling flexibility and computational tractability for system planners interested in calculating traffic equilibrium.

Keywords: Markovian traffic equilibrium, distributionally robust, convex optimization

Category 1: Applications -- OR and Management Sciences (Transportation )

Category 2: Robust Optimization

Citation: Engineering Systems and Design, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372. May / 2017.

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Entry Submitted: 05/22/2017
Entry Accepted: 05/23/2017
Entry Last Modified: 05/22/2017

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