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Bilevel programming applied to optimising urban transportation

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Publication details

JournalTransportation Research Part B: Methodological
DatePublished - Jan 2001
Issue number1
Number of pages30
Pages (from-to)41-70
Original languageEnglish


This paper outlines a multi-modal, elastic, equilibrium transportation model in which signal green-times and prices charged to traverse a route (public transport fares, parking charges or road-use charges) are explicitly included. An algorithm is specified which, for a fairly general objective function, continually moves current traffic flows, green-times and prices within the model toward locally optimal values while taking account of users' responses. The directions of movement of current traffic flows, green-times and prices are determined by solving linear approximations to the actual problem. The results of applying a simplified form of the algorithm to a small network model with five routes and two signal-controlled junctions are given.

It is proved that under realistic conditions the sequence of (traffic flows, green-times, prices) triples generated by the algorithm does indeed approach those triples which possess a reasonable local optimality property. However the optimal control problem discussed here is non-convex and just a Karush-Kuhn-Tucker point is the "answer" sought. (C) 2000 Elsevier Science Ltd. All rights reserved.

    Research areas

  • decision support system, bilevel programming, transportation networks, signal control, road pricing, TRAFFIC ASSIGNMENT, EQUILIBRIA, STABILITY, NETWORKS, SYSTEMS

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