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Solving the dynamic network user equilibrium problem with state-dependent time shifts

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  • Friesz, Terry L.
  • Mookherjee, Reetabrata

Abstract

In this paper we consider the infinite dimensional variational inequality (VI) formulation of dynamic user equilibrium (DUE) put forward by Friesz et al. (1993) [A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41, 179-191] as well as the differential variational inequality (DVI) version reported in Friesz et al. (2001) [Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1, 319-347]. We show how the theory of optimal control and the theory of infinite dimensional variational inequalities may be combined to create a simple and effective fixed point algorithm for calculating DUE network flows that are solutions of both formulations. A numerical example is provided.

Suggested Citation

  • Friesz, Terry L. & Mookherjee, Reetabrata, 2006. "Solving the dynamic network user equilibrium problem with state-dependent time shifts," Transportation Research Part B: Methodological, Elsevier, vol. 40(3), pages 207-229, March.
    • Handle: RePEc:eee:transb:v:40:y:2006:i:3:p:207-229
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    References listed on IDEAS

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    1. Daoli Zhu & Patrice Marcotte, 2000. "On the Existence of Solutions to the Dynamic User Equilibrium Problem," Transportation Science, INFORMS, vol. 34(4), pages 402-414, November.
    2. Terry L. Friesz & David Bernstein & Roger Stough, 1996. "Dynamic Systems, Variational Inequalities and Control Theoretic Models for Predicting Time-Varying Urban Network Flows," Transportation Science, INFORMS, vol. 30(1), pages 14-31, February.
    3. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, February.
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