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Discrete-Time System Optimal Dynamic Traffic Assignment (SO-DTA) with Partial Control for Physical Queuing Networks

Author

Listed:
  • Samitha Samaranayake

    (School of Civil and Environmental Engineering, Cornell University, Ithaca, New York 14850)

  • Walid Krichene

    (Department of Electrical Engineering and Computer Sciences, University of California Berkeley, Berkeley, California 94702)

  • Jack Reilly

    (Department of Civil and Environmental Engineering, Institute of Transportation Studies, University of California Berkeley, Berkeley, California 94702)

  • Maria Laura Delle Monache

    (Inria Sophia Antipolis Méditerranée, Université Côte d’Azur, Inria, CNRS, LJAD, 06902 Sophia Antipolis Cedex, France; Université Grenoble Alpes, 38400 Saint-Martin-d’Hères, France)

  • Paola Goatin

    (Inria Sophia Antipolis Méditerranée, Université Côte d’Azur, Inria, CNRS, LJAD, 06902 Sophia Antipolis Cedex, France)

  • Alexandre Bayen

    (Department of Electrical Engineering and Computer Sciences, University of California Berkeley, Berkeley, California 94702; Department of Civil and Environmental Engineering, Institute of Transportation Studies, University of California Berkeley, Berkeley, California 94702)

Abstract

We consider the System Optimal Dynamic Traffic Assignment (SO-DTA) problem with Partial Control for general networks with physical queuing. Our goal is to optimally control any subset of the networks agents to minimize the total congestion of all agents in the network. We adopt a flow dynamics model that is a Godunov discretization of the Lighthill–Williams–Richards partial differential equation with a triangular flux function and a corresponding multicommodity junction solver. The partial control formulation generalizes the SO-DTA problem to consider cases where only a fraction of the total flow can be controlled, as may arise in the context of certain incentive schemes. This leads to a nonconvex multicommodity optimization problem. We define a multicommodity junction model that only requires full Lagrangian paths for the controllable agents, and aggregate turn ratios for the noncontrollable (selfish) agents. We show how the resulting finite horizon nonlinear optimal control problem can be efficiently solved using the discrete adjoint method, leading to gradient computations that are linear in the size of the state space and the controls.

Suggested Citation

  • Samitha Samaranayake & Walid Krichene & Jack Reilly & Maria Laura Delle Monache & Paola Goatin & Alexandre Bayen, 2018. "Discrete-Time System Optimal Dynamic Traffic Assignment (SO-DTA) with Partial Control for Physical Queuing Networks," Transportation Science, INFORMS, vol. 52(4), pages 982-1001, August.
    • Handle: RePEc:inm:ortrsc:v:52:y:2018:i:4:p:982-1001
    DOI: 10.1287/trsc.2017.0800
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    References listed on IDEAS

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    1. Adriano Festa & Paola Goatin & Fabio Vicini, 2023. "Navigation System-Based Routing Strategies in Traffic Flows on Networks," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 930-957, September.

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