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A continuous-time linear complementarity system for dynamic user equilibria in single bottleneck traffic flows

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Abstract

This paper formally introduces a linear complementarity system (LCS) formulation for a continuous-time, multi-user class, dynamic user equilibrium (DUE) model for the determination of trip timing decisions in a simplified single bottleneck model. Existence of a Lipschitz solution trajectory to the model is established by a constructive time-stepping method whose convergence is rigorously analyzed. The solvability of the time-discretized subproblems by Lemke’s algorithm is also proved. Combining linear complementarity with ordinary differential equations and being a new entry to the mathematical programming field, the LCS provides a computational tractable framework for the rigorous treatment of the DUE problem in continuous time; this paper makes a positive contribution in this promising research venue pertaining to the application of differential variational theory to dynamic traffic problems.

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Authors and Affiliations

  1. Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Jong-Shi Pang

  2. School of Civil Engineering, Purdue University, West Lafayette, IN, 47906, USA

    Lanshan Han & Satish Ukkusuri

  3. Department of Civil Engineering, Indian Institute of Technology, Madras, India

    Gitakrishnan Ramadurai

Authors
  1. Jong-Shi Pang
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  2. Lanshan Han
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  3. Gitakrishnan Ramadurai
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  4. Satish Ukkusuri
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Corresponding author

Correspondence to Jong-Shi Pang.

Additional information

The work of this Jong-Shi Pang is based on research supported by the National Science Foundation under grants DMS-0754374, CMMI-0969600, and EFRI-1024984.

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Pang, JS., Han, L., Ramadurai, G. et al. A continuous-time linear complementarity system for dynamic user equilibria in single bottleneck traffic flows. Math. Program. 133, 437–460 (2012). https://doi.org/10.1007/s10107-010-0433-z

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  • DOI: https://doi.org/10.1007/s10107-010-0433-z

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