Mathematical Programming

, Volume 133, Issue 1–2, pp 437–460 | Cite as

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

  • Jong-Shi PangEmail author
  • Lanshan Han
  • Gitakrishnan Ramadurai
  • Satish Ukkusuri
Full Length Paper Series A


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.

Mathematics Subject Classification (2000)

90C33 90C90 


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Copyright information

© Springer and Mathematical Optimization Society 2011

Authors and Affiliations

  • Jong-Shi Pang
    • 1
    Email author
  • Lanshan Han
    • 2
  • Gitakrishnan Ramadurai
    • 3
  • Satish Ukkusuri
    • 2
  1. 1.Department of Industrial and Enterprise Systems EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.School of Civil EngineeringPurdue UniversityWest LafayetteUSA
  3. 3.Department of Civil EngineeringIndian Institute of TechnologyMadrasIndia

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