A continuous-time linear complementarity system for dynamic user equilibria in single bottleneck traffic flows |
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Authors: | Jong-Shi Pang Lanshan Han Gitakrishnan Ramadurai Satish Ukkusuri |
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Institution: | 1. Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA 2. School of Civil Engineering, Purdue University, West Lafayette, IN, 47906, USA 3. Department of Civil Engineering, Indian Institute of Technology, Madras, India
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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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