The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation

The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation

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Article ID: iaor2004312
Country: United Kingdom
Volume: 36B
Issue: 10
Start Page Number: 897
End Page Number: 918
Publication Date: Dec 2002
Journal: Transportation Research. Part B: Methodological
Authors: , ,
Keywords: networks
Abstract:

In this paper, a dynamic user equilibrium traffic assignment model with simultaneous departure time/route choices and elastic demands is formulated as an arc-based nonlinear complementarity problem on congested traffic networks. The four objectives of this paper are (1) to develop an arc-based formulation which obviates the use of path-specific variables, (2) to establish existence of a dynamic user equilibrium solution to the model using Brouwer's fixed-point theorem, (3) to show that the vectors of total arc inflows and associated minimum unit travel costs are unique by imposing strict monotonicity conditions on the arc travel cost and demand functions along with a smoothness condition on the equilibria, and (4) to develop a heuristic algorithm that requires neither a path enumeration nor a storage of path-specific flow and cost information. Computational results are presented for a simple test network with 4 arcs, 3 nodes, and 2 origin–destination pairs over the time interval of 120 periods.

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