Existence of optima and equilibria for traffic flow on networks

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16 Scopus citations

Abstract

This paper is concerned with a conservation law model of traffic flow on a network of roads, where each driver chooses his flown departure time in order to minimize the sum of a departure cost and an arrival cost. The model includes various groups of drivers, with different origins and destinations and having different cost functions. Under a natural set of assumptions, two main results are proved: (i) the existence of a globally optimal solution, minimizing the sum of the costs to all drivers, and (ii) the existence of a Nash equilibrium solution, where no driver can lflower his flown cost by changing his departure time or the route taken to reach destination. In the case of Nash solutions, all departure rates are uniformly bounded and have compact support.

Original languageEnglish (US)
Pages (from-to)627-648
Number of pages22
JournalNetworks and Heterogeneous Media
Volume8
Issue number3
DOIs
StatePublished - Sep 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics

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