Abstract
Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are N groups of drivers, The i-th group consists of κi drivers, sharing the same departure and arrival costs φi(t),ψi(t). For any given population sizes κ1,...,κn, we prove the existence of a Nash equilibrium solution, where no driver can lower his own total cost by choosing a different departure time. The possible non-uniqueness, and a characterization of this Nash equilibrium solution, are also discussed.
Original language | English (US) |
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Pages (from-to) | 969-986 |
Number of pages | 18 |
Journal | ESAIM - Control, Optimisation and Calculus of Variations |
Volume | 18 |
Issue number | 4 |
DOIs | |
State | Published - Oct 2012 |
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Control and Optimization
- Computational Mathematics