TY - JOUR

T1 - Variational analysis of nash equilibria for a model of traffic flow

AU - Bressan, Alberto

AU - Liu, Chen Jie

AU - Shen, Wen

AU - Yu, Fang

PY - 2012

Y1 - 2012

N2 - The paper is concerned with Nash equilibrium solutions for the Lighthill-Whitham model of traffic flow, where each driver chooses his own departure time in order to minimize the sum of a departure cost and an arrival cost. Estimates are provided on how much the Nash solution may change, depending on the cost functions and on the flux function of the conservation law. It is shown that this equilibrium solution can also be determined as a global minimizer for a functional Φ, measuring the maximum total cost among all drivers, in a given traffic pattern. The last section of the paper introduces two evolution models, describing how the traffic pattern can change, day after day. It is assumed that each driver adjusts his departure time based on previous experience, in order to lower his own cost. Numerical simulations are reported, indicating a possible instability of the Nash equilibrium.

AB - The paper is concerned with Nash equilibrium solutions for the Lighthill-Whitham model of traffic flow, where each driver chooses his own departure time in order to minimize the sum of a departure cost and an arrival cost. Estimates are provided on how much the Nash solution may change, depending on the cost functions and on the flux function of the conservation law. It is shown that this equilibrium solution can also be determined as a global minimizer for a functional Φ, measuring the maximum total cost among all drivers, in a given traffic pattern. The last section of the paper introduces two evolution models, describing how the traffic pattern can change, day after day. It is assumed that each driver adjusts his departure time based on previous experience, in order to lower his own cost. Numerical simulations are reported, indicating a possible instability of the Nash equilibrium.

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U2 - 10.1090/S0033-569X-2012-01304-9

DO - 10.1090/S0033-569X-2012-01304-9

M3 - Article

AN - SCOPUS:84871138933

SN - 0033-569X

VL - 70

SP - 495

EP - 515

JO - Quarterly of Applied Mathematics

JF - Quarterly of Applied Mathematics

IS - 3

ER -