VARIATIONAL ANALYSIS OF NASH EQUILIBRIA FOR A MODEL OF TRAFFIC FLOW

被引：8

作者：

Bressan, Alberto ^{[1
]}

Liu, Chen Jie ^{[2
]}

Shen, Wen ^{[1
]}

Yu, Fang ^{[2
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

来源：

QUARTERLY OF APPLIED MATHEMATICS | 2012年 / 70卷 / 03期

关键词：

D O I：

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

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 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.

引用

页码：495 / 515

页数：21

共 10 条

[1] OPTIMA AND EQUILIBRIA FOR A MODEL OF TRAFFIC FLOW
Bressan, Alberto
Han, Ke
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2011, 43 (05) : 2384 - 2417
[2] Evans L.C., 2010, Grad. Stud. Math., V19, DOI DOI 10.1090/GSM/019
[3] Friesz T. L., 2010, TRANSPORTATION RES B
[4] Combinatorial and continuous models for the optimization of traffic flows on networks
Fügenschuh, A
Herty, M
Klar, A
Martin, A
[J]. SIAM JOURNAL ON OPTIMIZATION, 2006, 16 (04) : 1155 - 1176
[5] Garavello M., 2006, Traffic Flow on Networks
[6] Optimal control for traffic flow networks
Gugat, M
Herty, M
Klar, A
Leugering, G
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2005, 126 (03) : 589 - 616
[7] Instantaneous control for traffic flow
Herty, M.
Kirchner, C.
Klar, A.
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2007, 30 (02) : 153 - 169
[8] HYPERBOLIC SYSTEMS OF CONSERVATION LAWS .2.
LAX, PD
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1957, 10 (04) : 537 - 566
[9] ON KINEMATIC WAVES .2. A THEORY OF TRAFFIC FLOW ON LONG CROWDED ROADS
LIGHTHILL, MJ
WHITHAM, GB
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1955, 229 (1178): : 317 - 345
[10] Smoller J., 1994, Shock Waves and ReactionDiffusion Equations, DOI [10.1007/978-1-4612-0873-0, DOI 10.1007/978-1-4612-0873-0]

← 1 →