The Hamilton-Jacobi partial differential equation and the three representations of traffic flow

被引：69
作者：
Laval, Jorge A. [1 ]
Leclercq, Ludovic [2 ]
机构：
[1] Georgia Inst Technol, Sch Civil & Environm Engn, Atlanta, GA 30332 USA
[2] Univ Lyon, ENTPE, IFSTTAR, Lab Ingn Circulat Transport LICIT, Lyon, France
来源：
TRANSPORTATION RESEARCH PART B-METHODOLOGICAL | 2013年 / 52卷
基金：
美国国家科学基金会;
关键词：
Hamilton-Jacobi partial differential equation; Stochastic traffic flow; Kinematic wave model; CAR-FOLLOWING THEORY; KINEMATIC WAVES; VARIATIONAL FORMULATION; BOUNDARY-CONDITIONS; HIGHWAY; MODEL;
D O I：
10.1016/j.trb.2013.02.008
中图分类号：
F [经济];
学科分类号：
02 ;
摘要：
This paper applies the theory of Hamilton-Jacobi partial differential equations to the case of first-order traffic flow models. The traffic flow surface is analyzed with respect to the three 2-dimensional coordinate systems arising in the space of vehicle number, time and distance. In each case, the solution to the initial and boundary value problems are presented. Explicit solution methods and examples are shown for the triangular flow-density diagram case. This unveils new models and shows how a number of existing models are cast as special cases. (C) 2013 Elsevier Ltd. All rights reserved.
引用
收藏
页码：17 / 30
页数：14
相关论文
共 29 条
[11]  
Hopf E., 1970, INDIANA U MATH J, V19, P483
[12]  
Laval J.A., 2013, TRANSPORTAT IN PRESS
[13]   Lane-changing in traffic streams [J].
Laval, JA ;
Daganzo, CF .
TRANSPORTATION RESEARCH PART B-METHODOLOGICAL, 2006, 40 (03) :251-264
[14]   Stochastic Extension of Newell's Three-Detector Method [J].
Laval, Jorge A. ;
He, Zhengbing ;
Castrillon, Felipe .
TRANSPORTATION RESEARCH RECORD, 2012, (2315) :73-80
[15]   HYPERBOLIC SYSTEMS OF CONSERVATION LAWS .2. [J].
LAX, PD .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1957, 10 (04) :537-566
[16]  
Leclercq L, 2004, TRANSPORT RES REC, P3
[17]  
Leclercq L., 2007, 17 INT S TRANSP TRAF
[18]  
Leclercq L., 2012, P 91 TRANSP RES BOAR, p10p
[19]  
LEVEQUE RL, 1993, NUMERICAL METHODS CO
[20]   ON KINEMATIC WAVES .1. FLOOD MOVEMENT IN LONG RIVERS [J].
LIGHTHILL, MJ ;
WHITHAM, GB .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1955, 229 (1178) :281-316
123