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

页码：17 / 30

页数：14

共 29 条

[1] Verification of a simplified car-following theory [J].

Ahn, S ;

Cassidy, MJ ;

Laval, J .

TRANSPORTATION RESEARCH PART B-METHODOLOGICAL, 2004, 38 (05) :431-440

[2]

Banks J.H., 1989, Transportation Research Record, P53

[3]

Cassidy M., 1997, TRANSPORT RES REC, P1

[4] Lax-Hopf Based Incorporation of Internal Boundary Conditions Into Hamilton-Jacobi Equation. Part II: Computational Methods [J].

Claudel, Christian G. ;

Bayen, Alexandre M. .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2010, 55 (05) :1158-1174

[5] On the variational theory of traffic flow: Well-posedness, duality and applications [J].

Daganzo, Carlos F. .

NETWORKS AND HETEROGENEOUS MEDIA, 2006, 1 (04) :601-619

[6] In traffic flow, cellular automata = kinematic waves [J].

Daganzo, CF .

TRANSPORTATION RESEARCH PART B-METHODOLOGICAL, 2006, 40 (05) :396-403

[7] A variational formulation of kinematic waves: Solution methods [J].

Daganzo, CF .

TRANSPORTATION RESEARCH PART B-METHODOLOGICAL, 2005, 39 (10) :934-950

[8] A variational formulation of kinematic waves: basic theory and complex boundary conditions [J].

Daganzo, CF .

TRANSPORTATION RESEARCH PART B-METHODOLOGICAL, 2005, 39 (02) :187-196

[9]

Evans LC, 2010, Partial Differential Equations

[10]

Hofleitner A., 2012, 51 IEEE C DEC CONTR

← 1 2 3 →