FOLLOW-THE-LEADER MODELS CAN BE VIEWED AS A NUMERICAL APPROXIMATION TO THE LIGHTHILL-WHITHAM-RICHARDS MODEL FOR TRAFFIC FLOW

被引：20
|
作者：
Holden, Helge [1 ]
Risebro, Nils Henrik [2 ]
机构：
[1] NTNU Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway
[2] Univ Oslo, Dept Math, POB 1053, NO-0316 Oslo, Norway
来源：
NETWORKS AND HETEROGENEOUS MEDIA | 2018年 / 13卷 / 03期
关键词：
Follow-the-Leader model; Lighthill-Whitham-Richards model; traffic flow; continuum limit; SCALAR CONSERVATION-LAWS; MICRO-MACRO LIMIT; WAVES;
D O I：
10.3934/nhm.2018018
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show how to view the standard Follow-the-Leader (FtL) model as a numerical method to compute numerically the solution of the Lighthill-Whitham-Richards (LWR) model for traffic flow. As a result we offer a simple proof that FtL models converge to the LWR model for traffic flow when traffic becomes dense. The proof is based on techniques used in the analysis of numerical schemes for conservation laws, and the equivalence of weak entropy solutions of conservation laws in the Lagrangian and Eulerian formulation.
引用
收藏
页码：409 / 421
页数：13
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