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Exact Solutions for a Discrete System Arising in Traffic Flow

Whitham, G. B. (1990) Exact Solutions for a Discrete System Arising in Traffic Flow. Proceedings of the Royal Society of London. Series A, Mathematical, Physical and Engineering Sciences, 428 (1874). pp. 49-69. ISSN 0962-8444. https://resolver.caltech.edu/CaltechAUTHORS:20150126-100606399

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Abstract

This paper concerns wave propagation in a discrete nonlinear system of equations proposed and studied by G. F. Newell as a model for car-following in traffic flow. In particular, Newell found exact solutions for shock waves and related phenomena. Here, exact solutions representing periodic waves and solitary waves are obtained. The method relates travelling wave solutions to the Toda and Kac-van-Moerbeke discrete systems. In this and other ways, much of the interest is in the general phenomena possible in discrete systems, here including also a time lag, rather than in just the specific traffic flow setting.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://www.jstor.org/stable/51724JSTORArticle
http://dx.doi.org/10.1098/rspa.1990.0025DOIArticle
http://rspa.royalsocietypublishing.org/content/428/1874/49PublisherArticle
Additional Information:© 1990 The Royal Society.
Issue or Number:1874
Record Number:CaltechAUTHORS:20150126-100606399
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150126-100606399
Official Citation:Exact Solutions for a Discrete System Arising in Traffic Flow G. B. Whitham Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences Vol. 428, No. 1874 (Mar. 8, 1990) , pp. 49-69 Published by: The Royal Society Stable URL: http://www.jstor.org/stable/51724
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54070
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Jan 2015 19:03
Last Modified:03 Oct 2019 07:54

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