Eur. Phys. J. B 39, 397-408 (2004)
https://doi.org/10.1140/epjb/e2004-00205-y

Many-neighbour interaction and non-locality in traffic models

¹ Department of Engineering Mathematics, University of Bristol, University Walk, Bristol BS8 1TR, UK
² School of Science, UOIT, 2000 Simcoe St North, Oshawa, ON, L1H 7L7, Canada
³ TRL Ltd., Old Wokingham Road, Crowthorne, RG45 6AU, UK

Corresponding authors: ^a re.wilson@bristol.ac.uk - ^b peterberg@pims.math.ca

Received: 3 December 2003
Revised: 27 March 2004
Published online: 12 July 2004

Abstract

The optimal-velocity model, as proposed by Bando et al. [1], shows unrealistic values of the acceleration for various optimal-velocity functions [2,3]. We discuss different approaches of how to correct this problem. Multiple look-ahead (many-neighbour interaction) models are the most promising candidates in reducing accelerations and decelerations to realistic values. We focus on two such models and, in particular, their linear stability and how these affect the vehicle dynamics and wave solutions. As found earlier [4], multiple look-ahead models reproduce many real flow features, and our results further support the necessity of this ansatz. However, the problem of non-locality arises when they are transformed into the corresponding continuum model. We discuss three methods of how to interpret many-neighbour interaction in macroscopic models.