Ward, JA and Wilson, RE (2011) Criteria for convective versus absolute string instability in car-following models. Proceedings of the Royal Society of London: Mathematical, Physical and Engineering Sciences, 467 (2132). pp. 2185-2208. ISSN 1364-5021
Abstract
The linear stability properties of car-following models of highway traffic are analysed. A general family of models is introduced and the subsequent analysis developed in terms of its partial derivatives. Two measures of wave propagation, namely (i) the group velocity and (ii) the signal velocity, are introduced and computed. These measures are used to classify how instability propagates disturbances, measured relative to the frame of the road along which the vehicles drive. Detector data suggest that disturbances should propagate only in an upstream direction (convective upstream instability), and it is shown how to parametrize models to agree with data and avoid unrealistic downstream propagation (absolute and convective downstream instability).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2011,The Royal Society . This is an author produced version of a paper published in Proceedings of the Royal Society of London: Mathematical, Physical and Engineering Sciences. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | highway traffic; car-following models; instability; wave propagation |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Nov 2017 13:25 |
Last Modified: | 23 Jan 2018 13:14 |
Status: | Published |
Publisher: | The Royal Society |
Identification Number: | 10.1098/rspa.2010.0437 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:96411 |