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Multiscale analysis of a spatially heterogeneous microscopic traffic model

Multiscale analysis of a spatially heterogeneous microscopic traffic model
Multiscale analysis of a spatially heterogeneous microscopic traffic model
The microscopic Optimal Velocity (OV) model is posed on an inhomogeneous ring-road, consisting of two spatial regimes which differ by a scaled OV function. Parameters are chosen throughout for which all uniform flows are linearly stable. The large time behaviour of this discrete system is stationary and exhibits three types of macroscopic traffic pattern, each consisting of plateaus joined together by sharp interfaces. At a coarse level, these patterns are determined by simple flow and density balances, which in some cases have non-unique solutions. The theory of characteristics for the classical Lighthill–Whitham PDE model is then applied to explain which pattern the OV model selects. A global analysis of a second-order PDE model is then performed in an attempt to explain some qualitative details of interface structure. Finally, the full microscopic model is analysed at the linear level to explain features which cannot be described by the present macroscopic approaches
traffic modelling, multiscale analysis, optimal velocity model, bottlenecks, wave patterns, phase-plane analysis
0167-2789
1-12
Ward, Jonathan
a8107b98-069d-4263-bd70-d29d79f07edc
Wilson, R. Eddie
01d7f1f2-f8ee-4661-b713-dcefcddb89bd
Berg, Peter
50af338c-1cc2-4dee-8e4f-5ade4a5f6e3e
Ward, Jonathan
a8107b98-069d-4263-bd70-d29d79f07edc
Wilson, R. Eddie
01d7f1f2-f8ee-4661-b713-dcefcddb89bd
Berg, Peter
50af338c-1cc2-4dee-8e4f-5ade4a5f6e3e

Ward, Jonathan, Wilson, R. Eddie and Berg, Peter (2007) Multiscale analysis of a spatially heterogeneous microscopic traffic model. Physica D: Nonlinear Phenomena, 236 (1), 1-12. (doi:10.1016/j.physd.2007.07.008).

Record type: Article

Abstract

The microscopic Optimal Velocity (OV) model is posed on an inhomogeneous ring-road, consisting of two spatial regimes which differ by a scaled OV function. Parameters are chosen throughout for which all uniform flows are linearly stable. The large time behaviour of this discrete system is stationary and exhibits three types of macroscopic traffic pattern, each consisting of plateaus joined together by sharp interfaces. At a coarse level, these patterns are determined by simple flow and density balances, which in some cases have non-unique solutions. The theory of characteristics for the classical Lighthill–Whitham PDE model is then applied to explain which pattern the OV model selects. A global analysis of a second-order PDE model is then performed in an attempt to explain some qualitative details of interface structure. Finally, the full microscopic model is analysed at the linear level to explain features which cannot be described by the present macroscopic approaches

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More information

Published date: December 2007
Keywords: traffic modelling, multiscale analysis, optimal velocity model, bottlenecks, wave patterns, phase-plane analysis
Organisations: Civil Engineering & the Environment

Identifiers

Local EPrints ID: 184255
URI: https://eprints.soton.ac.uk/id/eprint/184255
ISSN: 0167-2789
PURE UUID: 9128a6b9-031f-4274-a40f-aed2fb2d6cc3

Catalogue record

Date deposited: 12 May 2011 09:58
Last modified: 16 Jul 2019 23:40

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