Multiscale analysis of a spatially heterogeneous microscopic traffic model |
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Authors: | Jonathan Ward R Eddie Wilson |
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Institution: | a University of Bristol, Department of Engineering Mathematics, Bristol, BS8 1TR, United Kingdom b UOIT, Faculty of Science, Oshawa, ON, L1H 7K4, Canada |
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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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Keywords: | Traffic modelling Multiscale analysis Optimal velocity model Bottlenecks Wave patterns Phase-plane analysis |
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