Wave Selection Problems in the Presence of a Bottleneck

Jonathan Ward, R. Eddie Wilson and Peter Berg
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Jonathan Ward: University of Bristol, Department of Engineering Mathematics
R. Eddie Wilson: University of Bristol, Department of Engineering Mathematics
Peter Berg: UOIT, Faculty of Science

A chapter in Traffic and Granular Flow’05, 2007, pp 565-575 from Springer

Abstract: Summary The Optimal-Velocity (OV) model is posed on an inhomogeneous ring- road and the consequent spatial traffic patterns are described and analysed. Parameters are chosen throughout for which all uniform flows are linearly stable, and a simple model for a bottleneck is used in which the OV function is scaled down on a subsection of the road. The large-time behaviour of this system is stationary and it is shown that there are three types of macroscopic traffic pattern, each consisting of plateaus joined together by sharp fronts. These patterns solve simple flow and density balances, which in some cases have non-unique solutions. It is shown how the theory of characteristics for the classical Lighthill-Whitham PDE model may be used to explain qualitatively which solutions the OV model selects. However, fine details of the OV model solution structure may only be explained by higher order PDE modelling.

Date: 2007
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DOI: 10.1007/978-3-540-47641-2_55

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