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Travel times, rational queueing and the macroscopic fundamental diagram of traffic flow

Abstract : We propose a Markovian queueing model for computing travel times at a macroscopic scale during rush hour. The service rates of the queueing model are state-dependent, reflecting the speed/density relation of the fundamental diagram of traffic flow. In the fluid limit, the dynamics of the transient queue size and travel time processes are governed by a set of differential equations. As an application of the model, we consider the rational time-dependent choice between public and private transport, assuming that there is a congestion-free public alternative to private transportation. Numerical examples reveal that a small reduction in peak traffic can significantly reduce the average travel times.
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Dieter Fiems, Balakrishna Prabhu, Koen de Turck. Travel times, rational queueing and the macroscopic fundamental diagram of traffic flow. Physica A: Statistical Mechanics and its Applications, Elsevier, 2019, 524, pp.412-421. ⟨10.1016/j.physa.2019.04.127⟩. ⟨hal-02393141⟩

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