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Macroscopic modelling and analysis of rush-hour congestion

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Abstract

We consider a Markovian queueing model for computing the traffic density and travel times in a city at a macroscopic scale during rush hour. Accounting for the speed/density relation of the macroscopic fundamental diagram of traffic flow, we assume that the service rates of the queueing model at hand are state-dependent. We focus on the fluid limit and obtain a set of differential equations that describe the evolution of the traffic density at the level of neighbourhoods. We also calculate the time dependent travel times and 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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Dates and versions

hal-03007545 , version 1 (16-11-2020)

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Dieter Fiems, Balakrishna Prabhu. Macroscopic modelling and analysis of rush-hour congestion. VALUETOOLS '20: 13th EAI International Conference on Performance Evaluation Methodologies and Tools, 2020, Tsukuba, Japan. pp.11-18, ⟨10.1145/3388831.3388849⟩. ⟨hal-03007545⟩
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