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

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  • Fiems, Dieter
  • Prabhu, Balakrishna
  • De Turck, Koen

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.

Suggested Citation

  • Fiems, Dieter & Prabhu, Balakrishna & De Turck, Koen, 2019. "Travel times, rational queueing and the macroscopic fundamental diagram of traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 412-421.
    • Handle: RePEc:eee:phsmap:v:524:y:2019:i:c:p:412-421
    DOI: 10.1016/j.physa.2019.04.127
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    Cited by:

    1. Shao, Feng & Shao, Hu & Wang, Dongle & Lam, William H.K. & Cao, Shuhan, 2023. "A generative model for vehicular travel time distribution prediction considering spatial and temporal correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
    2. Matthias Deceuninck & Stijn Vuyst & Dieter Claeys & Dieter Fiems, 2021. "Appointment games with unobservable and observable schedules," Annals of Operations Research, Springer, vol. 307(1), pages 93-110, December.

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