A Diffusion-Based Analysis of a Multiclass Road Traffic Network

Michel Mandjes, Jaap Storm

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows based on conservation laws that incorporate the macroscopic fundamental diagram (a functional relationship between vehicle density and flow). Our setup is capable of handling multiple types of vehicle densities, with general macroscopic fundamental diagrams, on a network with arbitrary topology. Interpreting our system as a spatial population process, we derive, under natural scaling, fluid, and diffusion limits. More specifically, the vehicle density process can be approximated with a suitable Gaussian process, which yield accurate normal approximations to the joint (in the spatial and temporal sense) vehicle density process. The corresponding means and variances can be computed efficiently. Along the same lines, we develop an approximation to the vehicles’ travel time distribution between any given origin and destination pair. Finally, we present a series of numerical experiments that demonstrate the accuracy of the approximations and illustrate the usefulness of the results.

Original languageEnglish
Pages (from-to)60-81
Number of pages22
JournalStochastic Systems
Volume11
Issue number1
Early online date17 Feb 2021
DOIs
Publication statusPublished - Mar 2021

Bibliographical note

Funding Information:
This research is partly funded by the Netherlands Organization for Scientific Research (NWO) Gravitation project Networks [Grant 024.002.003].

Publisher Copyright:
© 2021 The Author(s).

Funding

This research is partly funded by the Netherlands Organization for Scientific Research (NWO) Gravitation project Networks [Grant 024.002.003].

FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek024.002.003
Nederlandse Organisatie voor Wetenschappelijk Onderzoek

    Keywords

    • conservation laws
    • diffusion approximation
    • functional central limit theorem
    • functional law of large numbers
    • fundamental diagram
    • road traffic networks
    • traffic flow theory
    • travel time

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