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Stability Analysis of Transportation Networks with Multiscale Driver Decisions

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Author

  • Giacomo Como
  • Ketan Savla
  • Daron Acemoglu
  • Munther A. Dahleh
  • Emilio Frazzoli

Summary, in English

Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of nonatomic indistinguishable drivers commuting between a common origin-destination pair in an acyclic transportation network. The drivers' route choices are affected by their relatively infrequent perturbed best responses to global information about the current network congestion levels, as well as their instantaneous local observation of the immediate surroundings as they transit through the network. A novel model is proposed for driver route choice behavior, exhibiting local consistency with their preference toward globally less congested paths as well as myopic decisions in favor of locally less congested paths. The simultaneous evolution of the traffic congestion on the network and of the aggregate path preference is modeled by a system of coupled ordinary differential equations. The main result shows that if the frequency of updates of path preferences is sufficiently small as compared to the frequency of the traffic flow dynamics, then the state of the transportation network ultimately approaches a neighborhood of the Wardrop equilibrium. The presented results may be read as further evidence in support of Wardrop's postulate of equilibrium, showing robustness of it with respect to nonpersistent perturbations. The proposed analysis combines techniques from singular perturbation theory, evolutionary game theory, and cooperative dynamical systems.

Publishing year

2013

Language

English

Pages

230-252

Publication/Series

SIAM Journal of Control and Optimization

Volume

51

Issue

1

Document type

Journal article

Publisher

Society for Industrial and Applied Mathematics

Topic

  • Control Engineering

Keywords

  • transportation networks
  • Wardrop equilibrium
  • traffic flows
  • evolutionary game dynamics
  • route choice behavior
  • multiscale decisions

Status

Published

Research group

  • LCCC

ISBN/ISSN/Other

  • ISSN: 1095-7138