Stability Analysis of Transportation Networks with Multiscale Driver Decisions
Name
110820804.pdf
Description
Published version
Size
302.14 KB
Format
Adobe PDF
Checksum (MD5)
9d45641c6204fcfdee511750b1a689e6
Author(s)
Como, Giacomo
Savla, Ketan
Acemoglu, Daron
Dahleh, Munther A
Frazzoli, Emilio
Date Issued
2013
Journal
SIAM Journal on Control and Optimization
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
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. © 2013 Society for Industrial and Applied Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Economics
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DOI of Published Version
https://doi.org/10.1137/110820804
