2011/01/11 by Giacomo Como, Ketan Savla, Como, Giacomo +7
Engineering · Physics and Astronomy · Social Sciences · #Adaptation and Self-Organizing Systems (nlin.AO) #Computer Science and Game Theory (cs.GT) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Systems and Control (eess.SY) #Traffic control and management #Transportation Planning and Optimization #Urban Transport and Accessibility #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1101.2220
openalex publication_date 2011/01/11 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
Stability of Wardrop equilibria is analyzed for dynamical transportation\nnetworks in which the drivers' route choices are influenced by information at\nmultiple temporal and spatial scales. The considered model involves a continuum\nof indistinguishable drivers commuting between a common origin/destination pair\nin an acyclic transportation network. The drivers' route choices are affected\nby their, relatively infrequent, perturbed best responses to global information\nabout the current network congestion levels, as well as their instantaneous\nlocal observation of the immediate surroundings as they transit through the\nnetwork. A novel model is proposed for the drivers' route choice behavior,\nexhibiting local consistency with their preference toward globally less\ncongested paths as well as myopic decisions in favor of locally less congested\npaths. The simultaneous evolution of the traffic congestion on the network and\nof the aggregate path preference is modeled by a system of coupled ordinary\ndifferential equations. The main result shows that, if the frequency of updates\nof path preferences is sufficiently small as compared to the frequency of the\ntraffic flow dynamics, then the state of the transportation network ultimately\napproaches a neighborhood of the Wardrop equilibrium. The presented results may\nbe read as a further evidence in support of Wardrop's postulate of equilibrium,\nshowing robustness of it with respect to non-persistent perturbations. The\nproposed analysis combines techniques from singular perturbation theory,\nevolutionary game theory, and cooperative dynamical systems.\n