Stability Analysis of Transportation Networks with Multiscale Driver Decisions
(2013) In SIAM Journal of Control and Optimization 51(1). p.230-252- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3669831
- author
- Como, Giacomo LU ; Savla, Ketan ; Acemoglu, Daron ; Dahleh, Munther A. and Frazzoli, Emilio
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- transportation networks, Wardrop equilibrium, traffic flows, evolutionary game dynamics, route choice behavior, multiscale decisions
- in
- SIAM Journal of Control and Optimization
- volume
- 51
- issue
- 1
- pages
- 230 - 252
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- wos:000315578000010
- scopus:84876140876
- ISSN
- 1095-7138
- DOI
- 10.1137/110820804
- language
- English
- LU publication?
- yes
- id
- 6300fb54-b968-4550-8529-35d57b5ef4d2 (old id 3669831)
- date added to LUP
- 2016-04-01 10:19:39
- date last changed
- 2024-05-19 12:58:12
@article{6300fb54-b968-4550-8529-35d57b5ef4d2,
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.}},
author = {{Como, Giacomo and Savla, Ketan and Acemoglu, Daron and Dahleh, Munther A. and Frazzoli, Emilio}},
issn = {{1095-7138}},
keywords = {{transportation networks; Wardrop equilibrium; traffic flows; evolutionary game dynamics; route choice behavior; multiscale decisions}},
language = {{eng}},
number = {{1}},
pages = {{230--252}},
publisher = {{Society for Industrial and Applied Mathematics}},
series = {{SIAM Journal of Control and Optimization}},
title = {{Stability Analysis of Transportation Networks with Multiscale Driver Decisions}},
url = {{http://dx.doi.org/10.1137/110820804}},
doi = {{10.1137/110820804}},
volume = {{51}},
year = {{2013}},
}