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On stability of users equilibria in heterogeneous routing games

Cianfanelli, Leonardo and Como, Giacomo LU (2019) 58th IEEE Conference on Decision and Control, CDC 2019 In Proceedings of the IEEE Conference on Decision and Control 2019-December. p.355-360
Abstract

The asymptotic behaviour of deterministic logit dynamics in heterogeneous routing games is analyzed. It is proved that in directed multigraphs with parallel routes, and in series composition of such multigraphs, the dynamics admits a globally asymptotically stable fixed point. Moreover, the unique fixed point of the dynamics approaches the set of Wardrop equilibria, as the noise vanishes. The result relies on the fact that the dynamics of aggregate flows is monotone, and its Jacobian is strictly diagonally dominant by columns.

Please use this url to cite or link to this publication:
author
and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Heterogeneous routing games, Logit dynamics, Transportation networks, Wardrop equilibrium
host publication
2019 IEEE 58th Conference on Decision and Control, CDC 2019
series title
Proceedings of the IEEE Conference on Decision and Control
volume
2019-December
article number
9030230
pages
6 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
58th IEEE Conference on Decision and Control, CDC 2019
conference location
Nice, France
conference dates
2019-12-11 - 2019-12-13
external identifiers
  • scopus:85082501439
ISSN
0743-1546
ISBN
9781728113982
DOI
10.1109/CDC40024.2019.9030230
project
Modeling and Control of Large Scale Transportation Networks
language
English
LU publication?
no
id
8c733815-66ed-40f0-a9a8-d974de6281ba
date added to LUP
2021-02-08 22:49:45
date last changed
2022-04-19 04:40:37
@inproceedings{8c733815-66ed-40f0-a9a8-d974de6281ba,
  abstract     = {{<p>The asymptotic behaviour of deterministic logit dynamics in heterogeneous routing games is analyzed. It is proved that in directed multigraphs with parallel routes, and in series composition of such multigraphs, the dynamics admits a globally asymptotically stable fixed point. Moreover, the unique fixed point of the dynamics approaches the set of Wardrop equilibria, as the noise vanishes. The result relies on the fact that the dynamics of aggregate flows is monotone, and its Jacobian is strictly diagonally dominant by columns.</p>}},
  author       = {{Cianfanelli, Leonardo and Como, Giacomo}},
  booktitle    = {{2019 IEEE 58th Conference on Decision and Control, CDC 2019}},
  isbn         = {{9781728113982}},
  issn         = {{0743-1546}},
  keywords     = {{Heterogeneous routing games; Logit dynamics; Transportation networks; Wardrop equilibrium}},
  language     = {{eng}},
  pages        = {{355--360}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{Proceedings of the IEEE Conference on Decision and Control}},
  title        = {{On stability of users equilibria in heterogeneous routing games}},
  url          = {{http://dx.doi.org/10.1109/CDC40024.2019.9030230}},
  doi          = {{10.1109/CDC40024.2019.9030230}},
  volume       = {{2019-December}},
  year         = {{2019}},
}