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Distributed optimal equilibrium selection for traffic flow over networks

Ba, Qin; Savla, Ketan and Como, Giacomo LU (2016) 54th IEEE Conference on Decision and Control, CDC 2015 In Proceedings of the IEEE Conference on Decision and Control 2016. p.6942-6947
Abstract

In this paper, we present two distributed algorithms to compute an equilibrium, that is optimal with respect to strictly convex and separable cost functions, for controlled traffic flow dynamics over networks under constant exogenous inflows. The dynamics is modeled in continuous time by the Cell Transmission Model and a non-FIFO Dynamic Network Loading Model, with traffic control. The two algorithms are adaptations of the alternating direct method of multipliers (ADMM) and the accelerated dual descent (ADD) method from network flow optimization literature. When the demand and supply inequality constraints in the uncontrolled dynamics are relaxed to be independent over links, the resulting feasible set is convex if the demand and supply... (More)

In this paper, we present two distributed algorithms to compute an equilibrium, that is optimal with respect to strictly convex and separable cost functions, for controlled traffic flow dynamics over networks under constant exogenous inflows. The dynamics is modeled in continuous time by the Cell Transmission Model and a non-FIFO Dynamic Network Loading Model, with traffic control. The two algorithms are adaptations of the alternating direct method of multipliers (ADMM) and the accelerated dual descent (ADD) method from network flow optimization literature. When the demand and supply inequality constraints in the uncontrolled dynamics are relaxed to be independent over links, the resulting feasible set is convex if the demand and supply functions are concave, thereby imparting convexity to the optimal equilibrium selection problem. Each point in the feasible set is an equilibrium for the original dynamics under appropriately designed control. For the ADMM method, explicit expressions for the primal update show that no auxiliary variables are necessary. Convergence analysis for the primal variables is also provided. The standard ADD method is extended to also incorporate non-negativity constraints on the density and flow variables, and demand and supply inequality constraints. Illustrative simulation results are also presented.

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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Adaptation models, Bismuth, Computational modeling, Cost function, Heuristic algorithms, Load modeling, Loading
in
Proceedings of the IEEE Conference on Decision and Control
volume
2016
pages
6 pages
publisher
Institute of Electrical and Electronics Engineers Inc.
conference name
54th IEEE Conference on Decision and Control, CDC 2015
external identifiers
  • scopus:84962013989
ISBN
9781479978861
DOI
10.1109/CDC.2015.7403313
language
English
LU publication?
yes
id
982bc965-12c9-4717-a0aa-6f234b4f0564
date added to LUP
2016-07-14 14:50:56
date last changed
2017-07-30 05:13:12
@inproceedings{982bc965-12c9-4717-a0aa-6f234b4f0564,
  abstract     = {<p>In this paper, we present two distributed algorithms to compute an equilibrium, that is optimal with respect to strictly convex and separable cost functions, for controlled traffic flow dynamics over networks under constant exogenous inflows. The dynamics is modeled in continuous time by the Cell Transmission Model and a non-FIFO Dynamic Network Loading Model, with traffic control. The two algorithms are adaptations of the alternating direct method of multipliers (ADMM) and the accelerated dual descent (ADD) method from network flow optimization literature. When the demand and supply inequality constraints in the uncontrolled dynamics are relaxed to be independent over links, the resulting feasible set is convex if the demand and supply functions are concave, thereby imparting convexity to the optimal equilibrium selection problem. Each point in the feasible set is an equilibrium for the original dynamics under appropriately designed control. For the ADMM method, explicit expressions for the primal update show that no auxiliary variables are necessary. Convergence analysis for the primal variables is also provided. The standard ADD method is extended to also incorporate non-negativity constraints on the density and flow variables, and demand and supply inequality constraints. Illustrative simulation results are also presented.</p>},
  author       = {Ba, Qin and Savla, Ketan and Como, Giacomo},
  booktitle    = {Proceedings of the IEEE Conference on Decision and Control},
  isbn         = {9781479978861},
  keyword      = {Adaptation models,Bismuth,Computational modeling,Cost function,Heuristic algorithms,Load modeling,Loading},
  language     = {eng},
  month        = {02},
  pages        = {6942--6947},
  publisher    = {Institute of Electrical and Electronics Engineers Inc.},
  title        = {Distributed optimal equilibrium selection for traffic flow over networks},
  url          = {http://dx.doi.org/10.1109/CDC.2015.7403313},
  volume       = {2016},
  year         = {2016},
}