Distributed optimal equilibrium selection for traffic flow over networks
(2016) 54th IEEE Conference on Decision and Control, CDC 2015 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.
(Less)
- author
- Ba, Qin ; Savla, Ketan and Como, Giacomo LU
- organization
- publishing date
- 2016-02-08
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Adaptation models, Bismuth, Computational modeling, Cost function, Heuristic algorithms, Load modeling, Loading
- host publication
- Proceedings of the IEEE Conference on Decision and Control
- volume
- 2016
- article number
- 7403313
- pages
- 6 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 54th IEEE Conference on Decision and Control, CDC 2015
- conference location
- Osaka, Japan
- conference dates
- 2015-12-15 - 2015-12-18
- 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
- 2022-05-09 23:58:14
@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}},
keywords = {{Adaptation models; Bismuth; Computational modeling; Cost function; Heuristic algorithms; Load modeling; Loading}},
language = {{eng}},
month = {{02}},
pages = {{6942--6947}},
publisher = {{IEEE - 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}},
doi = {{10.1109/CDC.2015.7403313}},
volume = {{2016}},
year = {{2016}},
}