Discrete-Time System Optimal Dynamic Traffic Assignment (SO-DTA) with Partial Control for Physical Queuing Networks

Samitha Samaranayake (), Walid Krichene (), Jack Reilly (), Maria Laura Delle Monache (), Paola Goatin () and Alexandre Bayen ()
Additional contact information
Samitha Samaranayake: School of Civil and Environmental Engineering, Cornell University, Ithaca, New York 14850
Walid Krichene: Department of Electrical Engineering and Computer Sciences, University of California Berkeley, Berkeley, California 94702
Jack Reilly: Department of Civil and Environmental Engineering, Institute of Transportation Studies, University of California Berkeley, Berkeley, California 94702
Maria Laura Delle Monache: Inria Sophia Antipolis Méditerranée, Université Côte d’Azur, Inria, CNRS, LJAD, 06902 Sophia Antipolis Cedex, France; Université Grenoble Alpes, 38400 Saint-Martin-d’Hères, France
Paola Goatin: Inria Sophia Antipolis Méditerranée, Université Côte d’Azur, Inria, CNRS, LJAD, 06902 Sophia Antipolis Cedex, France
Alexandre Bayen: Department of Electrical Engineering and Computer Sciences, University of California Berkeley, Berkeley, California 94702; Department of Civil and Environmental Engineering, Institute of Transportation Studies, University of California Berkeley, Berkeley, California 94702

Transportation Science, 2018, vol. 52, issue 4, 982-1001

Abstract: We consider the System Optimal Dynamic Traffic Assignment (SO-DTA) problem with Partial Control for general networks with physical queuing. Our goal is to optimally control any subset of the networks agents to minimize the total congestion of all agents in the network. We adopt a flow dynamics model that is a Godunov discretization of the Lighthill–Williams–Richards partial differential equation with a triangular flux function and a corresponding multicommodity junction solver. The partial control formulation generalizes the SO-DTA problem to consider cases where only a fraction of the total flow can be controlled, as may arise in the context of certain incentive schemes. This leads to a nonconvex multicommodity optimization problem. We define a multicommodity junction model that only requires full Lagrangian paths for the controllable agents, and aggregate turn ratios for the noncontrollable (selfish) agents. We show how the resulting finite horizon nonlinear optimal control problem can be efficiently solved using the discrete adjoint method, leading to gradient computations that are linear in the size of the state space and the controls.

Keywords: transportation: assignment models; network models; vehicle routing; networks/graphs: flow algorithms; multicommodity (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://doi.org/10.1287/trsc.2017.0800 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:52:y:2018:i:4:p:982-1001

Access Statistics for this article

More articles in Transportation Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().