On the continuum approximation of the on-and-off signal control on dynamic traffic networks

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Title: On the continuum approximation of the on-and-off signal control on dynamic traffic networks
Authors: Han, K
Gayah, V
Piccoli, B
Friesz, TL
Yao, T
Item Type: Journal Article
Abstract: In the modeling of traffic networks, a signalized junction is typically treated using a binary variable to model the on-and-off nature of signal operation. While accurate, the use of binary variables can cause problems when studying large networks with many intersections. Instead, the signal control can be approximated through a continuum approach where the on-and-off control variable is replaced by a continuous priority parameter. Advantages of such approximation include elimination of the need for binary variables, lower time resolution requirements, and more flexibility and robustness in a decision environment. It also resolves the issue of discontinuous travel time functions arising from the context of dynamic traffic assignment. Despite these advantages in application, it is not clear from a theoretical point of view how accurate is such continuum approach; i.e., to what extent is this a valid approximation for the on-and-off case. The goal of this paper is to answer these basic research questions and provide further guidance for the application of such continuum signal model. In particular, by employing the Lighthill-Whitham-Richards model (Lighthill and Whitham, 1955; Richards, 1956) on a traffic network, we investigate the convergence of the on-and-off signal model to the continuum model in regimes of diminishing signal cycles. We also provide numerical analyses on the continuum approximation error when the signal cycles are not infinitesimal. As we explain, such convergence results and error estimates depend on the type of fundamental diagram assumed and whether or not vehicle spillback occurs to the signalized intersection in question. Finally, a traffic signal optimization problem is presented and solved which illustrates the unique advantages of applying the continuum signal model instead of the on-and-off model.
Issue Date: 19-Feb-2014
Date of Acceptance: 8-Jan-2014
Publisher: Elsevier
Start Page: 73
End Page: 97
Journal / Book Title: Transportation Research Part B - Methodological
Volume: 61
Copyright Statement: © 2016, Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Keywords: Logistics & Transportation
1507 Transportation And Freight Services
0102 Applied Mathematics
Publication Status: Published
Article Number: TRB_1193
Appears in Collections:Faculty of Engineering
Civil and Environmental Engineering

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