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Stochastic flow models with delays, blocking and applications to multi-intersection traffic light control

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Abstract

We extend Stochastic Flow Models (SFMs), used for a large class of discrete event and hybrid systems, by including the delays which typically arise in flow movements, as well as blocking effects due to space constraints. We apply this framework to the multi-intersection traffic light control problem by including transit delays for vehicles moving from one intersection to the next and possible blocking between two intersections. Using Infinitesimal Perturbation Analysis (IPA) for this SFM with delays and possible blocking, we derive new on-line gradient estimates of several congestion cost metrics with respect to the controllable green and red cycle lengths. The IPA estimators are used to iteratively adjust light cycle lengths to improve performance and, in conjunction with a standard gradient-based algorithm, to obtain optimal values which adapt to changing traffic conditions. We introduce two new cost metrics to better capture congestions and show that the inclusion of delays and possible blocking in our analysis lead to improved performance relative to models that ignore delays and/or blocking effects.

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Acknowledgments

This work was supported in part by NSF under grants ECCS-1509084, DMS-1664644, and CNS-1645681, by AFOSR under grant FA9550-19-1-0158, by ARPA-E’s NEXTCAR program under grant DE-AR0000796, and by the MathWorks.

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  1. Division of Systems Engineering, Boston University, Brookline, MA, USA

    Rui Chen & Christos G. Cassandras

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  1. Rui Chen
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  2. Christos G. Cassandras
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Correspondence to Rui Chen.

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This article belongs to the Topical Collection: Applications-2020

Guest Editors: Francesco Basile, Jan Komenda, and Christoforos Hadjicostis

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Chen, R., Cassandras, C.G. Stochastic flow models with delays, blocking and applications to multi-intersection traffic light control. Discrete Event Dyn Syst 30, 125–153 (2020). https://doi.org/10.1007/s10626-019-00298-6

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  • DOI: https://doi.org/10.1007/s10626-019-00298-6

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