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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Anderson MP, Woessner WW, Hunt RJ (2015) Applied groundwater modeling: simulation of flow and advective transport. Academic Press, Cambridge
Armony M, Israelit S, Mandelbaum A, Marmor YN, Tseytlin Y, Yom-Tov GB, et al. (2015) On patient flow in hospitals: a data-based queueing-science perspective. Stoch Syst 5(1):146–194
Cassandras CG, Wardi Y, Melamed B, Sun G, Panayiotou CG (2002) Perturbation analysis for on-line control and optimization of stochastic fluid models. IEEE Trans Autom Control 47(8):1234–1248
Cassandras CG, Lafortune S (2009) Introduction to discrete event systems. Springer, Berlin
Cassandras CG, Wardi Y, Panayiotou CG, Yao C (2010) Perturbation analysis and optimization of stochastic hybrid systems. Eur J Control 6(6):642–664
Chen R, Cassandras CG (2018) Stochastic flow models with delays and applications to multi-intersection traffic light control. Proc 2018 Intl Worksh Discret Event Syst 51 (7):39–44
Fleck JL, Cassandras CG, Geng Y (2016) Adaptive quasi-dynamic traffic light control. IEEE Trans Control Syst Technol 24(3):830–842
Fu MC, Howell WC (2003) Application of perturbation analysis to traffic light signal timing. Proc IEEE, Conf on Decision and Control, pp 4837–4840
Geng Y, Cassandras CG (2012) Traffic light control using infinitesimal perturbation analysis. In: 2012 IEEE 51St annual conf. on decision and control (CDC). IEEE, pp 7001–7006
Geng Y, Cassandras CG (2015) Multi-intersection traffic light control with blocking. Discret Event Dyn Syst 25(1-2):7–30
Head L, Ciarallo F, Kaduwela DL (1996) A perturbation analysis approach to traffic signal optimization. INFORMS National Meeting
Panayiotou CG, Howell WC, Fu MC (2005) Online traffic light control through gradient estimation usinf stochastic flow models. Proc IFAC World Congress
Wardi Y, Adams R, Melamed B (2010) A unified approach to infinitesimal perturbation analysis in stochastic flow models: the single-stage case. IEEE Trans Autom Control 55(1):89–103
Yao C, Cassandras CG (2011) Perturbation analysis of stochastic hybrid systems and applications to resource contention games. Front Electr Electron Eng China 6 (3):453–467
Yin S, Ding SX, Abandan Sari AH, Hao H (2013) Data-driven monitoring for stochastic systems and its application on batch process. Intl J Syst Sci 44(7):1366–1376
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.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This article belongs to the Topical Collection: Applications-2020
Guest Editors: Francesco Basile, Jan Komenda, and Christoforos Hadjicostis
About this article
Cite this article
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
- Performance evaluation
- Discrete approaches for hybrid systems