IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v73y2015icp81-90.html
   My bibliography  Save this article

Analysis of fixed-time control

Author

Listed:
  • Muralidharan, Ajith
  • Pedarsani, Ramtin
  • Varaiya, Pravin

Abstract

The paper presents an analysis of the traffic dynamics in a network of signalized intersections. The intersections are regulated by fixed-time (FT) controls, all with the same cycle length or period, T. The network is modeled as a queuing network. Vehicles arrive from outside the network at entry links in a deterministic periodic stream, also with period T. They take a fixed time to travel along each link, and at the end of the link they join a queue. There is a separate queue at each link for each movement or phase. Vehicles make turns at intersections in fixed proportions, and eventually leave the network, that is, a fraction r(i,j) of vehicles that leave queue i go to queue j and the fraction [1-∑jr(i,j)] leave the network. The storage capacity of the queues is infinite, so there is no spill back. The main contribution of the paper is to show that if the signal controls accommodate the demands then, starting in any initial condition, the network state converges to a unique periodic orbit. Thus, the effect of initial conditions disappears. More precisely, the state of the network at time t is the vector x(t) of all queue lengths, together with the position of vehicles traveling along the links. Suppose that the network is stable, that is, x(t) is bounded. Then

Suggested Citation

  • Muralidharan, Ajith & Pedarsani, Ramtin & Varaiya, Pravin, 2015. "Analysis of fixed-time control," Transportation Research Part B: Methodological, Elsevier, vol. 73(C), pages 81-90.
    • Handle: RePEc:eee:transb:v:73:y:2015:i:c:p:81-90
    DOI: 10.1016/j.trb.2014.12.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261514002197
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2014.12.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. S. Ramasubramanian, 2000. "A Subsidy-Surplus Model and the Skorokhod Problem in an Orthant," Mathematics of Operations Research, INFORMS, vol. 25(3), pages 509-538, August.
    2. Denos C. Gazis, 1964. "Optimum Control of a System of Oversaturated Intersections," Operations Research, INFORMS, vol. 12(6), pages 815-831, December.
    3. Ward Whitt, 2001. "The Reflection Map with Discontinuities," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 447-484, August.
    4. Improta, G. & Cantarella, G. E., 1984. "Control system design for an individual signalized junction," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 147-167, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yu, Chunhui & Ma, Wanjing & Yang, Xiaoguang, 2020. "A time-slot based signal scheme model for fixed-time control at isolated intersections," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 176-192.
    2. Smith, M.J. & Liu, R. & Mounce, R., 2015. "Traffic control and route choice: Capacity maximisation and stability," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 863-885.
    3. Como, Giacomo & Nilsson, Gustav, 2021. "On the well-posedness of deterministic queuing networks with feedback control," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 323-335.
    4. Kouvelas, Anastasios & Saeedmanesh, Mohammadreza & Geroliminis, Nikolas, 2017. "Enhancing model-based feedback perimeter control with data-driven online adaptive optimization," Transportation Research Part B: Methodological, Elsevier, vol. 96(C), pages 26-45.
    5. Mingwen Zheng & Lixiang Li & Haipeng Peng & Jinghua Xiao & Yixian Yang & Yanping Zhang & Hui Zhao, 2018. "Globally fixed-time synchronization of coupled neutral-type neural network with mixed time-varying delays," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-22, January.
    6. Coogan, Samuel & Kim, Eric & Gomes, Gabriel & Arcak, Murat & Varaiya, Pravin, 2017. "Offset optimization in signalized traffic networks via semidefinite relaxation," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 82-92.
    7. Gongquan Zhang & Fangrong Chang & Helai Huang & Zilong Zhou, 2024. "Dual-Objective Reinforcement Learning-Based Adaptive Traffic Signal Control for Decarbonization and Efficiency Optimization," Mathematics, MDPI, vol. 12(13), pages 1-24, June.
    8. Hao, Zhenzhen & Boel, René, 2022. "Convergence analysis on control for traffic signals in urban road network," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 35-62.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lee, Seunghyeon & Wong, S.C. & Varaiya, Pravin, 2017. "Group-based hierarchical adaptive traffic-signal control part I: Formulation," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 1-18.
    2. Yu, Chunhui & Ma, Wanjing & Yang, Xiaoguang, 2020. "A time-slot based signal scheme model for fixed-time control at isolated intersections," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 176-192.
    3. Abu-Lebdeh, Ghassan & Benekohal, Rahim F., 2003. "Design and evaluation of dynamic traffic management strategies for congested conditions," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(2), pages 109-127, February.
    4. Yin, Yafeng, 2008. "Robust optimal traffic signal timing," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 911-924, December.
    5. Cantarella, G.E. & Pavone, G. & Vitetta, A., 2006. "Heuristics for urban road network design: Lane layout and signal settings," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1682-1695, December.
    6. Wang Yu & Zhang Dongbo & Zhang Yu, 2022. "GPS data Mining at Signalized Intersections for Congestion Charging," Computational Economics, Springer;Society for Computational Economics, vol. 59(4), pages 1713-1734, April.
    7. Offer Kella & S. Ramasubramanian, 2012. "Asymptotic Irrelevance of Initial Conditions for Skorohod Reflection Mapping on the Nonnegative Orthant," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 301-312, May.
    8. Delarue, F. & Inglis, J. & Rubenthaler, S. & Tanré, E., 2015. "Particle systems with a singular mean-field self-excitation. Application to neuronal networks," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2451-2492.
    9. Ramasubramanian, S., 2006. "An insurance network: Nash equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 374-390, April.
    10. Nie, Tianyang & Rutkowski, Marek, 2014. "Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2672-2698.
    11. Denos C. Gazis, 2002. "The Origins of Traffic Theory," Operations Research, INFORMS, vol. 50(1), pages 69-77, February.
    12. Quantao Yang & Feng Lu & Jingsheng Wang & Dan Zhao & Lijie Yu, 2020. "Analysis of the Insertion Angle of Lane-Changing Vehicles in Nearly Saturated Fast Road Segments," Sustainability, MDPI, vol. 12(3), pages 1-17, January.
    13. Memoli, Silvio & Cantarella, Giulio E. & de Luca, Stefano & Pace, Roberta Di, 2017. "Network signal setting design with stage sequence optimisation," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 20-42.
    14. Wong, C. K. & Wong, S. C., 2003. "Lane-based optimization of signal timings for isolated junctions," Transportation Research Part B: Methodological, Elsevier, vol. 37(1), pages 63-84, January.
    15. Bohan Chen & Jose Blanchet & Chang-Han Rhee & Bert Zwart, 2019. "Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 919-942, August.
    16. Wang, Yi & Szeto, W.Y. & Han, Ke & Friesz, Terry L., 2018. "Dynamic traffic assignment: A review of the methodological advances for environmentally sustainable road transportation applications," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 370-394.
    17. Heydecker, B. G., 1996. "A decomposition approach for signal optimisation in road networks," Transportation Research Part B: Methodological, Elsevier, vol. 30(2), pages 99-114, April.
    18. Xuan, Yiguang & Daganzo, Carlos F. & Cassidy, Michael J., 2011. "Increasing the capacity of signalized intersections with separate left turn phases," Transportation Research Part B: Methodological, Elsevier, vol. 45(5), pages 769-781, June.
    19. Yan, Fei & Qiu, Jiangchen & Tian, Jianyan, 2022. "An iterative learning identification strategy for nonlinear macroscopic traffic flow model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    20. Wong, C.K. & Heydecker, B.G., 2011. "Optimal allocation of turns to lanes at an isolated signal-controlled junction," Transportation Research Part B: Methodological, Elsevier, vol. 45(4), pages 667-681, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:73:y:2015:i:c:p:81-90. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.