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Analysis of fixed-time control

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  • 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
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    References listed on IDEAS

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    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.
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    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. 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.

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