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Quasi-dynamic traffic assignment with spatial queueing, control and blocking back

Author

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  • Smith, Mike
  • Huang, Wei
  • Viti, Francesco
  • Tampère, Chris M.J.
  • Lo, Hong K.

Abstract

This paper introduces a steady-state, fixed (or inelastic) demand equilibrium model with explicit link-exit capacities, explicit bottleneck or queueing delays and explicit bounds on queue storage capacities. The model is a quasi-dynamic model. The link model at the heart of this quasi-dynamic equilibrium model is a spatial queueing model, which takes account of the space taken up by queues both when there is no blocking back and also when there is blocking back. The paper shows that if this quasi-dynamic model is utilised then for any feasible demand there is an equilibrium solution, provided (i) queue storage capacities are large or (ii) prices are used to help impose capacity restrictions; the prices either remove queueing delays entirely or just reduce spatial queues sufficiently to ensure that blocking back does not occur at equilibrium. Similar results, but now involving the P0 control policy (introduced in Smith (1979a, 1987)) and two new variations of this policy (i.e., the spatial P0 control policy, and the biased spatial P0 control policy) are obtained. In these results, the control policies allow green-times to vary in response to prices as well as spatial queueing delays. These three policies are also tested on a small simple network. In these tests, the biased spatial version of P0 is much the best in reducing equilibrium delays (on this simple network). The paper further illustrates how the spatial queueing model works on simple networks with different merge models; it is demonstrated that equilibrium may be prevented by certain (fixed ratio) merge models. It is also shown in this case that equilibrium may be imposed on just the controlled area itself by a variety of (merge model, gating strategy) combinations. Opportunities for developing such combined gating and merging control strategies are finally discussed.

Suggested Citation

  • Smith, Mike & Huang, Wei & Viti, Francesco & Tampère, Chris M.J. & Lo, Hong K., 2019. "Quasi-dynamic traffic assignment with spatial queueing, control and blocking back," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 140-166.
    • Handle: RePEc:eee:transb:v:122:y:2019:i:c:p:140-166
    DOI: 10.1016/j.trb.2019.01.018
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    References listed on IDEAS

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    1. Carlos F. Daganzo, 1998. "Queue Spillovers in Transportation Networks with a Route Choice," Transportation Science, INFORMS, vol. 32(1), pages 3-11, February.
    2. Tampère, Chris M.J. & Corthout, Ruben & Cattrysse, Dirk & Immers, Lambertus H., 2011. "A generic class of first order node models for dynamic macroscopic simulation of traffic flows," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 289-309, January.
    3. A. de Palma & Y. Nesterov, 2001. "Stationary Dynamic Solutions in Congested Transportation Networks: Summary and Perspectives," THEMA Working Papers 2001-19, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    4. Bliemer, Michiel C.J. & Raadsen, Mark P.H. & Smits, Erik-Sander & Zhou, Bojian & Bell, Michael G.H., 2014. "Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 363-384.
    5. 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.
    6. Gentile, Guido & Meschini, Lorenzo & Papola, Natale, 2007. "Spillback congestion in dynamic traffic assignment: A macroscopic flow model with time-varying bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 41(10), pages 1114-1138, December.
    7. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    8. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    9. Larsson, Torbjörn & Patriksson, Michael, 1995. "An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 433-455, December.
    10. Zhong, R.X. & Chen, C. & Huang, Y.P. & Sumalee, A. & Lam, W.H.K. & Xu, D.B., 2018. "Robust perimeter control for two urban regions with macroscopic fundamental diagrams: A control-Lyapunov function approach," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 687-707.
    11. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    12. Gentile, Guido & Meschini, Lorenzo & Papola, Natale, 2005. "Macroscopic arc performance models with capacity constraints for within-day dynamic traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 39(4), pages 319-338, May.
    13. Hillel Bar-Gera, 2002. "Origin-Based Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 36(4), pages 398-417, November.
    14. Nie, Yu & Zhang, H. M. & Lee, Der-Horng, 2004. "Models and algorithms for the traffic assignment problem with link capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 285-312, May.
    15. He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2010. "A link-based day-to-day traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 597-608, May.
    16. Bar-Gera, Hillel, 2010. "Traffic assignment by paired alternative segments," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1022-1046, September.
    17. Jin, Wen-Long, 2010. "Continuous kinematic wave models of merging traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1084-1103, September.
    18. Viti, Francesco & van Zuylen, Henk J., 2010. "Probabilistic models for queues at fixed control signals," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 120-135, January.
    19. Keyvan-Ekbatani, Mehdi & Kouvelas, Anastasios & Papamichail, Ioannis & Papageorgiou, Markos, 2012. "Exploiting the fundamental diagram of urban networks for feedback-based gating," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1393-1403.
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    Cited by:

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    2. Yahyamozdarani, Raheleh & Tampère, Chris M.J., 2023. "The continuous signalized (COS) node model for dynamic traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 168(C), pages 56-80.

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