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Dynamic network loading: A stochastic differentiable model that derives link state distributions

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  • Osorio, Carolina
  • Flötteröd, Gunnar
  • Bierlaire, Michel

Abstract

We present a dynamic network loading model that yields queue length distributions, accounts for spillbacks, and maintains a differentiable mapping from the dynamic demand on the dynamic queue lengths. The model also captures the spatial correlation of all queues adjacent to a node, and derives their joint distribution. The approach builds upon an existing stationary queueing network model that is based on finite capacity queueing theory. The original model is specified in terms of a set of differentiable equations, which in the new model are carried over to a set of equally smooth difference equations. The physical correctness of the new model is experimentally confirmed in several congestion regimes. A comparison with results predicted by the kinematic wave model (KWM) shows that the new model correctly represents the dynamic build-up, spillback and dissipation of queues. It goes beyond the KWM in that it captures queue lengths and spillbacks probabilistically, which allows for a richer analysis than the deterministic predictions of the KWM. The new model also generates a plausible fundamental diagram, which demonstrates that it captures well the stationary flow/density relationships in both congested and uncongested conditions.

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  • Osorio, Carolina & Flötteröd, Gunnar & Bierlaire, Michel, 2011. "Dynamic network loading: A stochastic differentiable model that derives link state distributions," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1410-1423.
    • Handle: RePEc:eee:transb:v:45:y:2011:i:9:p:1410-1423
    DOI: 10.1016/j.trb.2011.05.014
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    1. R. M. Oliver & E. F. Bisbee, 1962. "Queuing for Gaps in High Flow Traffic Streams," Operations Research, INFORMS, vol. 10(1), pages 105-114, February.
    2. Dirk Heidemann, 2001. "A Queueing Theory Model of Nonstationary Traffic Flow," Transportation Science, INFORMS, vol. 35(4), pages 405-412, November.
    3. Rajat Jain & J. Macgregor Smith, 1997. "Modeling Vehicular Traffic Flow using M/G/C/C State Dependent Queueing Models," Transportation Science, INFORMS, vol. 31(4), pages 324-336, November.
    4. Boel, René & Mihaylova, Lyudmila, 2006. "A compositional stochastic model for real time freeway traffic simulation," Transportation Research Part B: Methodological, Elsevier, vol. 40(4), pages 319-334, May.
    5. Osorio, Carolina & Bierlaire, Michel, 2009. "An analytic finite capacity queueing network model capturing the propagation of congestion and blocking," European Journal of Operational Research, Elsevier, vol. 196(3), pages 996-1007, August.
    6. 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.
    7. Heidemann, Dirk, 1994. "Queue length and delay distributions at traffic signals," Transportation Research Part B: Methodological, Elsevier, vol. 28(5), pages 377-389, October.
    8. Hilliges, Martin & Weidlich, Wolfgang, 1995. "A phenomenological model for dynamic traffic flow in networks," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 407-431, December.
    9. Michael D. Peterson & Dimitris J. Bertsimas & Amedeo R. Odoni, 1995. "Models and Algorithms for Transient Queueing Congestion at Airports," Management Science, INFORMS, vol. 41(8), pages 1279-1295, August.
    10. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
    11. Flötteröd, Gunnar & Rohde, Jannis, 2011. "Operational macroscopic modeling of complex urban road intersections," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 903-922, July.
    12. 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.
    13. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    14. Kerbache, Laoucine & Smith, J. MacGregor, 2000. "Multi-objective routing within large scale facilities using open finite queueing networks," European Journal of Operational Research, Elsevier, vol. 121(1), pages 105-123, February.
    15. Tom Van Woensel & Nico Vandaele, 2007. "Modeling Traffic Flows With Queueing Models: A Review," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(04), pages 435-461.
    16. Laoucine Kerbache & J. Macgregor Smith, 2000. "Multi-objective routing within large scale facilities using open finite queueing networks," Post-Print hal-00798811, HAL.
    17. Heidemann, Dirk & Wegmann, Helmut, 1997. "Queueing at unsignalized intersections," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 239-263, June.
    18. Attahiru Sule Alfa & Marcel F. Neuts, 1995. "Modelling Vehicular Traffic Using the Discrete Time Markovian Arrival Process," Transportation Science, INFORMS, vol. 29(2), pages 109-117, May.
    19. Sumalee, A. & Zhong, R.X. & Pan, T.L. & Szeto, W.Y., 2011. "Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 507-533, March.
    20. Daganzo, Carlos F., 1995. "A finite difference approximation of the kinematic wave model of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 261-276, August.
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    Cited by:

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    3. Zheng, Fangfang & Jabari, Saif Eddin & Liu, Henry X. & Lin, DianChao, 2018. "Traffic state estimation using stochastic Lagrangian dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 143-165.
    4. Osorio, Carolina & Wang, Carter, 2017. "On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 305-339.
    5. Flötteröd, G. & Osorio, C., 2017. "Stochastic network link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 180-209.
    6. Yu, Hao & Ma, Rui & Zhang, H. Michael, 2018. "Optimal traffic signal control under dynamic user equilibrium and link constraints in a general network," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 302-325.
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    8. Boon, Marko A.A. & van Leeuwaarden, Johan S.H., 2018. "Networks of fixed-cycle intersections," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 254-271.
    9. Jabari, Saif Eddin & Zheng, Jianfeng & Liu, Henry X., 2014. "A probabilistic stationary speed–density relation based on Newell’s simplified car-following model," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 205-223.
    10. Carolina Osorio & Gunnar Flötteröd, 2015. "Capturing Dependency Among Link Boundaries in a Stochastic Dynamic Network Loading Model," Transportation Science, INFORMS, vol. 49(2), pages 420-431, May.
    11. Carolina Osorio & Jana Yamani, 2017. "Analytical and Scalable Analysis of Transient Tandem Markovian Finite Capacity Queueing Networks," Transportation Science, INFORMS, vol. 51(3), pages 823-840, August.
    12. Ngoduy, D. & Hoang, N.H. & Vu, H.L. & Watling, D., 2016. "Optimal queue placement in dynamic system optimum solutions for single origin-destination traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 148-169.
    13. Ma, Rui & Ban, Xuegang (Jeff) & Pang, Jong-Shi, 2014. "Continuous-time dynamic system optimum for single-destination traffic networks with queue spillbacks," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 98-122.
    14. António Pacheco & Maria Lurdes Simões Simões & Paula Milheiro-Oliveira, 2017. "Queues with Server Vacations as a Model for Pretimed Signalized Urban Traffic," Transportation Science, INFORMS, vol. 51(3), pages 841-851, August.
    15. Watling, David P. & Hazelton, Martin L., 2018. "Asymptotic approximations of transient behaviour for day-to-day traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 90-105.
    16. Ke Han & Gabriel Eve & Terry L. Friesz, 2019. "Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation," Networks and Spatial Economics, Springer, vol. 19(3), pages 869-902, September.
    17. Yang, Xia & Ban, Xuegang (Jeff) & Mitchell, John, 2018. "Modeling multimodal transportation network emergency evacuation considering evacuees’ cooperative behavior," Transportation Research Part A: Policy and Practice, Elsevier, vol. 114(PB), pages 380-397.
    18. Mohebifard, Rasool & Hajbabaie, Ali, 2019. "Optimal network-level traffic signal control: A benders decomposition-based solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 252-274.
    19. Long, Jiancheng & Wang, Chao & Szeto, W.Y., 2018. "Dynamic system optimum simultaneous route and departure time choice problems: Intersection-movement-based formulations and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 166-206.
    20. Rui Ma & Xuegang (Jeff) Ban & Jong-Shi Pang, 2018. "A Link-Based Differential Complementarity System Formulation for Continuous-Time Dynamic User Equilibria with Queue Spillbacks," Transportation Science, INFORMS, vol. 52(3), pages 564-592, June.
    21. Yuan, Yun & Zhang, Zhao & Yang, Xianfeng Terry & Zhe, Shandian, 2021. "Macroscopic traffic flow modeling with physics regularized Gaussian process: A new insight into machine learning applications in transportation," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 88-110.
    22. Jabari, Saif Eddin & Liu, Henry X., 2013. "A stochastic model of traffic flow: Gaussian approximation and estimation," Transportation Research Part B: Methodological, Elsevier, vol. 47(C), pages 15-41.
    23. Linsen Chong & Carolina Osorio, 2018. "A Simulation-Based Optimization Algorithm for Dynamic Large-Scale Urban Transportation Problems," Transportation Science, INFORMS, vol. 52(3), pages 637-656, June.
    24. Ma, Rui & Ban, Xuegang (Jeff) & Szeto, W.Y., 2017. "Emission modeling and pricing on single-destination dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 255-283.

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