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A reactive dynamic user equilibrium model in network with queues

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  • Li, Jun
  • Fujiwara, Okitsugu
  • Kawakami, Shogo

Abstract

A discrete time reactive dynamic user equilibrium (DUE) model for network with queues is presented. Based on the point queue model, each link is assumed to have a constant running time and queuing delay caused by link exit capacity. The link performance function and link exit function are given as functions of the arrival rate and the queue length, where the first-in-first-out (FIFO) rule is shown to be satisfied. The DUE problem is then formulated as a variational inequality (VI) problem over a polyhedral set by constructing a new network so that the path enumeration is avoided. Therefore the proposed model is applicable for large-scale networks. The existence of solution for VI problem is proved, and an iteration method is discussed in detail. A static capacity constrained model is employed to initialize the network and avoid the zero-flow network at initial time. Finally, the advantages of the new model and method proposed are tested by numerical examples.

Suggested Citation

  • Li, Jun & Fujiwara, Okitsugu & Kawakami, Shogo, 2000. "A reactive dynamic user equilibrium model in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 605-624, November.
    • Handle: RePEc:eee:transb:v:34:y:2000:i:8:p:605-624
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    Cited by:

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    2. Rui Ma & Xuegang Ban & Jong-Shi Pang & Henry Liu, 2015. "Submission to the DTA2012 Special Issue: Convergence of Time Discretization Schemes for Continuous-Time Dynamic Network Loading Models," Networks and Spatial Economics, Springer, vol. 15(3), pages 419-441, September.
    3. Ban, Xuegang (Jeff) & Pang, Jong-Shi & Liu, Henry X. & Ma, Rui, 2012. "Continuous-time point-queue models in dynamic network loading," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 360-380.
    4. Han, Ke & Friesz, Terry L. & Yao, Tao, 2013. "A partial differential equation formulation of Vickrey’s bottleneck model, part I: Methodology and theoretical analysis," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 55-74.
    5. Georgia Perakis & Guillaume Roels, 2006. "An Analytical Model for Traffic Delays and the Dynamic User Equilibrium Problem," Operations Research, INFORMS, vol. 54(6), pages 1151-1171, December.
    6. Yan-Qun Jiang & S.C. Wong & Peng Zhang & Keechoo Choi, 2017. "Dynamic Continuum Model with Elastic Demand for a Polycentric Urban City," Transportation Science, INFORMS, vol. 51(3), pages 931-945, August.
    7. Han, Ke & Friesz, Terry L. & Yao, Tao, 2013. "A partial differential equation formulation of Vickrey’s bottleneck model, part II: Numerical analysis and computation," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 75-93.
    8. Friesz, Terry L. & Kim, Taeil & Kwon, Changhyun & Rigdon, Matthew A., 2011. "Approximate network loading and dual-time-scale dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 176-207, January.

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