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A Dynamic Traffic Assignment Model and a Solution Algorithm

Author

Listed:
  • Omar Drissi-Kaïtouni

    (Université de Montréal, Québec, Canada H3C 3J7)

  • Abdelhamid Hameda-Benchekroun

    (Université de Montréal, Québec, Canada H3C 3J7)

Abstract

This paper is concerned with the modeling of the Dynamic Traffic Assignment Problem (DTAP) for predicting the flows of urban transportation networks, mainly at peak periods. During the past 40 years, most of the research has been for the Static Traffic Assignment Problem (STAP) where it is assumed that demand is constant over time. This assumption is realistic for the analysis of intercity freight transportation networks over long periods of time, but it does not hold in an urban area, for simulating the flow variations during short periods (peak hours). Hence, during the past 20 years, the interest to the DTAP has been increasing. The seventies have been a transition period between heuristic models (where the demand is assigned to instantaneous minimum cost paths), and optimization models that take into account the demand over the whole study horizon of time, but all of them incorporate important limitations (only one destination; unrealistic conditions on the cost functions so that the flow “reaches” the destination; possible violation of the link capacities; etc.). In this paper, we propose a Dynamic Traffic Assignment Model which is mainly based on the following assumption: the time spent by a vehicle on a link may be decomposed into a fixed travel time plus a waiting time. The fixed travel time corresponds to the free or uncongested travel time over the link. Then the vehicle is put in an exit queue (which resides on the same link) until it becomes possible to enter a forward link; this decision is based on the link costs and their capacities. We show that this model leads to a network structure (a temporal expansion of the base network, including the queues) and therefore the DTAP may be viewed as a “simple” STAP over the expanded network. Hence, all the theories developed during the past 40 years for the STAP may be used to solve the DTAP.

Suggested Citation

  • Omar Drissi-Kaïtouni & Abdelhamid Hameda-Benchekroun, 1992. "A Dynamic Traffic Assignment Model and a Solution Algorithm," Transportation Science, INFORMS, vol. 26(2), pages 119-128, May.
    • Handle: RePEc:inm:ortrsc:v:26:y:1992:i:2:p:119-128
    DOI: 10.1287/trsc.26.2.119
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    Cited by:

    1. Mohri, Seyed Sina & Asgari, Nasrin & Zanjirani Farahani, Reza & Bourlakis, Michael & Laker, Benjamin, 2020. "Fairness in hazmat routing-scheduling: A bi-objective Stackelberg game," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 140(C).
    2. Liu, Jiangtao & Zhou, Xuesong, 2016. "Capacitated transit service network design with boundedly rational agents," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 225-250.
    3. 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.
    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. Shen, Wei & Zhang, H.M., 2014. "System optimal dynamic traffic assignment: Properties and solution procedures in the case of a many-to-one network," Transportation Research Part B: Methodological, Elsevier, vol. 65(C), pages 1-17.
    6. 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.
    7. Wen-Long Jin, 2021. "A Link Queue Model of Network Traffic Flow," Transportation Science, INFORMS, vol. 55(2), pages 436-455, March.
    8. Yang, Hai & Meng, Qiang, 1998. "Departure time, route choice and congestion toll in a queuing network with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 32(4), pages 247-260, May.
    9. Brunilde Sansò & Luc Milot, 1999. "Performability of a Congested Urban Transportation Network When Accident Information is Available," Transportation Science, INFORMS, vol. 33(1), pages 68-79, February.
    10. Jin, Wen-Long, 2015. "Point queue models: A unified approach," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 1-16.
    11. 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.
    12. Qipeng Zheng & Ashwin Arulselvan, 2011. "Discrete time dynamic traffic assignment models and solution algorithm for managed lanes," Journal of Global Optimization, Springer, vol. 51(1), pages 47-68, September.
    13. Liu, Jiangtao & Zhou, Xuesong, 2019. "Observability quantification of public transportation systems with heterogeneous data sources: An information-space projection approach based on discretized space-time network flow models," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 302-323.
    14. Huang, Hai-Jun & Xu, Gang, 1998. "Aggregate scheduling and network solving of multi-stage and multi-item manufacturing systems," European Journal of Operational Research, Elsevier, vol. 105(1), pages 52-65, February.

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