IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v197y2025ics0191261525000979.html
   My bibliography  Save this article

Modeling instantaneous queuing effects in the traffic assignment problem with consideration of demand fluctuations in the modeling period

Author

Listed:
  • Shi, Yuxin
  • Lam, William H.K.
  • Fu, Hao
  • Ho, H.W.
  • Tam, Mei Lam
  • Ma, Wei

Abstract

Instantaneous traffic queues, introducing fluctuated queuing delays, significantly affect the journey times and route choices of travelers particularly during the peak hour periods in congested road networks. Distinguished from average residual queues in static traffic assignment problems, instantaneous queues form and dissipate within minuscule time frames of a modeling period, triggered by an inflow exceeding link capacity, owning to instantaneous demand fluctuations. The inclusion of instantaneous queuing effects is of paramount importance, given their more frequent occurrence compared to residual queues. However, little attention has been given to these instantaneous queuing effects in static traffic assignment models for strategic planning. To fill this gap, this paper proposes a novel instantaneous traffic assignment (ITA) model to incorporate instantaneous queuing effects in congested road networks, accounting for within-period demand fluctuations. The enhanced ITA modeling framework is proposed encompassing two fixed-point problems for network loading and a logit-based stochastic user equilibrium assignment model. The ITA model is formulated as an equivalent variational inequality problem. The mathematical properties of the proposed model such as the stability of the unique solutions can be rigorously proved. An improved method of successive weighted average algorithm with an adaptive step size is developed to solve the proposed model in order to facilitate the examination of instantaneous queuing effects in real-world contexts for large-scale networks. Numerical examples are conducted to demonstrate the merits and efficacy of the proposed ITA model. The feasibility and applicability of the proposed model in reality are further illustrated in case studies of three different road networks.

Suggested Citation

  • Shi, Yuxin & Lam, William H.K. & Fu, Hao & Ho, H.W. & Tam, Mei Lam & Ma, Wei, 2025. "Modeling instantaneous queuing effects in the traffic assignment problem with consideration of demand fluctuations in the modeling period," Transportation Research Part B: Methodological, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:transb:v:197:y:2025:i:c:s0191261525000979
    DOI: 10.1016/j.trb.2025.103248
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261525000979
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2025.103248?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Fisk, Caroline, 1980. "Some developments in equilibrium traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 243-255, September.
    2. Akçelik, Rahmi & Rouphail, Nagui M., 1993. "Estimation of delays at traffic signals for variable demand conditions," Transportation Research Part B: Methodological, Elsevier, vol. 27(2), pages 109-131, April.
    3. Lam, William H.K. & Shao, Hu & Sumalee, Agachai, 2008. "Modeling impacts of adverse weather conditions on a road network with uncertainties in demand and supply," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 890-910, December.
    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. Wang, Yi & Szeto, W.Y. & Han, Ke & Friesz, Terry L., 2018. "Dynamic traffic assignment: A review of the methodological advances for environmentally sustainable road transportation applications," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 370-394.
    6. 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.
    7. Hu Shao & William Lam & Mei Tam, 2006. "A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand," Networks and Spatial Economics, Springer, vol. 6(3), pages 173-204, September.
    8. 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.
    9. Michiel C. J. Bliemer & Mark P. H. Raadsen & Luuk J. N. Brederode & Michael G. H. Bell & Luc J. J. Wismans & Mike J. Smith, 2017. "Genetics of traffic assignment models for strategic transport planning," Transport Reviews, Taylor & Francis Journals, vol. 37(1), pages 56-78, January.
    10. Xu, Zhandong & Xie, Jun & Liu, Xiaobo & Nie, Yu (Marco), 2020. "Hyperpath-based algorithms for the transit equilibrium assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    11. 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.
    12. Fatemeh Nourmohammadi & Mohammadhadi Mansourianfar & Sajjad Shafiei & Ziyuan Gu & Meead Saberi, 2021. "An Open GMNS Dataset of a Dynamic Multi-Modal Transportation Network Model of Melbourne, Australia," Data, MDPI, vol. 6(2), pages 1-9, February.
    13. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.
    14. 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.
    15. Raadsen, Mark P.H. & Bliemer, Michiel C.J. & Bell, Michael G.H., 2016. "An efficient and exact event-based algorithm for solving simplified first order dynamic network loading problems in continuous time," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 191-210.
    16. Bliemer, Michiel C.J. & Raadsen, Mark P.H., 2020. "Static traffic assignment with residual queues and spillback," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 303-319.
    17. Henry Liu & Xiaozheng He & Bingsheng He, 2009. "Method of Successive Weighted Averages (MSWA) and Self-Regulated Averaging Schemes for Solving Stochastic User Equilibrium Problem," Networks and Spatial Economics, Springer, vol. 9(4), pages 485-503, December.
    18. Richard E. Allsop, 1972. "Delay at a Fixed Time Traffic Signal---I: Theoretical Analysis," Transportation Science, INFORMS, vol. 6(3), pages 260-285, August.
    19. Jin, W. L. & Zhang, H. M., 2003. "On the distribution schemes for determining flows through a merge," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 521-540, July.
    20. 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.
    21. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    22. Claudia Castaldi & Paolo Delle Site & Francesco Filippi, 2019. "Stochastic user equilibrium in the presence of state dependence," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 535-559, December.
    23. Xu, Zhandong & Chen, Anthony & Liu, Xiaobo, 2023. "Time and toll trade-off with heterogeneous users: A continuous time surplus maximization bi-objective user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 31-58.
    24. 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.
    25. Yang, Hai & Yagar, Sam, 1994. "Traffic assignment and traffic control in general freeway-arterial corridor systems," Transportation Research Part B: Methodological, Elsevier, vol. 28(6), pages 463-486, December.
    26. Fu, Hao & Lam, William H.K. & Ma, Wei & Shi, Yuxin & Jiang, Rui & Sun, Huijun & Gao, Ziyou, 2025. "Modeling the residual queue and queue-dependent capacity in a static traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 192(C).
    27. Wei Huang & Guangming Xu & Hong K. Lo, 2020. "Pareto-Optimal Sustainable Transportation Network Design under Spatial Queuing," Networks and Spatial Economics, Springer, vol. 20(3), pages 637-673, September.
    28. Gentile, Guido, 2016. "Solving a Dynamic User Equilibrium model based on splitting rates with Gradient Projection algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 120-147.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fu, Hao & Lam, William H.K. & Ma, Wei & Shi, Yuxin & Jiang, Rui & Sun, Huijun & Gao, Ziyou, 2025. "Modeling the residual queue and queue-dependent capacity in a static traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 192(C).
    2. 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.
    3. Brederode, Luuk & Pel, Adam & Wismans, Luc & Rijksen, Bernike & Hoogendoorn, Serge, 2023. "Travel demand matrix estimation for strategic road traffic assignment models with strict capacity constraints and residual queues," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 1-31.
    4. Raadsen, Mark P.H. & Bliemer, Michiel C.J., 2023. "General solution scheme for the static link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 169(C), pages 108-135.
    5. Bliemer, Michiel C.J. & Raadsen, Mark P.H., 2020. "Static traffic assignment with residual queues and spillback," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 303-319.
    6. Raadsen, Mark P.H. & Bliemer, Michiel C.J., 2019. "Steady-state link travel time methods: Formulation, derivation, classification, and unification," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 167-191.
    7. Wei Huang & Guangming Xu & Hong K. Lo, 2020. "Pareto-Optimal Sustainable Transportation Network Design under Spatial Queuing," Networks and Spatial Economics, Springer, vol. 20(3), pages 637-673, September.
    8. Gong, Xiaolin & Bliemer, Michiel C.J. & Raadsen, Mark P.H., 2025. "Extended macroscopic node model for multilane traffic," Transportation Research Part B: Methodological, Elsevier, vol. 195(C).
    9. Tan, Heqing & Xu, Xiangdong & Chen, Anthony, 2024. "On endogenously distinguishing inactive paths in stochastic user equilibrium: A convex programming approach with a truncated path choice model," Transportation Research Part B: Methodological, Elsevier, vol. 183(C).
    10. Himpe, Willem & Corthout, Ruben & Tampère, M.J. Chris, 2016. "An efficient iterative link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 170-190.
    11. Du, Muqing & Tan, Heqing & Chen, Anthony, 2021. "A faster path-based algorithm with Barzilai-Borwein step size for solving stochastic traffic equilibrium models," European Journal of Operational Research, Elsevier, vol. 290(3), pages 982-999.
    12. Wang, Yi & Szeto, W.Y. & Han, Ke & Friesz, Terry L., 2018. "Dynamic traffic assignment: A review of the methodological advances for environmentally sustainable road transportation applications," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 370-394.
    13. Nie, Yu (Marco), 2011. "Multi-class percentile user equilibrium with flow-dependent stochasticity," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1641-1659.
    14. 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.
    15. Babak Javani & Abbas Babazadeh, 2020. "Path-Based Dynamic User Equilibrium Model with Applications to Strategic Transportation Planning," Networks and Spatial Economics, Springer, vol. 20(2), pages 329-366, June.
    16. Jiang, Gege & Fosgerau, Mogens & Lo, Hong K., 2020. "Route choice, travel time variability, and rational inattention," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 188-207.
    17. Li, Guoyuan & Chen, Anthony & Ryu, Seungkyu & Kitthamkesorn, Songyot & Xu, Xiangdong, 2024. "Modeling elasticity, similarity, stochasticity, and congestion in a network equilibrium framework using a paired combinatorial weibit choice model," Transportation Research Part B: Methodological, Elsevier, vol. 179(C).
    18. František Kolovský & Ivana Kolingerová, 2022. "The Piecewise Constant/Linear Solution for Dynamic User Equilibrium," Networks and Spatial Economics, Springer, vol. 22(4), pages 737-765, December.
    19. Jian Wang & Muqing Du & Lili Lu & Xiaozheng He, 2018. "Maximizing Network Throughput under Stochastic User Equilibrium with Elastic Demand," Networks and Spatial Economics, Springer, vol. 18(1), pages 115-143, March.
    20. Nakayama, Shoichiro & Watling, David, 2014. "Consistent formulation of network equilibrium with stochastic flows," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 50-69.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:197:y:2025:i:c:s0191261525000979. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.