IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v92y2016ipap3-21.html
   My bibliography  Save this article

A general stochastic process for day-to-day dynamic traffic assignment: Formulation, asymptotic behaviour, and stability analysis

Author

Listed:
  • Cantarella, Giulio E.
  • Watling, David P.

Abstract

This paper presents a general modelling approach to day-to-day dynamic assignment to a congested network through discrete-time stochastic and deterministic process models including an explicit modelling of users’ habit as a part of route choice behaviour, through an exponential smoothing filter, and of their memory of network conditions on past days, through a moving average or an exponentially smoothing filter. An asymptotic analysis of the mean process is carried out to provide a better insight. Results of such analyses are also used for deriving conditions, about values of the system parameters, assuring that the mean process is dissipative and/or converges to some kind of attractor. Numerical small examples are also provided in order to illustrate the theoretical results obtained.

Suggested Citation

  • Cantarella, Giulio E. & Watling, David P., 2016. "A general stochastic process for day-to-day dynamic traffic assignment: Formulation, asymptotic behaviour, and stability analysis," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 3-21.
    • Handle: RePEc:eee:transb:v:92:y:2016:i:pa:p:3-21
    DOI: 10.1016/j.trb.2016.05.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261516302776
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2016.05.005?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Martin L. Hazelton & David P. Watling, 2004. "Computation of Equilibrium Distributions of Markov Traffic-Assignment Models," Transportation Science, INFORMS, vol. 38(3), pages 331-342, August.
    2. 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.
    3. Shao, Hu & Lam, William H.K. & Sumalee, Agachai & Chen, Anthony & Hazelton, Martin L., 2014. "Estimation of mean and covariance of peak hour origin–destination demands from day-to-day traffic counts," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 52-75.
    4. Watling, David, 1996. "Asymmetric problems and stochastic process models of traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 339-357, October.
    5. Parry, Katharina & Hazelton, Martin L., 2013. "Bayesian inference for day-to-day dynamic traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 50(C), pages 104-115.
    6. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Tan, Zhijia, 2015. "Link-based day-to-day network traffic dynamics and equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 248-260.
    7. G. E. Cantarella & E. Cascetta, 1995. "Dynamic Processes and Equilibrium in Transportation Networks: Towards a Unifying Theory," Transportation Science, INFORMS, vol. 29(4), pages 305-329, November.
    8. David Watling & Giulio Cantarella, 2015. "Model Representation & Decision-Making in an Ever-Changing World: The Role of Stochastic Process Models of Transportation Systems," Networks and Spatial Economics, Springer, vol. 15(3), pages 843-882, September.
    9. Gary A. Davis & Nancy L. Nihan, 1993. "Large Population Approximations of a General Stochastic Traffic Assignment Model," Operations Research, INFORMS, vol. 41(1), pages 169-178, February.
    10. Liu, Ronghui & Van Vliet, Dirck & Watling, David, 2006. "Microsimulation models incorporating both demand and supply dynamics," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(2), pages 125-150, February.
    11. G. E. Cantarella & D. P. Watling, 2016. "Modelling road traffic assignment as a day-to-day dynamic, deterministic process: a unified approach to discrete- and continuous-time models," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 69-98, March.
    12. Giulio Erberto Cantarella, 1997. "A General Fixed-Point Approach to Multimode Multi-User Equilibrium Assignment with Elastic Demand," Transportation Science, INFORMS, vol. 31(2), pages 107-128, May.
    13. Horowitz, Joel L., 1984. "The stability of stochastic equilibrium in a two-link transportation network," Transportation Research Part B: Methodological, Elsevier, vol. 18(1), pages 13-28, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kucharski, Rafał & Gentile, Guido, 2019. "Simulation of rerouting phenomena in Dynamic Traffic Assignment with the Information Comply Model," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 414-441.
    2. Li, Ruijie & Liu, Xiaobo & Nie, Yu (Marco), 2018. "Managing partially automated network traffic flow: Efficiency vs. stability," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 300-324.
    3. Xu, Xiangdong & Qu, Kai & Chen, Anthony & Yang, Chao, 2021. "A new day-to-day dynamic network vulnerability analysis approach with Weibit-based route adjustment process," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 153(C).
    4. Vittorio Astarita & Ciro Caliendo & Vincenzo Pasquale Giofrè & Isidoro Russo, 2020. "Surrogate Safety Measures from Traffic Simulation: Validation of Safety Indicators with Intersection Traffic Crash Data," Sustainability, MDPI, vol. 12(17), pages 1-21, August.
    5. Satsukawa, Koki & Wada, Kentaro & Iryo, Takamasa, 2020. "Reprint of “Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach”," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 117-135.
    6. Guo, Ren-Yong & Szeto, W.Y., 2018. "Day-to-day modal choice with a Pareto improvement or zero-sum revenue scheme," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 1-25.
    7. Barroso, Joana Maia Fernandes & Albuquerque-Oliveira, João Lucas & Oliveira-Neto, Francisco Moraes, 2020. "Correlation analysis of day-to-day origin-destination flows and traffic volumes in urban networks," Journal of Transport Geography, Elsevier, vol. 89(C).
    8. Ren-Yong Guo & Hai Yang & Hai-Jun Huang, 2018. "Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?," Transportation Science, INFORMS, vol. 52(3), pages 603-620, June.
    9. Qi, Hang & Jia, Ning & Qu, Xiaobo & He, Zhengbing, 2023. "Investigating day-to-day route choices based on multi-scenario laboratory experiments, Part I: Route-dependent attraction and its modeling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 167(C).
    10. Satsukawa, Koki & Wada, Kentaro & Iryo, Takamasa, 2019. "Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach," Transportation Research Part B: Methodological, Elsevier, vol. 125(C), pages 229-247.
    11. Liu, Peng & Liao, Feixiong & Tian, Qiong & Huang, Hai-Jun & Timmermans, Harry, 2020. "Day-to-day needs-based activity-travel dynamics and equilibria in multi-state supernetworks," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 208-227.
    12. Santos Sánchez-Cambronero & Fernando Álvarez-Bazo & Ana Rivas & Inmaculada Gallego, 2021. "Dynamic Route Flow Estimation in Road Networks Using Data from Automatic Number of Plate Recognition Sensors," Sustainability, MDPI, vol. 13(8), pages 1-30, April.
    13. Zhong, R.X. & Xie, X.X. & Luo, J.C. & Pan, T.L. & Lam, W.H.K. & Sumalee, A., 2020. "Modeling double time-scale travel time processes with application to assessing the resilience of transportation systems," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 228-248.
    14. Borja Alonso & Vittorio Astarita & Luigi Dell’Olio & Vincenzo Pasquale Giofrè & Giuseppe Guido & Marcella Marino & William Sommario & Alessandro Vitale, 2020. "Validation of Simulated Safety Indicators with Traffic Crash Data," Sustainability, MDPI, vol. 12(3), pages 1-22, January.
    15. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Li, Xinwei, 2018. "Day-to-day departure time choice under bounded rationality in the bottleneck model," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 832-849.
    16. Sun, Mingmei, 2023. "A day-to-day dynamic model for mixed traffic flow of autonomous vehicles and inertial human-driven vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 173(C).

    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. Sun, Mingmei, 2023. "A day-to-day dynamic model for mixed traffic flow of autonomous vehicles and inertial human-driven vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 173(C).
    2. G. E. Cantarella & D. P. Watling, 2016. "Modelling road traffic assignment as a day-to-day dynamic, deterministic process: a unified approach to discrete- and continuous-time models," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 69-98, March.
    3. David Watling & Giulio Cantarella, 2015. "Model Representation & Decision-Making in an Ever-Changing World: The Role of Stochastic Process Models of Transportation Systems," Networks and Spatial Economics, Springer, vol. 15(3), pages 843-882, September.
    4. Paolo Delle Site, 2017. "On the Equivalence Between SUE and Fixed-Point States of Day-to-Day Assignment Processes with Serially-Correlated Route Choice," Networks and Spatial Economics, Springer, vol. 17(3), pages 935-962, September.
    5. 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.
    6. Zhu, Zheng & Mardan, Atabak & Zhu, Shanjiang & Yang, Hai, 2021. "Capturing the interaction between travel time reliability and route choice behavior based on the generalized Bayesian traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 143(C), pages 48-64.
    7. Meneguzzer, Claudio, 2022. "Day-to-day dynamics in a simple traffic network with mixed direct and contrarian route choice behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    8. Hazelton, Martin L., 2022. "The emergence of stochastic user equilibria in day-to-day traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 102-112.
    9. Rambha, Tarun & Boyles, Stephen D., 2016. "Dynamic pricing in discrete time stochastic day-to-day route choice models," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 104-118.
    10. Xu, Xiangdong & Qu, Kai & Chen, Anthony & Yang, Chao, 2021. "A new day-to-day dynamic network vulnerability analysis approach with Weibit-based route adjustment process," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 153(C).
    11. Jiayang Li & Zhaoran Wang & Yu Marco Nie, 2023. "Wardrop Equilibrium Can Be Boundedly Rational: A New Behavioral Theory of Route Choice," Papers 2304.02500, arXiv.org, revised Feb 2024.
    12. 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.
    13. Katharina Parry & David P. Watling & Martin L. Hazelton, 2016. "A new class of doubly stochastic day-to-day dynamic traffic assignment models," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 5-23, March.
    14. Ye, Hongbo & Xiao, Feng & Yang, Hai, 2021. "Day-to-day dynamics with advanced traveler information," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 23-44.
    15. Wei, Fangfang & Jia, Ning & Ma, Shoufeng, 2016. "Day-to-day traffic dynamics considering social interaction: From individual route choice behavior to a network flow model," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 335-354.
    16. Wang, Jian & He, Xiaozheng & Peeta, Srinivas, 2016. "Sensitivity analysis based approximation models for day-to-day link flow evolution process," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 35-53.
    17. Watling, David, 1999. "Stability of the stochastic equilibrium assignment problem: a dynamical systems approach," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 281-312, May.
    18. Mohamed Wahba & Amer Shalaby, 2014. "Learning-based framework for transit assignment modeling under information provision," Transportation, Springer, vol. 41(2), pages 397-417, March.
    19. Watling, David, 1998. "Perturbation stability of the asymmetric stochastic equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 155-171, April.
    20. Li, Ruijie & Liu, Xiaobo & Nie, Yu (Marco), 2018. "Managing partially automated network traffic flow: Efficiency vs. stability," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 300-324.

    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:92:y:2016:i:pa:p:3-21. 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.