IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v166y2022icp374-395.html
   My bibliography  Save this article

Can day-to-day dynamic model be solved analytically? New insights on portraying equilibrium and accommodating autonomous vehicles

Author

Listed:
  • Li, Pengbo
  • Tian, Lijun
  • Xiao, Feng
  • Zhu, Hongwei

Abstract

This paper develops a new approach to portray the equilibrium and analyze the appropriate lane policy during different deployment stages of autonomous vehicles (AVs) by innovatively integrating Vickrey's bottleneck model into the day-to-day dynamic model. The travel cost function in the classical bottleneck model is described by considering the impact of AVs’ value of time (VOT) reduction and AV gain. The evolution of lane choice behaviors is described using the first-order and second-order day-to-day dynamic model. Furthermore, three lane policies are proposed to accommodate AVs’ development, and the properties for the endogenous market penetration of AVs and travel cost under three lane policies are examined to recognize which policy is more suitable at different development stages of AVs. The results demonstrate that such equilibrium solutions as traffic flow, total travel cost, the convergence time are all analytically solvable and thus can perfectly answer the problem of stability and convergence involved in the day-to-day dynamic model. Finally, the numerical analysis is conducted to verify the previous findings and get some intuitive insights on system performance. This work not only provides new insights on the evolutionary process of AVs’ and regular vehicles (RVs)’ lane choice behaviors, but also recognizes appropriate lane policy to accommodate AVs from a novel perspective.

Suggested Citation

  • Li, Pengbo & Tian, Lijun & Xiao, Feng & Zhu, Hongwei, 2022. "Can day-to-day dynamic model be solved analytically? New insights on portraying equilibrium and accommodating autonomous vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 374-395.
    • Handle: RePEc:eee:transb:v:166:y:2022:i:c:p:374-395
    DOI: 10.1016/j.trb.2022.11.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261522001849
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2022.11.003?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. Ren-Yong Guo & Hai Yang & Hai-Jun Huang & Zhijia Tan, 2016. "Day-to-Day Flow Dynamics and Congestion Control," Transportation Science, INFORMS, vol. 50(3), pages 982-997, August.
    2. Huang, Hai-Jun & Lam, William H. K., 2002. "Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 253-273, March.
    3. Luo, Qi & Saigal, Romesh & Chen, Zhibin & Yin, Yafeng, 2019. "Accelerating the adoption of automated vehicles by subsidies: A dynamic games approach," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 226-243.
    4. Shi, Xiaowei & Li, Xiaopeng, 2021. "Constructing a fundamental diagram for traffic flow with automated vehicles: Methodology and demonstration," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 279-292.
    5. Wang, Jian & Peeta, Srinivas & He, Xiaozheng, 2019. "Multiclass traffic assignment model for mixed traffic flow of human-driven vehicles and connected and autonomous vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 139-168.
    6. Yang, Fan & Zhang, Ding, 2009. "Day-to-day stationary link flow pattern," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 119-126, January.
    7. Tian, Li-Jun & Sheu, Jiuh-Biing & Huang, Hai-Jun, 2019. "The morning commute problem with endogenous shared autonomous vehicle penetration and parking space constraint," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 258-278.
    8. Jin, Wen-Long, 2021. "Stable local dynamics for day-to-day departure time choice," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 463-479.
    9. Smith, M. J., 1983. "The existence and calculation of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 17(4), pages 291-303, August.
    10. 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.
    11. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    12. Ghiasi, Amir & Hussain, Omar & Qian, Zhen (Sean) & Li, Xiaopeng, 2017. "A mixed traffic capacity analysis and lane management model for connected automated vehicles: A Markov chain method," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 266-292.
    13. Michael J. Smith, 1984. "The Stability of a Dynamic Model of Traffic Assignment---An Application of a Method of Lyapunov," Transportation Science, INFORMS, vol. 18(3), pages 245-252, August.
    14. 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.
    15. Hani S. Mahmassani, 2016. "50th Anniversary Invited Article—Autonomous Vehicles and Connected Vehicle Systems: Flow and Operations Considerations," Transportation Science, INFORMS, vol. 50(4), pages 1140-1162, November.
    16. Ye, Hongbo & Yang, Hai, 2013. "Continuous price and flow dynamics of tradable mobility credits," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 436-450.
    17. 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.
    18. Terry L. Friesz & David Bernstein & Nihal J. Mehta & Roger L. Tobin & Saiid Ganjalizadeh, 1994. "Day-To-Day Dynamic Network Disequilibria and Idealized Traveler Information Systems," Operations Research, INFORMS, vol. 42(6), pages 1120-1136, December.
    19. van den Berg, Vincent A.C. & Verhoef, Erik T., 2016. "Autonomous cars and dynamic bottleneck congestion: The effects on capacity, value of time and preference heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 43-60.
    20. Sala, Marcel & Soriguera, Francesc, 2021. "Capacity of a freeway lane with platoons of autonomous vehicles mixed with regular traffic," Transportation Research Part B: Methodological, Elsevier, vol. 147(C), pages 116-131.
    21. 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.
    22. Xiao, Ling-Ling & Liu, Tian-Liang & Huang, Hai-Jun, 2016. "On the morning commute problem with carpooling behavior under parking space constraint," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 383-407.
    23. Zhang, Ding & Nagurney, Anna, 1996. "On the local and global stability of a travel route choice adjustment process," Transportation Research Part B: Methodological, Elsevier, vol. 30(4), pages 245-262, August.
    24. Kumar, Amit & Peeta, Srinivas, 2015. "A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 235-256.
    25. Bie, Jing & Lo, Hong K., 2010. "Stability and attraction domains of traffic equilibria in a day-to-day dynamical system formulation," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 90-107, January.
    26. Rapoport, Amnon & Gisches, Eyran J. & Daniel, Terry & Lindsey, Robin, 2014. "Pre-trip information and route-choice decisions with stochastic travel conditions: Experiment," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 154-172.
    27. Chen, Danjue & Ahn, Soyoung & Chitturi, Madhav & Noyce, David A., 2017. "Towards vehicle automation: Roadway capacity formulation for traffic mixed with regular and automated vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 196-221.
    28. 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.
    29. Yang, Hai & Kitamura, Ryuichi & Jovanis, Paul P. & Vaughn, Kenneth M. & Abdel-aty, Mohammed A. & Reddy, Prasuna Dvg, 1993. "Exploration Of Driver Route Choice With Advanced Traveler Information Using Neural Network Concepts," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt53d2t6df, Institute of Transportation Studies, UC Berkeley.
    30. Wen-Long Jin, 2020. "Stable Day-to-Day Dynamics for Departure Time Choice," Transportation Science, INFORMS, vol. 54(1), pages 42-61, January.
    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. 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. Ren-Yong Guo & Hai Yang & Hai-Jun Huang & Zhijia Tan, 2016. "Day-to-Day Flow Dynamics and Congestion Control," Transportation Science, INFORMS, vol. 50(3), pages 982-997, August.
    3. 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.
    4. Peeta, Srinivas, 2016. "A marginal utility day-to-day traffic evolution model based on one-step strategic thinkingAuthor-Name: He, Xiaozheng," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 237-255.
    5. Han, Linghui & Wang, David Z.W. & Lo, Hong K. & Zhu, Chengjuan & Cai, Xingju, 2017. "Discrete-time day-to-day dynamic congestion pricing scheme considering multiple equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 1-16.
    6. Ren-Yong Guo & Hai-Jun Huang & Hai Yang, 2019. "Tradable Credit Scheme for Control of Evolutionary Traffic Flows to System Optimum: Model and its Convergence," Networks and Spatial Economics, Springer, vol. 19(3), pages 833-868, September.
    7. 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.
    8. 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.
    9. Feng Xiao & Minyu Shen & Zhengtian Xu & Ruijie Li & Hai Yang & Yafeng Yin, 2019. "Day-to-Day Flow Dynamics for Stochastic User Equilibrium and a General Lyapunov Function," Transportation Science, INFORMS, vol. 53(3), pages 683-694, May.
    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. Iryo, Takamasa, 2019. "Instability of departure time choice problem: A case with replicator dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 353-364.
    13. Kumar, Amit & Peeta, Srinivas, 2015. "A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 235-256.
    14. 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.
    15. Xiaomei Zhao & Chunhua Wan & Jun Bi, 2019. "Day-to-Day Assignment Models and Traffic Dynamics Under Information Provision," Networks and Spatial Economics, Springer, vol. 19(2), pages 473-502, June.
    16. 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.
    17. 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.
    18. Watling, David P., 2016. "A route-swapping dynamical system and Lyapunov function for stochastic user equilibriumAuthor-Name: Smith, Michael J," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 132-141.
    19. Lie Han, 2022. "Proportional-Switch Adjustment Process with Elastic Demand and Congestion Toll in the Absence of Demand Functions," Networks and Spatial Economics, Springer, vol. 22(4), pages 709-735, December.
    20. Ye, Hongbo & Yang, Hai, 2013. "Continuous price and flow dynamics of tradable mobility credits," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 436-450.

    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:166:y:2022:i:c:p:374-395. 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.