IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v20y2020i3d10.1007_s11067-020-09498-2.html
   My bibliography  Save this article

Arrival Time Reliability in Strategic User Equilibrium

Author

Listed:
  • Michael W. Levin

    (University of Minnesota)

  • Melissa Duell

    (University of Minnesota
    School of Civil & Environmental Engineering University of New South Wales)

  • S. Travis Waller

    (University of Minnesota
    School of Civil & Environmental Engineering University of New South Wales)

Abstract

Although traffic assignment models remain heavily utilized globally for the planning and evaluation of new transport infrastructure, commonly applied assignment approaches continue to make very restrictive assumptions regarding determinism and perfect system knowledge to achieve regional scalability. Strategic user equilibrium (StrUE) has been previously proposed as a computationally scalable network assignment model which incorporates demand variability and expectation-minimizing traveler behavior. The proposed model extends the StrUE model to account for travel time penalties thereby enhancing the travel behavioral assumptions which are critical for reliability analyses. Under mild assumptions, we show that the path arrival time penalty is additive by link, allowing us to formulate traffic assignment as a convex program. Furthermore, we show that strategic user equilibrium results in expected link travel times that differ significantly from those predicted by user equilibrium. Finally, the expected arrival time penalties are shown to deviate non-uniformly by link, thereby having diverse impacts on traveler route choice.

Suggested Citation

  • Michael W. Levin & Melissa Duell & S. Travis Waller, 2020. "Arrival Time Reliability in Strategic User Equilibrium," Networks and Spatial Economics, Springer, vol. 20(3), pages 803-831, September.
    • Handle: RePEc:kap:netspa:v:20:y:2020:i:3:d:10.1007_s11067-020-09498-2
    DOI: 10.1007/s11067-020-09498-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11067-020-09498-2
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-020-09498-2?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. Steven A. Gabriel & David Bernstein, 1997. "The Traffic Equilibrium Problem with Nonadditive Path Costs," Transportation Science, INFORMS, vol. 31(4), pages 337-348, November.
    2. 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.
    3. Anselmo Ramalho Pitombeira-Neto & Carlos Felipe Grangeiro Loureiro & Luis Eduardo Carvalho, 2020. "A Dynamic Hierarchical Bayesian Model for the Estimation of day-to-day Origin-destination Flows in Transportation Networks," Networks and Spatial Economics, Springer, vol. 20(2), pages 499-527, June.
    4. Khani, Alireza & Boyles, Stephen D., 2015. "An exact algorithm for the mean–standard deviation shortest path problem," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 252-266.
    5. 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.
    6. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, February.
    7. 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.
    8. Avinash Unnikrishnan & Steven Waller, 2009. "User Equilibrium with Recourse," Networks and Spatial Economics, Springer, vol. 9(4), pages 575-593, December.
    9. Liu, Yang & Nie, Yu (Marco), 2011. "Morning commute problem considering route choice, user heterogeneity and alternative system optima," Transportation Research Part B: Methodological, Elsevier, vol. 45(4), pages 619-642.
    10. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    11. 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.
    12. Nie, Yu (Marco), 2010. "A class of bush-based algorithms for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 73-89, January.
    13. Pitu Mirchandani & Hossein Soroush, 1987. "Generalized Traffic Equilibrium with Probabilistic Travel Times and Perceptions," Transportation Science, INFORMS, vol. 21(3), pages 133-152, August.
    14. Clark, Stephen & Watling, David, 2005. "Modelling network travel time reliability under stochastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 119-140, February.
    15. Watling, David, 2006. "User equilibrium traffic network assignment with stochastic travel times and late arrival penalty," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1539-1556, December.
    16. Lo, Hong K. & Luo, X.W. & Siu, Barbara W.Y., 2006. "Degradable transport network: Travel time budget of travelers with heterogeneous risk aversion," Transportation Research Part B: Methodological, Elsevier, vol. 40(9), pages 792-806, November.
    17. Bliemer, Michiel C. J. & Bovy, Piet H. L., 2003. "Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 501-519, July.
    18. Bell, Michael G. H., 2000. "A game theory approach to measuring the performance reliability of transport networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(6), pages 533-545, August.
    19. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    20. Xie, Chi & Liu, Zugang, 2014. "On the stochastic network equilibrium with heterogeneous choice inertia," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 90-109.
    21. Bar-Gera, Hillel, 2010. "Traffic assignment by paired alternative segments," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1022-1046, September.
    22. W. Szeto & L. O'Brien & M. O'Mahony, 2006. "Risk-Averse Traffic Assignment with Elastic Demands: NCP Formulation and Solution Method for Assessing Performance Reliability," Networks and Spatial Economics, Springer, vol. 6(3), pages 313-332, September.
    23. S. Waller & David Fajardo & Melissa Duell & Vinayak Dixit, 2013. "Linear Programming Formulation for Strategic Dynamic Traffic Assignment," Networks and Spatial Economics, Springer, vol. 13(4), pages 427-443, December.
    24. Lo, Hong K. & Tung, Yeou-Koung, 2003. "Network with degradable links: capacity analysis and design," Transportation Research Part B: Methodological, Elsevier, vol. 37(4), pages 345-363, May.
    25. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
    26. W. Burke Jackson & James V. Jucker, 1982. "An Empirical Study of Travel Time Variability and Travel Choice Behavior," Transportation Science, INFORMS, vol. 16(4), pages 460-475, November.
    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. Liang Shen & Feiran Wang & Yueyuan Chen & Xinyi Lv & Zongliang Wen, 2022. "A Reliability-Based Stochastic Traffic Assignment Model for Signalized Traffic Network with Consideration of Link Travel Time Correlations," Sustainability, MDPI, vol. 14(21), pages 1-18, November.

    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. Zhaoqi Zang & Xiangdong Xu & Kai Qu & Ruiya Chen & Anthony Chen, 2022. "Travel time reliability in transportation networks: A review of methodological developments," Papers 2206.12696, arXiv.org, revised Jul 2022.
    2. Prakash, A. Arun & Seshadri, Ravi & Srinivasan, Karthik K., 2018. "A consistent reliability-based user-equilibrium problem with risk-averse users and endogenous travel time correlations: Formulation and solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 171-198.
    3. Wang, Judith Y.T. & Ehrgott, Matthias & Chen, Anthony, 2014. "A bi-objective user equilibrium model of travel time reliability in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 4-15.
    4. Chen, Anthony & Zhou, Zhong, 2010. "The [alpha]-reliable mean-excess traffic equilibrium model with stochastic travel times," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 493-513, May.
    5. Chen, Anthony & Zhou, Zhong & Lam, William H.K., 2011. "Modeling stochastic perception error in the mean-excess traffic equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1619-1640.
    6. Teppei Kato & Kenetsu Uchida & William H. K. Lam & Agachai Sumalee, 2021. "Estimation of the value of travel time and of travel time reliability for heterogeneous drivers in a road network," Transportation, Springer, vol. 48(4), pages 1639-1670, August.
    7. Xie, Chi & Liu, Zugang, 2014. "On the stochastic network equilibrium with heterogeneous choice inertia," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 90-109.
    8. Connors, Richard D. & Sumalee, Agachai, 2009. "A network equilibrium model with travellers' perception of stochastic travel times," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 614-624, July.
    9. Amirgholy, Mahyar & Gonzales, Eric J., 2017. "Efficient frontier of route choice for modeling the equilibrium under travel time variability with heterogeneous traveler preferences," Economics of Transportation, Elsevier, vol. 11, pages 1-14.
    10. Li-Jun Tian & Hai-Jun Huang & Zi-You Gao, 2012. "A Cumulative Perceived Value-Based Dynamic User Equilibrium Model Considering the Travelers’ Risk Evaluation on Arrival Time," Networks and Spatial Economics, Springer, vol. 12(4), pages 589-608, December.
    11. 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.
    12. Xiangdong Xu & Anthony Chen & Lin Cheng, 2013. "Assessing the effects of stochastic perception error under travel time variability," Transportation, Springer, vol. 40(3), pages 525-548, May.
    13. 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.
    14. Xiangfeng Ji & Xuegang (Jeff) Ban & Mengtian Li & Jian Zhang & Bin Ran, 2017. "Non-expected Route Choice Model under Risk on Stochastic Traffic Networks," Networks and Spatial Economics, Springer, vol. 17(3), pages 777-807, September.
    15. Ehrgott, Matthias & Wang, Judith Y.T. & Watling, David P., 2015. "On multi-objective stochastic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 704-717.
    16. Ng, ManWo & Waller, S. Travis, 2010. "A computationally efficient methodology to characterize travel time reliability using the fast Fourier transform," Transportation Research Part B: Methodological, Elsevier, vol. 44(10), pages 1202-1219, December.
    17. Xu, Xiangdong & Chen, Anthony & Cheng, Lin & Yang, Chao, 2017. "A link-based mean-excess traffic equilibrium model under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 53-75.
    18. 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.
    19. Tan, Zhijia & Yang, Hai & Guo, Renyong, 2014. "Pareto efficiency of reliability-based traffic equilibria and risk-taking behavior of travelers," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 16-31.
    20. Ng, ManWo & Szeto, W.Y. & Travis Waller, S., 2011. "Distribution-free travel time reliability assessment with probability inequalities," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 852-866, July.

    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:kap:netspa:v:20:y:2020:i:3:d:10.1007_s11067-020-09498-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.