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Traffic equilibrium with a continuously distributed bound on travel weights: the rise of range anxiety and mental account

Author

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  • Chi Xie

    (Tongji University
    Tongji University)

  • Xing Wu

    (Lamar University)

  • Stephen Boyles

    (University of Texas at Austin)

Abstract

A new traffic network equilibrium problem with continuously distributed bounds on path weights is introduced in this paper, as an emerging modeling tool for evaluating traffic networks in which the route choice behavior of individual motorists is subject to some physical or psychological upper limit of a travel weight. Such a problem may arise from at least two traffic network instances. First, in a traffic network serving electric vehicles, the driving range of these vehicles is subject to a distance constraint formed by onboard battery capacities and electricity consumption rates as well as network-wide battery-recharging opportunities, which cause the range anxiety issue in the driving population. Second, in a tolled traffic network, while drivers take into account both travel time and road toll in their route choice decisions, many of them implicitly or explicitly set a budget constraint in their mental account for toll expense, subject to their own income levels and other personal and household socio-economic factors. In both cases, we model the upper limit of the path travel weight (i.e., distance or toll) as a continuously distributed stochastic parameter across the driving population, to reflect the diverse heterogeneity of vehicle- and/or motorist-related travel characteristics. For characterizing this weight-constrained network equilibrium problem, we proposed a convex programming model with a finite number of constraints, on the basis of a newly introduced path flow variable named interval path flow rate. We also analyzed the problem’s optimality conditions for the case of path distance limits, and studied the existence of optimal tolls for the case of path toll limits. A linear approximation algorithm was further developed for this complex network equilibrium problem, which encapsulates an efficient weight-constrained k-minimum time path search procedure to perform the network loading. Numerical results obtained from conducting quantitative analyses on example networks clearly illustrate the applicability of the modeling and solution methods for the proposed problem and reveal the mechanism of stochastic weight limits reshaping the network equilibrium.

Suggested Citation

  • Chi Xie & Xing Wu & Stephen Boyles, 2019. "Traffic equilibrium with a continuously distributed bound on travel weights: the rise of range anxiety and mental account," Annals of Operations Research, Springer, vol. 273(1), pages 279-310, February.
  • Handle: RePEc:spr:annopr:v:273:y:2019:i:1:d:10.1007_s10479-018-2990-0
    DOI: 10.1007/s10479-018-2990-0
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    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. Thaler, Richard H, 1990. "Saving, Fungibility, and Mental Accounts," Journal of Economic Perspectives, American Economic Association, vol. 4(1), pages 193-205, Winter.
    3. Robert B. Dial, 1999. "Network-Optimized Road Pricing: Part II: Algorithms and Examples," Operations Research, INFORMS, vol. 47(2), pages 327-336, April.
    4. Verhoef, Erik T., 2002. "Second-best congestion pricing in general static transportation networks with elastic demands," Regional Science and Urban Economics, Elsevier, vol. 32(3), pages 281-310, May.
    5. Kaj Holmberg & Di Yuan, 2003. "A Multicommodity Network-Flow Problem with Side Constraints on Paths Solved by Column Generation," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 42-57, February.
    6. Robert B. Dial, 1996. "Bicriterion Traffic Assignment: Basic Theory and Elementary Algorithms," Transportation Science, INFORMS, vol. 30(2), pages 93-111, May.
    7. Richard H. Thaler, 2008. "Mental Accounting and Consumer Choice," Marketing Science, INFORMS, vol. 27(1), pages 15-25, 01-02.
    8. Jin Y. Yen, 1971. "Finding the K Shortest Loopless Paths in a Network," Management Science, INFORMS, vol. 17(11), pages 712-716, July.
    9. Verhoef, Erik T., 2002. "Second-best congestion pricing in general networks. Heuristic algorithms for finding second-best optimal toll levels and toll points," Transportation Research Part B: Methodological, Elsevier, vol. 36(8), pages 707-729, September.
    10. Wang, Judith Y.T. & Ehrgott, Matthias, 2013. "Modelling route choice behaviour in a tolled road network with a time surplus maximisation bi-objective user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 342-360.
    11. Franke, Thomas & Krems, Josef F., 2013. "What drives range preferences in electric vehicle users?," Transport Policy, Elsevier, vol. 30(C), pages 56-62.
    12. Xie, Chi & Wang, Tong-Gen & Pu, Xiaoting & Karoonsoontawong, Ampol, 2017. "Path-constrained traffic assignment: Modeling and computing network impacts of stochastic range anxiety," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 136-157.
    13. Larsson, Torbjörn & Patriksson, Michael, 1995. "An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 433-455, December.
    14. (Jeff) Ban, Xuegang & Ferris, Michael C. & Tang, Lisa & Lu, Shu, 2013. "Risk-neutral second best toll pricing," Transportation Research Part B: Methodological, Elsevier, vol. 48(C), pages 67-87.
    15. Andrea Raith & Judith Wang & Matthias Ehrgott & Stuart Mitchell, 2014. "Solving multi-objective traffic assignment," Annals of Operations Research, Springer, vol. 222(1), pages 483-516, November.
    16. Mokhtarian, Patricia L. & Chen, Cynthia, 2004. "TTB or not TTB, that is the question: a review and analysis of the empirical literature on travel time (and money) budgets," Transportation Research Part A: Policy and Practice, Elsevier, vol. 38(9-10), pages 643-675.
    17. Robert B. Dial, 1999. "Network-Optimized Road Pricing: Part I: A Parable and a Model," Operations Research, INFORMS, vol. 47(1), pages 54-64, February.
    18. Gulipalli, Pradeep K. & Kockelman, Kara M., 2008. "Credit-based congestion pricing: A Dallas-Fort Worth application," Transport Policy, Elsevier, vol. 15(1), pages 23-32, January.
    19. Larsson, Torbjörn & Patriksson, Michael, 1999. "Side constrained traffic equilibrium models-- analysis, computation and applications," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 233-264, May.
    20. Olaf Jahn & Rolf H. Möhring & Andreas S. Schulz & Nicolás E. Stier-Moses, 2005. "System-Optimal Routing of Traffic Flows with User Constraints in Networks with Congestion," Operations Research, INFORMS, vol. 53(4), pages 600-616, August.
    21. He, Fang & Yin, Yafeng & Lawphongpanich, Siriphong, 2014. "Network equilibrium models with battery electric vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 306-319.
    22. Zhang, H. M. & Ge, Y. E., 2004. "Modeling variable demand equilibrium under second-best road pricing," Transportation Research Part B: Methodological, Elsevier, vol. 38(8), pages 733-749, September.
    23. 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.
    24. Leurent, Fabien, 1993. "Cost versus time equilibrium over a network," European Journal of Operational Research, Elsevier, vol. 71(2), pages 205-221, December.
    25. H. Yang & S.C. Wong, 1999. "Estimation of the most likely equilibrium traffic queueing pattern in a capacityconstrained network," Annals of Operations Research, Springer, vol. 87(0), pages 73-85, April.
    26. Batarce, Marco & Ivaldi, Marc, 2014. "Urban travel demand model with endogenous congestion," Transportation Research Part A: Policy and Practice, Elsevier, vol. 59(C), pages 331-345.
    27. Larry J. LeBlanc & Richard V. Helgason & David E. Boyce, 1985. "Improved Efficiency of the Frank-Wolfe Algorithm for Convex Network Programs," Transportation Science, INFORMS, vol. 19(4), pages 445-462, November.
    28. Y. Arezki & D. Van Vliet, 1990. "A Full Analytical Implementation of the PARTAN/Frank–Wolfe Algorithm for Equilibrium Assignment," Transportation Science, INFORMS, vol. 24(1), pages 58-62, February.
    29. Zhenhong Lin, 2014. "Optimizing and Diversifying Electric Vehicle Driving Range for U.S. Drivers," Transportation Science, INFORMS, vol. 48(4), pages 635-650, November.
    30. Yang, Hai & Huang, Hai-Jun, 2004. "The multi-class, multi-criteria traffic network equilibrium and systems optimum problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(1), pages 1-15, January.
    31. 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.
    32. Luce Brotcorne & Martine Labbé & Patrice Marcotte & Gilles Savard, 2001. "A Bilevel Model for Toll Optimization on a Multicommodity Transportation Network," Transportation Science, INFORMS, vol. 35(4), pages 345-358, November.
    33. Yang, Hai & Wang, Xiaolei & Yin, Yafeng, 2012. "The impact of speed limits on traffic equilibrium and system performance in networks," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1295-1307.
    34. Lo, Hong K. & Chen, Anthony, 2000. "Traffic equilibrium problem with route-specific costs: formulation and algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 34(6), pages 493-513, August.
    35. Dial, Robert B., 1997. "Bicriterion traffic assignment: Efficient algorithms plus examples," Transportation Research Part B: Methodological, Elsevier, vol. 31(5), pages 357-379, October.
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    3. Anders F. Jensen & Thomas K. Rasmussen & Carlo G. Prato, 2020. "A Route Choice Model for Capturing Driver Preferences When Driving Electric and Conventional Vehicles," Sustainability, MDPI, vol. 12(3), pages 1-18, February.

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