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On the value of distribution tail in the valuation of travel time variability

Author

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  • Zhaoqi Zang
  • Richard Batley
  • Xiangdong Xu
  • David Z. W. Wang
Abstract
Extensive empirical studies show that the long distribution tail of travel time and the corresponding unexpected delay can have much more serious consequences than expected or moderate delay. However, the unexpected delay due to the distribution tail of travel time has received limited attention in recent studies of the valuation of travel time variability. As a complement to current valuation research, this paper proposes the concept of the value of travel time distribution tail, which quantifies the value that travelers place on reducing the unexpected delay for hedging against travel time variability. Methodologically, we define the summation of all unexpected delays as the unreliability area to quantify travel time distribution tail and show that it is a key element of two well-defined measures accounting for unreliable aspects of travel time. We then formally derive the value of distribution tail, show that it is distinct from the more established value of reliability (VOR), and combine it and the VOR in an overall value of travel time variability (VOV). We prove theoretically that the VOV exhibits diminishing marginal benefit in terms of the traveler's punctuality requirements under a validity condition. This implies that it may be economically inefficient for travelers to blindly pursue a higher probability of not being late. We then proceed to develop the concept of the travel time variability ratio, which gives the implicit cost of the punctuality requirement imposed on any given trip. Numerical examples reveal that the cost of travel time distribution tail can account for more than 10% of the trip cost, such that its omission could introduce non-trivial bias into route choice models and transportation appraisal more generally.

Suggested Citation

  • Zhaoqi Zang & Richard Batley & Xiangdong Xu & David Z. W. Wang, 2022. "On the value of distribution tail in the valuation of travel time variability," Papers 2207.06293, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2207.06293
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    References listed on IDEAS

    as
    1. Hollander, Yaron, 2006. "Direct versus indirect models for the effects of unreliability," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(9), pages 699-711, November.
    2. 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.
    3. de Jong, Gerard C. & Bliemer, Michiel C.J., 2015. "On including travel time reliability of road traffic in appraisal," Transportation Research Part A: Policy and Practice, Elsevier, vol. 73(C), pages 80-95.
    4. Wu, Xing & (Marco) Nie, Yu, 2011. "Modeling heterogeneous risk-taking behavior in route choice: A stochastic dominance approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(9), pages 896-915, November.
    5. Jenelius, Erik, 2012. "The value of travel time variability with trip chains, flexible scheduling and correlated travel times," Transportation Research Part B: Methodological, Elsevier, vol. 46(6), pages 762-780.
    6. Beaud, Mickael & Blayac, Thierry & Stéphan, Maïté, 2016. "The impact of travel time variability and travelers’ risk attitudes on the values of time and reliability," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 207-224.
    7. van Lint, J.W.C. & van Zuylen, Henk J. & Tu, H., 2008. "Travel time unreliability on freeways: Why measures based on variance tell only half the story," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(1), pages 258-277, January.
    8. 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.
    9. Fosgerau, Mogens & Karlström, Anders, 2010. "The value of reliability," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 38-49, January.
    10. Nikhil Sikka & Paul Hanley, 2013. "What do commuters think travel time reliability is worth? Calculating economic value of reducing the frequency and extent of unexpected delays," Transportation, Springer, vol. 40(5), pages 903-919, September.
    11. Brownstone, David & Small, Kenneth A., 2005. "Valuing time and reliability: assessing the evidence from road pricing demonstrations," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(4), pages 279-293, May.
    12. Kim, Jiwon & Mahmassani, Hani S., 2015. "Compound Gamma representation for modeling travel time variability in a traffic network," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 40-63.
    13. Kenneth A. Small & Clifford Winston & Jia Yan, 2005. "Uncovering the Distribution of Motorists' Preferences for Travel Time and Reliability," Econometrica, Econometric Society, vol. 73(4), pages 1367-1382, July.
    14. Nicolas Coulombel & André de Palma, 2014. "The marginal social cost of travel time variability," Post-Print hal-01100105, HAL.
    15. Liu Su & Changhyun Kwon, 2020. "Risk-Averse Network Design with Behavioral Conditional Value-at-Risk for Hazardous Materials Transportation," Transportation Science, INFORMS, vol. 54(1), pages 184-203, January.
    16. Xiao, Yu & Fukuda, Daisuke, 2015. "On the cost of misperceived travel time variability," Transportation Research Part A: Policy and Practice, Elsevier, vol. 75(C), pages 96-112.
    17. Hall, Randolph W., 1983. "Travel outcome and performance: The effect of uncertainty on accessibility," Transportation Research Part B: Methodological, Elsevier, vol. 17(4), pages 275-290, August.
    18. Orhan FeyzioÄŸlu & Nilay Noyan, 2017. "Risk-averse toll pricing in a stochastic transportation network," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 11(2), pages 133-167.
    19. Fosgerau, Mogens & Engelson, Leonid, 2011. "The value of travel time variance," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 1-8, January.
    20. Leilei Zhang & Tito Homem-de-Mello, 2017. "An Optimal Path Model for the Risk-Averse Traveler," Transportation Science, INFORMS, vol. 51(2), pages 518-535, May.
    21. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-479, June.
    22. 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.
    23. Xu, Xiangdong & Chen, Anthony & Cheng, Lin & Lo, Hong K., 2014. "Modeling distribution tail in network performance assessment: A mean-excess total travel time risk measure and analytical estimation method," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 32-49.
    24. Uchida, Kenetsu, 2014. "Estimating the value of travel time and of travel time reliability in road networks," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 129-147.
    25. Iakovos Toumazis & Changhyun Kwon, 2016. "Worst-Case Conditional Value-at-Risk Minimization for Hazardous Materials Transportation," Transportation Science, INFORMS, vol. 50(4), pages 1174-1187, November.
    26. Li, Zheng & Hensher, David A. & Rose, John M., 2010. "Willingness to pay for travel time reliability in passenger transport: A review and some new empirical evidence," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(3), pages 384-403, May.
    27. Tseng, Yin-Yen & Verhoef, Erik T., 2008. "Value of time by time of day: A stated-preference study," Transportation Research Part B: Methodological, Elsevier, vol. 42(7-8), pages 607-618, August.
    28. Beaud, Mickael & Blayac, Thierry & Stéphan, Maïté, 2016. "The impact of travel time variability and travelers’ risk attitudes on the values of time and reliability," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 207-224.
    29. 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.
    30. Engelson, Leonid & Fosgerau, Mogens, 2020. "Scheduling preferences and the value of travel time information," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 256-265.
    31. Han, Xiao & Yu, Yun & Gao, Zi-You & Zhang, H. Michael, 2021. "The value of pre-trip information on departure time and route choice in the morning commute under stochastic traffic conditions," Transportation Research Part B: Methodological, Elsevier, vol. 152(C), pages 205-226.
    32. Li, Baibing, 2019. "Measuring travel time reliability and risk: A nonparametric approach," Transportation Research Part B: Methodological, Elsevier, vol. 130(C), pages 152-171.
    33. 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).
    34. André de Palma & Robin Lindsey & Nathalie Picard, 2012. "Risk Aversion, the Value of Information, and Traffic Equilibrium," Transportation Science, INFORMS, vol. 46(1), pages 1-26, February.
    35. Zang, Zhaoqi & Xu, Xiangdong & Yang, Chao & Chen, Anthony, 2018. "A closed-form estimation of the travel time percentile function for characterizing travel time reliability," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 228-247.
    36. Shams, Kollol & Asgari, Hamidreza & Jin, Xia, 2017. "Valuation of travel time reliability in freight transportation: A review and meta-analysis of stated preference studies," Transportation Research Part A: Policy and Practice, Elsevier, vol. 102(C), pages 228-243.
    37. Rietveld, P. & Bruinsma, F. R. & van Vuuren, D. J., 2001. "Coping with unreliability in public transport chains: A case study for Netherlands," Transportation Research Part A: Policy and Practice, Elsevier, vol. 35(6), pages 539-559, July.
    38. Lindsey, Robin & Daniel, Terry & Gisches, Eyran & Rapoport, Amnon, 2014. "Pre-trip information and route-choice decisions with stochastic travel conditions: Theory," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 187-207.
    39. Batley, Richard, 2007. "Marginal valuations of travel time and scheduling, and the reliability premium," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(4), pages 387-408, July.
    40. Jenelius, Erik & Mattsson, Lars-Göran & Levinson, David, 2011. "Traveler delay costs and value of time with trip chains, flexible activity scheduling and information," Transportation Research Part B: Methodological, Elsevier, vol. 45(5), pages 789-807, June.
    41. André de Palma & Nathalie Picard, 2006. "Equilibria and Information Provision in Risky Networks with Risk-Averse Drivers," Transportation Science, INFORMS, vol. 40(4), pages 393-408, November.
    42. 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.
    43. 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.
    44. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    45. Zheng Li & Alejandro Tirachini & David A. Hensher, 2012. "Embedding Risk Attitudes in a Scheduling Model: Application to the Study of Commuting Departure Time," Transportation Science, INFORMS, vol. 46(2), pages 170-188, May.
    46. Small, Kenneth A., 2001. "The Value of Pricing," University of California Transportation Center, Working Papers qt0rm449sx, University of California Transportation Center.
    47. 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.
    48. Asensio, Javier & Matas, Anna, 2008. "Commuters' valuation of travel time variability," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(6), pages 1074-1085, November.
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