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Integrating the mean–variance and scheduling approaches to allow for schedule delay and trip time variability under uncertainty

Listed author(s):
  • Li, Hao
  • Tu, Huizhao
  • Hensher, David A.

Uncertainty of travel times and the impact on travel choice behavior has been recognized as an increasingly important research direction in the past decade. This paper proposes an extension to the popular scheduling approach to model traveler’s departure time choice behavior under uncertainty, with the main focus on a richer representation of uncertainty. This more general approach incorporates a separate term to reflect the risk aversion associated with uncertainty. Recognizing the correlation between expected schedule delay and travel time variability, the schedule delay components in the generalized approach are defined in terms of expected travel time, which differs from the scheduling approach. This approach is developed based on the analytical investigation of the relationship between the expected schedule delay and the mean and standard deviation of travel time. An analytical equivalence was found between the scheduling approach and the general approach given a departure time t. To investigate the empirical performance of the generalized approach, two state preference (SP) data sets are used; one from China with a symmetric travel time distribution and the other from Australia with an asymmetric distribution. Both studies show empirical evidence of an equivalence in respect of statistical fit between the generalized and the scheduling approaches, as found from analytical investigations. The Chinese study gives support in the generalized model to including both the mean–variance and the scheduling effects; whereas the Australian study finds only the mean–variance specification has statistical merit. Despite the different travel contexts, it is noteworthy in both empirical settings, that the parameter estimate for arriving earlier than the preferred arrival time (PAT) in the generalized model is positive. This suggests that commuters tend to prefer to arrive earlier in order to guarantee he/she will not be late. This paper contributes to a better understanding of performances of different reliability measures and their relationships. The practical value of the various unreliability measures is provided showing that these indicators are easy to obtain for inclusion in project appraisal.

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Article provided by Elsevier in its journal Transportation Research Part A: Policy and Practice.

Volume (Year): 89 (2016)
Issue (Month): C ()
Pages: 151-163

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Handle: RePEc:eee:transa:v:89:y:2016:i:c:p:151-163
DOI: 10.1016/j.tra.2016.05.014
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  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. 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.
  3. Erel Avineri & Joseph Prashker, 2006. "The Impact of Travel Time Information on Travelers’ Learning under Uncertainty," Transportation, Springer, vol. 33(4), pages 393-408, July.
  4. Hensher, David A. & Greene, William H. & Li, Zheng, 2011. "Embedding risk attitude and decision weights in non-linear logit to accommodate time variability in the value of expected travel time savings," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 954-972, August.
  5. Tu, Huizhao & Li, Hao & van Lint, Hans & van Zuylen, Henk, 2012. "Modeling travel time reliability of freeways using risk assessment techniques," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(10), pages 1528-1540.
  6. Fosgerau, Mogens, 2010. "On the relation between the mean and variance of delay in dynamic queues with random capacity and demand," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 598-603, April.
  7. Fosgerau, Mogens & Karlström, Anders, 2010. "The value of reliability," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 38-49, January.
  8. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
  9. Noland, Robert B. & Small, Kenneth A. & Koskenoja, Pia Maria & Chu, Xuehao, 1998. "Simulating travel reliability," Regional Science and Urban Economics, Elsevier, vol. 28(5), pages 535-564, September.
  10. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-479, June.
  11. Rose, John M. & Bliemer, Michiel C.J. & Hensher, David A. & Collins, Andrew T., 2008. "Designing efficient stated choice experiments in the presence of reference alternatives," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 395-406, May.
  12. 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.
  13. Robert B. Noland & John W. Polak, 2002. "Travel time variability: A review of theoretical and empirical issues," Transport Reviews, Taylor & Francis Journals, vol. 22(1), pages 39-54, January.
  14. de Palma, André & Picard, Nathalie, 2005. "Route choice decision under travel time uncertainty," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(4), pages 295-324, May.
  15. Dirk van Amelsfort & Piet Bovy & Michiel Bliemer & Barry Ubbels, 2008. "Travellers’ Responses to Road Pricing: Value of Time, Schedule Delay and Unreliability," Chapters,in: Pricing in Road Transport, chapter 4 Edward Elgar Publishing.
  16. 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.
  17. Hensher,David A. & Rose,John M. & Greene,William H., 2015. "Applied Choice Analysis," Cambridge Books, Cambridge University Press, number 9781107465923.
  18. David A. Hensher & Zheng Li, 2012. "Valuing Travel Time Variability within a Rank-Dependent Utility Framework and an Investigation of Unobserved Taste Heterogeneity," Journal of Transport Economics and Policy, University of Bath, vol. 46(2), pages 293-312, May.
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