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Distribution-free travel time reliability assessment with probability inequalities

Author

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  • Ng, ManWo
  • Szeto, W.Y.
  • Travis Waller, S.

Abstract

An assumption that pervades the current transportation system reliability assessment literature is that probability distributions of the sources of uncertainty are known explicitly. However, this distribution may be unavailable (inaccurate) in reality as we may have no (insufficient) data to calibrate the distribution. In this paper we relax this assumption and present a new method to assess travel time reliability that is distribution-free in the sense that the methodology only requires that the first N moments (where N is a user-specified positive integer) of the travel time to be known and that the travel times reside in a set of bounded and known intervals. Because of our modeling approach, all sources of uncertainty are automatically accounted for, as long as they are statistically independent. Instead of deriving exact probabilities on travel times exceeding certain thresholds via computationally intensive methods, we develop semi-analytical probability inequalities to quickly (i.e. within a fraction of a second) obtain upper bounds on the desired probability. Numerical experiments suggest that the inclusion of higher order moments can potentially significantly improve the bounds. The case study also demonstrates that the derived bounds are nontrivial for a large range of travel time values.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:transb:v:45:y:2011:i:6:p:852-866
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Ng, ManWo & Khattak, Asad & Talley, Wayne K., 2013. "Modeling the time to the next primary and secondary incident: A semi-Markov stochastic process approach," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 44-57.
    2. ManWo Ng & Hong Lo, 2013. "Regional Air Quality Conformity in Transportation Networks with Stochastic Dependencies: A Theoretical Copula-Based Model," Networks and Spatial Economics, Springer, vol. 13(4), pages 373-397, December.
    3. 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.
    4. He, Sheng-xue, 2013. "A graphical approach to identify sensor locations for link flow inference," Transportation Research Part B: Methodological, Elsevier, vol. 51(C), pages 65-76.
    5. Yin, Kai & Wang, Wen & Bruce Wang, Xiubin & Adams, Teresa M., 2015. "Link travel time inference using entry/exit information of trips on a network," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 303-321.
    6. Hamdouch, Younes & Szeto, W.Y. & Jiang, Y., 2014. "A new schedule-based transit assignment model with travel strategies and supply uncertainties," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 35-67.
    7. 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.
    8. Ng, ManWo, 2012. "Synergistic sensor location for link flow inference without path enumeration: A node-based approach," Transportation Research Part B: Methodological, Elsevier, vol. 46(6), pages 781-788.

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