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Distribution-free travel time reliability assessment with probability inequalities

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

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    Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

    Volume (Year): 45 (2011)
    Issue (Month): 6 (July)
    Pages: 852-866

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    Handle: RePEc:eee:transb:v:45:y:2011:i:6:p:852-866
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    1. 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.
    2. Chen, Anthony & Yang, Hai & Lo, Hong K. & Tang, Wilson H., 2002. "Capacity reliability of a road network: an assessment methodology and numerical results," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 225-252, March.
    3. S. Illeris & G. Akehurst, 2002. "Introduction," The Service Industries Journal, Taylor & Francis Journals, vol. 22(1), pages 1-3, January.
    4. 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.
    5. Siu, Barbara W.Y. & Lo, Hong K., 2008. "Doubly uncertain transportation network: Degradable capacity and stochastic demand," European Journal of Operational Research, Elsevier, vol. 191(1), pages 166-181, November.
    6. 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.
    7. 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.
    8. 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.
    9. Du, Zhen-Ping & Nicholson, Alan, 1997. "Degradable transportation systems: Sensitivity and reliability analysis," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 225-237, June.
    10. 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.
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