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Modeling distribution tail in network performance assessment: A mean-excess total travel time risk measure and analytical estimation method

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  • Xu, Xiangdong
  • Chen, Anthony
  • Cheng, Lin
  • Lo, Hong K.

Abstract

Risk measures are often used by decision makers (DMs) as a scalar risk characterization by integrating the statistical characteristics of risk as well as the DMs’ risk strategy towards uncertainty. A good risk measure typically needs to have a risk preference control mechanism, a complete uncertainty characterization, and a practical implementation strategy. Total travel time reliability (TTTR) and total travel time budget (TTTB) are two risk measures recently proposed for assessing transportation network performance under uncertainty. In this paper, we propose the mean-excess total travel time (METTT) as an alternative network-wide risk measure to more cost-effectively capture the distribution tail, and develop an analytical method to estimate risk measures without knowing the explicit distribution form of TTT uncertainty. Methodologically, the METTT measure characterizes the distribution tail of exceeding the TTTB via the conditional expectation without requiring an extraordinary reliability level. It is able to account for the tradeoff between planners’ risk-aversion attitude and the unacceptable risk, which avoids the need of setting a too conservative reliability requirement in the TTTB to reduce the unacceptable risk. The explicit distribution tail consideration in the METTT could lower the construction cost and substantially reduce the unacceptable risk of network capacity enhancement under uncertainty. To enhance the practicality of METTT, we develop an analytical estimation method to efficiently calculate the METTT by using the first four TTT moments as well as the planners’ risk attitude. The TTTR and TTTB measures can also be analytically estimated as a byproduct of the proposed method for assessing the METTT. The analytical feature of the proposed method avoids the burdensome computation of simulation method and also circumvents the need of fitting the explicit TTT distribution form. Numerical results indicate that the proposed method has a desirable and comparable estimation quality in comparison with the theoretical derivation and curve fitting methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:66:y:2014:i:c:p:32-49
    DOI: 10.1016/j.trb.2013.09.011
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    Cited by:

    1. 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.
    2. Li, Baibing, 2019. "Measuring travel time reliability and risk: A nonparametric approach," Transportation Research Part B: Methodological, Elsevier, vol. 130(C), pages 152-171.
    3. 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).
    4. Jie Liu & Paul Schonfeld & Jinqu Chen & Yong Yin & Qiyuan Peng, 2021. "Perceived Trip Time Reliability and Its Cost in a Rail Transit Network," Sustainability, MDPI, vol. 13(13), pages 1-22, July.
    5. 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.
    6. Saif Eddin Jabari & Nikolaos M. Freris & Deepthi Mary Dilip, 2020. "Sparse Travel Time Estimation from Streaming Data," Transportation Science, INFORMS, vol. 54(1), pages 1-20, January.
    7. Xu, Xiangdong & Chen, Anthony & Wong, S.C. & Cheng, Lin, 2015. "Selection bias in build-operate-transfer transportation project appraisals," Transportation Research Part A: Policy and Practice, Elsevier, vol. 75(C), pages 245-251.
    8. Xu, Xiangdong & Chen, Anthony & Cheng, Lin & Yang, Chao, 2017. "A link-based mean-excess traffic equilibrium model under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 53-75.
    9. Shuang Wang & Jing Lu & Liping Jiang, 2019. "Time Reliability of the Maritime Transportation Network for China’s Crude Oil Imports," Sustainability, MDPI, vol. 12(1), pages 1-18, December.
    10. 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.
    11. Xiangfeng Ji & Xuegang (Jeff) Ban & Mengtian Li & Jian Zhang & Bin Ran, 2017. "Non-expected Route Choice Model under Risk on Stochastic Traffic Networks," Networks and Spatial Economics, Springer, vol. 17(3), pages 777-807, September.
    12. Jing, Weiwei & Xu, Xiangdong & Pu, Yichao, 2020. "Route redundancy-based approach to identify the critical stations in metro networks: A mean-excess probability measure," Reliability Engineering and System Safety, Elsevier, vol. 204(C).

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