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

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

36 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)32-49
Number of pages18
JournalTransportation Research Part B: Methodological
Publication statusPublished - 1 Jan 2014
Externally publishedYes


  • Distribution tail
  • Mean-excess total travel time
  • Reliability
  • Risk measure
  • Total travel time

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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