Modeling distributions of travel time variability for bus operations

Zhenliang Ma, Luis Ferreira, Mahmoud Mesbah, Sicong Zhu

Research output: Contribution to journalArticleResearchpeer-review

17 Citations (Scopus)


Bus travel time reliability performance influences service attractiveness, operating costs, and system efficiency. Better understanding of the distribution of travel time variability is a prerequisite for reliability analysis. A wide array of empirical studies has been conducted to model distribution of travel times in transport. However, depending on the data tested and approaches applied to examine the fitting performance, different conclusions have been reported. This paper aims to specify the most appropriate distribution model for the day-to-day travel time variability by using a novel evaluation approach and set of performance measures. Two important issues are explored using automatic vehicle location data collected on two typical bus routes over 6 months in Brisbane, namely, data aggregation influences on travel time distribution and comprehensive evaluation of performance of distribution models. The decrease of temporal aggregation of travel times tends to increase the normality of distributions. The spatial aggregation of link travel times would break up the link multimodality distributions for a busway route, but unlike for a non-busway route. The Gaussian mixture models are evaluated as superior to its alternatives in terms of fitting accuracy, robustness, and explanatory power. The reported distribution model shows promise to fit travel times for other services with different operation environments considering its flexibility in fitting symmetric, asymmetric, and multimodal distributions. The improved statistic fitting can support more effective service reliability analysis.

Original languageEnglish
Pages (from-to)6-24
Number of pages19
JournalJournal of Advanced Transportation
Issue number1
Publication statusPublished - 1 Jan 2016
Externally publishedYes


  • bus travel time distribution
  • data aggregation
  • Gaussian mixture models
  • service reliability analysis

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