Review on Statistical Modeling of Travel Time Variability for Road-Based Public Transport

Abstract

Accurately modeling the travel time of road-based public transport can help directly improve current passenger service and operating efficiency. Moreover, it paves the way for control of future high technology automated vehicles, which will share the same characteristics of sharing the road infrastructure with other vehicles; carrying multiple passengers; having a non-negligible dwell process; and run not completely demand-responsive, but in general following a schedule or a target frequency. Recent advances in sensor and communications technology, leading eventually to comprehensive vehicle connectivity, have significantly increased the amount and quality of travel time data available, making it possible to better model distributions of current buses' travel time. We assume that the choice of those distributions with regards to transport performance will hold also in the near future. This paper explains definitions of travel time components and explains how they contribute to variability. It focuses on the description of day-to-day variability, and systematically reviews the current state-of-the-art for statistically modeling bus travel, running, and dwell time distributions. It considers statistical distributions developed based on empirical data from the research literature. Statistical distributions are powerful tools, as they can describe the inherent variability in data with a limited number of parameters. The review finds that both spatial and temporal data aggregation have an important influence on the statistics as well as the choice of the most appropriate probability distribution. This influence is still not well-understood and remains a question for further studies. Furthermore, the review finds that mixture distributions provide good fitting performance. However, it is important to improve the description of components in such distributions to get meaningful and understandable distributions. The methodologies for fitting distributions, for proving if a distribution is suited, and for identifying best fitting, robust, and reproducible distribution should be reconsidered. Such a distribution will enable reporting, controlling operations, and disseminating information to operators and travelers. Finally, this review proposes directions for further work.