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-today 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.
Transport networks are becoming increasingly large and interconnected. This interconnectivity is a key enabler of accessibility; on the other hand, it results in vulnerability, i.e. reduced performance, in case any specific part is subject to disruptions. We analyse how railway systems are vulnerable to delay, and how delays propagate in railway networks, studying real-life delay propagation phenomena on empirical data, determining real-life impact and delay propagation for the uncommon case of railway disruptions. We take a unique approach by looking at the same system, in two different operating conditions, to disentangle processes and dynamics that are normally present and co-occurring in railway operations. We exploit the unique chance to observe a systematic change in railway operations conditions, without a correspondent system change of infrastructure or timetable, coming from the occurrence of the large-scale disruption at Rastatt, Germany, in 2017. We define new statistical methods able to detect weak signals in the noisy dataset of recorded punctuality for passenger traffic in Switzerland, in the disrupted and undisrupted state, along a period of 1 year. We determine how delay propagation changed, and quantify the heterogeneous, large-scale cascading effects of the Rastatt disruption towards the Swiss network, hundreds of kilometers away. Operational measures of transport performance (i.e. punctuality and delays), while globally being very decreased, had a statistically relevant positive increase (though very geographically heterogeneous) on the Swiss passenger traffic during the disruption period. We identify two factors for this: (1) the reduced delay propagation at an international scale; and (2) to a minor extent, rerouted railway freight traffic; which show to combine linearly in the observed outcomes.
Understanding the variability of bus travel time is a key issue in the optimization of schedules, transit reliability, route choice analysis, and transit simulation. The statistical modeling of bus travel time data is of increasing importance given the increasing availability of data. In this paper, we introduce a novel approach to modeling the day-to-day variability of urban bus running times on a section level. First, the explanatory power of conventionally used distributions is examined, based on likelihood and effect size. We show that a mixture model is a powerful tool to increase fitting performance, but the applied components need to be justified. To overcome this issue, we propose a novel model consisting of two individual characteristic distributions representing either off-peak or peak hour dynamics. The observed running time distribution at every hour of the day can be described as a combination (mixture) of the two dynamics. The proposed time varying model uses a small set of parameters, which are physically interpretable and capable of accurately describing running time distributions. With our modeling approach, we reduce the complexity of mixture models and increase the explanatory power and fit compared with conventional models.
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