Bus departure punctuality evaluation under stochastic travel time

The bus operation is significantly affected by its external driving environment, resulting in travel time variation; hence, the evaluation of bus service reliability should consider the influence of travel time variability. This research modeled the propagation of service deviation, which occurred at the start terminal, along the route under stochastic travel time. Three illustrative thresholds were found, namely the threshold of a cumulative directional deviation of dwell time (α), the threshold of an unrecoverable service deviation (β), and the threshold of a deteriorated service deviation (γ). They differentiate the degree of influence of the departure deviation at the start terminal on the service deviations at downstream stops. The theoretical model proved that αn < βn < γn at any stop on the route. With the aggravation of the departure deviation at the start terminal, a cumulative directional deviation of dwell time occurs first, then an unrecoverable service deviation, and finally a deteriorative service deviation. The numerical results showed that αn < βn < min(γ) always holds for any practical bus route with service intensities lower than 0.20 at stops and a route length shorter than 30 km. Therefore, taking α or β to regulate the punctuality of bus departure can prevent the deterioration of service deviation at any stop on the route. At the same time, the threshold α is less sensitive to passenger service intensity than β; thus, choosing α as the evaluation standard can enhance the universality among bus routes with different levels of passenger demand. Finally, to make full use of the self-repair ability of bus routes under stochastic travel time and take into account the flexibility of evaluation thresholds, this study recommended the threshold αN at the end terminal as a practical index to evaluate bus departure punctuality. © 2022 Systems Engineering Society of China. All rights reserved.