Distributed architecture for real-time coordination of bus holding in transit networks
IEEE Transactions on Intelligent Transportation Systems
Approximations and bounds for the variance of steady-state waiting times in a GI/G/1 queue
Operations Research Letters
OneBusAway: results from providing real-time arrival information for public transit
Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
Finding the K shortest paths in a schedule-based transit network
Computers and Operations Research
Bus bunching detection by mining sequences of headway deviations
ICDM'12 Proceedings of the 12th Industrial conference on Advances in Data Mining: applications and theoretical aspects
Finding interesting contexts for explaining deviations in bus trip duration using distribution rules
IDA'12 Proceedings of the 11th international conference on Advances in Intelligent Data Analysis
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To improve service reliability, many transit agencies include significant amounts of slack in the schedule. However, too much slack in the schedule reduces service frequency, given a fixed vehicle fleet size. We study the problem of determining the optimal slack that minimizes the passengers' expected waiting times under schedule-based control. By applying a D/G/c queue model, we show that the system is stable if slack is added in the schedule. For a single-bus loop transit network, we derive convexity of mean and variance of bus delays and provide an exact solution if the travel time is exponentially distributed. For the case of multiple buses and other travel time distributions, we provide several approximation approaches and compare them to simulation results. The simulation results show that our approximations are good for interval of appropriate slack, which often contains the optimal value.