Optimal Slack Time for Schedule-Based Transit Operations

In order to improve service reliability, many transit agencies add a significant amount of slack in the schedule. However, too much slack in the schedule reduces service frequency. We study the problem of determining the optimal slack that minimizes the passengers’ expected waiting times under schedule-based control. By associating with 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.