Transportation Science · 2006 · 143 citations · 14 references
Transport Network AnalysisEngineeringTransportation Systems ModelingQueueing TheoryOn-demand TransportOperations ResearchTrain Timetable OptimizationSystems EngineeringLogisticsTransportation Systems AnalysisCombinatorial OptimizationTransportation EngineeringPublic Transportation ManagementOptimal Slack TimeOptimal SlackInteger ProgrammingQueueing SystemsService FrequencyScheduling ProblemBusinessVehicle Routing ProblemService ReliabilityTransportation Systems
Transit agencies add slack to schedules to improve reliability, but excessive slack reduces service frequency when fleet size is fixed. The study seeks the optimal schedule slack that minimizes passengers’ expected waiting times under schedule-based control. The authors analyze a single‑bus loop network, deriving convex delay properties and an exact solution for exponential travel times, and extend to multiple buses and other distributions with approximation methods validated against simulation. Using a D/G/c queue model, the authors show that adding slack stabilizes the system, and simulations confirm that their approximations accurately capture performance over the slack range that typically contains the optimum.
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.
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