Optimization of transit scheduling with random travel times

This dissertation is focused on scheduling problems for single-route transit systems that have large uncertainties in the vehicles' travel times. The main purpose is to reduce passengers' average waiting time by optimizing the transit schedules. The research can be divided into three parts.; In the first part, we investigate the application of ITS (Intelligent Transport Systems) technologies to the bus-holding problem. A real-time distributed control approach based on marginal cost calculation is proposed to address the problem. Optimality conditions are discussed. Comparisons between the proposed strategy and other commonly used strategies are done through simulations, which verify the robustness of our algorithm under different transit environments.; In the second part, we study the problem of determining the optimal slack time for schedule-based transit operations to minimize the passengers' expected waiting times. By associating with a D/G/c queue model, we show that the system is stable if slack is added to the schedule. For a single-bus loop transit network, we prove the convexity of the 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.; Next, we extend our results from the previous part to a study on MAST (Mobility Allowance Shuttle Transit) systems. This time, scheduling becomes a key constraint of the problem, and the objective is to maximize the service capacity while maintaining a desired service level measured by the probability of the shuttles' on-time arrivals. A general algorithm framework is presented to solve the problem. We also provide a closed-form approximation to the problem and verify its effectiveness by comparing it to simulation results.