Optimal Time Point Locations on a Markovian Bus Route

Abstract

Transit agencies struggle daily with the randomness experienced by vehicles as they traverse their routes. Since reliability is one of the most important factors in determining the quality of a transit system, it is important that agencies use effective and data-informed strategies to combat this randomness as much as possible. One commonly used strategy is holding control, where early buses are held at specifically chosen stops known as time points. This strategy presents a trade-off between improved reliability and longer overall travel time, and leads to the central research question: for a route with varied travel times between stops and fluctuating passenger demand, what is the optimal number and location of time points along a route? This thesis develops a mathematical Markov chain model of bus behaviour on an urban bus route which can capture the effects of time point placement and is sensitive to individual inter-stop travel times. After formulating a cost function to account for the various impacts of unreliability on passengers and operators, two algorithms are presented to optimally locate time points, with an improvement on existing configurations used by Calgary Transit in Calgary, Canada. Finally, a simulation model shows that holding control drastically reduces the occurrence of the phenomenon of bus bunching.