Optimal holding times at transfer stations

Most bus transit systems only offer direct service between a small fraction of the origin/destination pairs that they serve. As a consequence, many travelers must transfer between bus lines to complete their journey. In this paper schedule control policies are created to minimize transfer time under stochastic conditions. We determine how long a bus should be held at a transfer stop in anticipation of the arrival of passengers from connecting bus lines. In general, the total expected waiting time function may have multiple local minima. However, we show there exists at most one non-boundary local minimum point for the special case where arrival times of connecting buses are identically and normally distributed. An application is provided based on bus lines in Los Angeles County's Metropolitan Transportation Agency to evaluate holding time policies.