OPTIMAL TIMETABLES FOR PUBLIC TRANSPORTATION

This paper discusses trip timing by users of public transportation and how a schedule or timetable for transit vehicles should be chosen to best serve demand. The optimal timetable for a given number of public transport vehicles on a single transit line is analyzed in light of the situation where riders differ with respect to the times at which they prefer to travel. Included in the analysis is a consideration of the schedule delay costs the riders incur from traveling earlier or later than desired. The problem of minimizing riders\u27 total schedule delay costs is formulated in continuous time and first-order optimality conditions are identified. The authors derive an explicit solution for the line model in which preferred travel times are uniformly distributed in the population over part of the day and trips cannot be rescheduled between days. This solution is compared with the optimal schedule for circle model in which preferred travel times are uniformly distributed over the full 24-hour day and trips can be rescheduled between days