Optimal Bus Timetables and Trip Timing Preferences

This paper explores the problem of determining the optimal bus frequency and associated timetable on a single bus route. Bus riders are assumed to differ as to the time at which they want to travel. Each rider selects the bus for which his/her schedule delay cost (the cost of traveling earlier or later than desired) is smallest. The transit planner minimizes the sum of travellers' costs and the cost of the bus fleet. An analytical solution to the optimal number of buses and timetable is derived for the case of a uniform distribution of desired travel times. A numerical solution is then obtained for a nonuniform distribution and compared with the analytical solution.