Transit passengers' average total trip time can be minimized by employing the schedule that achieves the optimal balance between initial delay (tardiness) and layover time (earliness). To compare different proposed schedules, we carry out a deterministic simulation which uses link times taken from historical data in the order that they originally occurred. The simulation?s arrival and departure times, in general, are not the same as those in the original data because a different schedule is in place. We measure total trip time by tracking deviations between the scheduled and simulation departure times and computing an appropriately weighted sum (reflecting the number of passengers affected by a given deviation).
We consider the number of vehicles serving the route, the number of time-points N, and the scheduled cycle length to be fixed. Schedules are represented by 1-by-N solution vectors whose elements correspond to intervals between scheduled departure times of consecutive time-points. A Modified Steepest Descent (MSD) algorithm is used to search for the optimal solution.
Throughout the project, North Carolina State University's Werewolf A bus route is used as a test case. Twenty-four days of historical data are utilized. Empirical results suggest that the space of feasible solutions may be convex. An optimal solution is identified and verified by a brute force search of all feasible solutions.
