Expected Passenger Travel Time for Train Schedule Evaluation and Optimization

When evaluating and optimizing the national railway timetable for all passenger trains in Belgium, we use the criterium of expected total passenger travel time in practice. During evaluation, we measure this, during optimization, we try to minimize this. The focus in this paper is to analytically derive the total passenger time as a stochastic function of the schedule. In a previous paper [9], we already derived the necessary local passenger flows from ticket sales data. These flows will serve as fixed weights in this new objective function. We start from measured delays in the current schedule and assume that they can be described well by a negative exponential distribution. In the case of constructing an optimized schedule, we assume delays will also occur in the new schedule according to the same distribution. We believe this is a conservative assumption, since the optimized schedule will be more robust against delays. We then decompose the global schedule of actions into local actions or pairs of subsequent actions, and derive probabilities and objective functions on the corresponding one or two local actions only. We sum these local functions to obtain a global objective function. This then becomes the schedules’ global quality criterium. We linearize this and use the result as the objective function of a linear programming based optimizer. With this objective function, we optimized the train schedule for the Belgian railways, which proves the method is scalable to large and complex real-life problems.status: publishe