Optimal temporal spreading of alternative trains in order to minimize passenger travel time in practice

In an earlier paper on timetabling, we derived a stochastic objective function for what we consider an ideal timetable: minimal expected passenger travel time in practice. This includes primary delay distributions and a degree of robustness against these via a knock-on delay model. This timetable is ideal for passengers who know the timetable in advance and plan their departure and/or arrival times accordingly. In general, it is considered as a good service to passengers that the different alternatives to get from an origin to a destination are equally spread in time. This is even more important for passengers who are not informed about the timetable or who cannot adapt their time of arrival in the station, for instance because they want to go home as soon as possible after a meeting. Spreading the trains decreases the average waiting time at departure and/or waiting time at arrival. In this paper, we add these terms to the objective function to also provide the advantage of low waiting times before and after the routes in the resulting timetable. We properly balance benefits of spreading the trains with the other objectives included in the objective function. The model solves quickly for a set of 26 trains and 12 sets of alternative routes but still proves to be difficult to solve for bigger instances.status: publishe