Railway Timetabling with Integrated Passenger Distribution

Timetabling for railway services often aims at optimizing travel times for passengers. At the same time, restricting assumptions on passenger behavior and passenger modeling are made. While research has shown that discrete choice models are suitable to estimate the distribution of passengers on routes, this has not been considered in timetabling yet. We investigate how to integrate a passenger distribution into an optimization framework for timetabling and present two mixed integer linear programs for this problem. Both approaches design timetables and simultaneously find a corresponding passenger distribution on available routes. One model uses a linear distribution model to estimate passenger route choices. The other model uses an integrated simulation framework to approximate a passenger distribution according to the logit model, a commonly used route choice model. We compare both new approaches with three state-of-the-art timetabling methods and a heuristic approach on a set of artificial instances and a partial network of Netherlands Railways (NS). Our experiments provide insights into the impact of considering multiple routes instead of a single route, and of integrated route choice versus predetermined route assignment with respect to the solution quality.