Train Timetabling Problem for Complex Railway Systems

This paper deals with the design of timetables for complex railway systems. Rail transportation has become a rapid, clean and efficient way to transport passengers and freights. A good timetable design is crucial to ensure the quality of the services trying to improve the efficiency of the whole system. Only such a sustainable transportation system will be in accordance to the requirements of future cities. Underground and commuter railway systems are becoming important backbones in providing access to downtowns and supporting the main pressure to move as many passengers as possible. So the timetable design as part of the capacity problem becomes crucial in providing good performance of the system. In this paper, a new model for solving the train timetabling problem considering general complex rail topologies and general operational policies is developed. This model overcomes some of the limitations of previous models found in the literature, such as their particularization to special topologies of the railway system, the difficulties of dealing with stations with a determined number of tracks or with train services accomplishing different routes and the difficulties of designing completely new timetables for those cases when no initial timetable is given. It also overcomes the difficulties of designing completely new timetables for those cases when no initial timetable is given. The model proposed yields to a large-scale combinatorial problem that is directly solved as a mixed integer programming problem.