Hybrid cyclicity: Combining the benefits of cyclic and non-cyclic timetables

Metro Timetabling for Time-Varying Passenger Demand and Congestion at Stations

“…Their work aims to minimize the total waiting times of passengers at stations. Robenek et al [5] define a timetable as a set of departure times of every train from its origin station on every line and consider four attributes in passenger satisfaction: the invehicle-time, the waiting time at transfers, the number of transfers, and the schedule passenger delay. They describe the hybrid timetables through additional constraints that are imposed on the original passenger centric train timetabling problem [2], so that the passengers would obtain the same level of service as a cyclic timetable, with more flexibility.…”

“…However, in a metro system, passengers usually arrive randomly at stations and wait for the next available train, without checking precise timetables beforehand. Besides, as pointed out by Robenek et al [5], a cyclic timetable provides an inefficient operation as there is a mismatch between the supply (determined by the timetables) and the demand (characterized by the time-varying demand). On the other hand, a noncyclic timetable imposes no special rules on the departure times of trains [6].…”

“…However, since his eigenmodel is general and resulting approaches are generic, important objectives described in this paper are not considered in his work, that is, passenger wait time, dwell time, and train capacity. These objectives are included in [2,5], whereas the frequency and dwell times are fixed in their studies. Besides, energy is not considered in [2,5].…”

“…These objectives are included in [2,5], whereas the frequency and dwell times are fixed in their studies. Besides, energy is not considered in [2,5].…”

“…The first subproblem is solved by branch-and-bound and frequency determining algorithms, and the second one is solved by a rolling optimization algorithm which optimizes the departure headways from the shunting yard (which are equivalent to arrival times of trains at their first station) and considers interdependent variables in each rolling step. The design of decision variables in this paper is similar to [2,5], but the models and solution approaches are different. Compared to Wang et al [3], which addresses the similar timetabling problem with traditional approaches such as sequential quadratic programming and a genetic algorithm, the approach proposed in this paper performs better computationally in terms of run time and solution quality.…”