A disjunctive program formulation to generate regular public transit timetables adhering to prioritized planning requirements

Abstract

Timetable regularity, that is, equability of headways, is an important measure for service quality in high frequency public transit systems, assuring an evenly distributed passenger load as well as improving product attractiveness. However, to be feasible during daily operation a timetable may also have to adhere to other planning requirements, such as departure time coordination with other service providers or deliberately short headways to reduce the passenger load of follow-up vehicles. In this article, a disjunctive program formulation combining aspects of two previous optimization models is proposed, to generate regular public transit timetables adhering to planning requirements. The modeled requirements not only allow for the consideration of feasibility constraints from daily operations, but also for the consideration of simultaneous departures for transfer connections, an objective traditionally opposed to regularity. To show its applicability the approach is applied to two models of artificial transit networks as well as to models of the public transit network of Cologne, Germany. The results show that the proposed formulation can be used to generate timetables for network instances of realistic size in acceptable time. For networks consisting of multiple connected components it is shown that a decomposition approach can significantly reduce run times. K E Y W O R D Sdisjunctive programming, mixed integer programming,

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“…Transit timetable generation is a well-researched complex optimization problem [30], too complex to describe here in detail. Generally, to accomplish resilience against small disturbances optimization models often aim for service regularity [31][32] [33][8], a measure of the equability of headways that can be used for static evaluation of a timetable during the planning phase as well as for dynamic assessment of operational performance.…”

“…This study applies a disjunctive program formulation producing regular timetables for multi-modal public transit systems adhering to planning requirements given by transit operators. That program was first introduced by Lückerath, Ullrich, Rishe, and Speckenmeyer [33] and allows for the consideration of feasibility constraints from daily operations as well as for the consideration of simultaneous departures for transfer connections, an objective traditionally opposed to regularity.…”

“…To validate the synchronization assurance strategies, two different timetables for the bi-modal public transit network of Cologne were generated using the approach from [33] and examined with regard to their suitability for the implementation of directed transfer connections between the two modes of transport. Departing bus vehicles are to wait at selected control points for arriving rail vehicles to allow transferring passengers quickly.…”

Combining Pre-Event Planning and Emergency Response in a Simulation Model to Increase the Resilience in Public Transit Networks

“…Transit timetable generation is a well-researched complex optimization problem [30], too complex to describe here in detail. Generally, to accomplish resilience against small disturbances optimization models often aim for service regularity [31][32] [33][8], a measure of the equability of headways that can be used for static evaluation of a timetable during the planning phase as well as for dynamic assessment of operational performance.…”