Do regular timetables help to reduce delays in tram networks? It depends!

Abstract

In public transit planning, regularity of timetables is seen as an important means to improve capacity efficiency by assuring an even trip distribution, as well as to improve product attractiveness and appreciation. This paper focuses on examining whether a regular timetable can also help to reduce network delay, especially resulting from inevitable small disturbances. Following the formulation of a mathematical optimization approach, we propose a number of conditions a network has to fulfill for timetable regularity to have a delay reducing impact. A set of three network properties is identified, which consists of (a) the sharing of resources between tram lines, (b) a low variability of driving times, and (c) the non-redundancy of the network's central resources. To test the impact of these properties, a series of optimization and simulation experiments is conducted on models of the tram network of the cities of Cologne, Germany, and Montpellier, France. Small disturbances are introduced to the simulated operations to check whether the presence of all three properties is necessary for a network to benefit from a regular timetable. The results show that while with all properties present a regular timetable can indeed help to reduce delays resulting from small disturbances, the non-compliance with any one of the conditions nullifies the impact of regularity on the result.

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

“…Optimization models to generate regular timetables are for example proposed by Genç [11], Bampas et al [1] and Ullrich et al [19][20][21]. Genç develops an integer linear programming formulation to generate periodic timetables with variable basic intervals, maximizing the minimum headway between consecutive departures at stops shared by multiple lines.…”

“…Ullrich et al [21] also solve a special case of the optimization problem formulated by Genç, addressing the generation of regular, periodic timetables with a common basic interval. They extend the model with the possibility to incorporate transit planning requirements (e.g., guaranteed transfer connections, amplifier lines serving only the city centers, coordination with intercity rail traffic) during optimization to assure the applicability of the resulting timetables during daily operation.…”

“…In the following the MILP first described by Genç [11] will be extended with the capability to incorporate planning requirements, following the approach described by Ullrich et al [19][20][21]. Therefore, the model by Genç, which up to now was only published in his German PhD thesis, will first be introduced in summary before the extensions for the incorporation of planning requirements are described.…”

“…While a timetable with optimum regularity can help to raise punctuality and product attractiveness as well as lower peaks in passenger load (see [21,22]), operational, political, or societal requirements may necessitate deviations from these objectives. Operational requirements mainly concern technical and managerial feasibility constraints, for example, minimum headways on bi-directional railway tracks to avoid collisions.…”

“…the transit system more attractive. Ullrich et al [21] showed that in systems where vehicles of different lines share common resources with limited capacity (i.e., most tram systems), regularity can also be used as a measure for the capability of a timetable to contain consequences of small delays, subsequently heightening the overall punctuality of the system.…”