On the delivery robustness of train timetables with respect to production replanning possibilities

Measuring timetable robustness is a complex task. Previous efforts have mainly been focused on simulation studies or measurements of time supplements. However, these measurements don't capture the production flexibility of a timetable, which is essential for measuring the robustness with regard to the trains' commercial activity commitments, and also for merging the goals of robustness and efficiency. In this article we differentiate between production timetables and delivery timetables. A production timetable contains all stops, meetings and switch crossings, while a delivery timetable only contains stops for commercial activities. If a production timetable is constructed such that it can easily be replanned to cope with delays without breaking any commercial activity commitments it provides delivery robustness without compromising travel efficiency. Changing meeting locations is one of the replanning tools available during operation, and this paper presents a new framework for heuristically optimising a given production timetable with regard to the number of alternative meeting locations. Mixed integer programming is used to find two delivery feasible production solutions, one early and one late. The area between the two solutions represents alternative meeting locations and therefore also the replanning enabled robustness. A case study from Sweden demonstrates how the method can be used to develop better production timetables

Stochastic Improvement of Cyclic Railway Timetables

Real-time railway operations are subject to stochastic disturbances. However, a railway timetable is a deterministic plan. Thus a timetable should be designed in such a way that it can cope with the stochastic disturbances as well as possible. For that purpose, a timetable usually contains time supplements in several process times and buffer times between pairs of consecutive trains. This paper describes a Stochastic Optimization Model that can be used to allocate the time supplements and the buffer times in a given timetable in such a way that the timetable becomes maximally robust against stochastic disturbances. The Stochastic Optimization Model was tested on several instances of NS Reizigers, the main operator of passenger trains in the Netherlands. Moreover, a timetable that was computed by the model was operated in practice in a timetable experiment on the so-called “Zaanlijnâ€. The results show that the average delays of trains can often be reduced significantly by applying relatively small modifications to a given timetable.Railway Timetabling;Stochastic Optimization;Robustness

Phase Synchronization in Railway Timetables

Timetable construction belongs to the most important optimization problems in public transport. Finding optimal or near-optimal timetables under the subsidiary conditions of minimizing travel times and other criteria is a targeted contribution to the functioning of public transport. In addition to efficiency (given, e.g., by minimal average travel times), a significant feature of a timetable is its robustness against delay propagation. Here we study the balance of efficiency and robustness in long-distance railway timetables (in particular the current long-distance railway timetable in Germany) from the perspective of synchronization, exploiting the fact that a major part of the trains run nearly periodically. We find that synchronization is highest at intermediate-sized stations. We argue that this synchronization perspective opens a new avenue towards an understanding of railway timetables by representing them as spatio-temporal phase patterns. Robustness and efficiency can then be viewed as properties of this phase pattern

Edges as Nodes - a New Approach to Timetable Information

In this paper we suggest a new approach to timetable information by introducing the ``edge-converted graph'' of a timetable. Using this model we present simple algorithms that solve the earliest arrival problem (EAP) and the minimum number of transfers problem (MNTP). For constant-degree graphs this yields linear-time algorithms for EAP and MNTP which improves upon the known \emph{Dijkstra}-based approaches. We also test the performance of our algorithms against the classical algorithms for EAP and MNTP in the time-expanded model

Appraisal Framework for Integrated Transport

This working paper outlines an appraisal framework for the Integrated Transport project. The project examined the demand implications from the introduction of a Taktfahrplan timetable onto the east coast mainline rail route. The Taktfahrplan concept is frequently referred to as an interval timetable and is based on trains leaving stations at the same time past the hour throughout the operational day. A stated preference exercise was conducted to estimated what values people placed on such a timetable and these values were added to the more conventional elements of generalised cost to obtain the changes in demand that would result from the introduction of a Taktfahrplan. The working paper is divided into a number of sections that will highlight, • the key implications to arise from the Integrated Transport project; • the demand model; • the appraisal framework; • the data sources used within the appraisal framework; and • the results of the appraisal framework. Interested readers are also referred to the a conference paper that will be presented at the European Transport Conference in Strasbourg later this year (Wardman et al, 2003)