Cyclic Railway Timetabling: a Stochastic Optimization Approach

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 absorb the stochastic disturbances as well as possible. To that end, a timetable contains buffer times between trains and supplements in running times and dwell times. This paper first describes a stochastic optimization model that can be used to find an optimal allocation of the running time supplements of a single train on a number of consecutive trips along the same line. The aim of this model is to minimize the average delay of the train. The model is then extended such that it can be used to improve a given cyclic timetable for a number of trains on a common infrastructure. Computational results show that the average delay of the trains can be reduced substantially by applying relatively small modifications to the timetable. In particular, allocating the running time supplements in a different way than what is usual in practice can be useful

Operations research in passenger railway transportation

In this paper, we give an overview of state-of-the-art OperationsResearch models and techniques used in passenger railwaytransportation. For each planning phase (strategic, tactical andoperational), we describe the planning problems arising there anddiscuss some models and algorithms to solve them. We do not onlyconsider classical, well-known topics such as timetabling, rollingstock scheduling and crew scheduling, but we also discuss somerecently developed topics as shunting and reliability oftimetables.Finally, we focus on several practical aspects for each of theseproblems at the largest Dutch railway operator, NS Reizigers.passenger railway transportation;operation research;planning problems

Improved stochastic optimization of railway timetables

We present a general model to find the best allocation of a limited amount of supplements (extra minutes added to a timetable in order to reduce delays) on a set of interfering railway lines. By the best allocation, we mean the solution under which the weighted sum of expected delays is minimal. Our aim is to finely adjust an already existing and well-functioning timetable. We model this inherently stochastic optimization problem by using two-stage recourse models from stochastic programming, building upon earlier research from the literature. We present an improved formulation, allowing for an efficient solution using a standard algorithm for recourse models. We show that our model may be solved using any of the following theoretical frameworks: linear programming, stochastic programming and convex non-linear programming, and present a comparison of these approaches based on a real-life case study. Finally, we introduce stochastic dependency into the model, and present a statistical technique to estimate the model parameters from empirical data

Train-scheduling optimization model for railway networks with multiplatform stations

This paper focuses on optimizing the schedule of trains on railway networks composed of busy complex stations. A mathematical formulation of this problem is provided as a Mixed Integer Linear Program (MILP). However, the creation of an optimal new timetable is an NP-hard problem; therefore, the MILP can be solved for easy cases, computation time being impractical for more complex examples. In these cases, a heuristic approach is provided that makes use of genetic algorithms to find a good solution jointly with heuristic techniques to generate an initial population. The algorithm was applied to a number of problem instances producing feasible, though not optimal, solutions in several seconds on a laptop, and compared to other proposals. Some improvements are suggested to obtain better results and further improve computation time. Rail transport is recognized as a sustainable and energy-efficient means of transport. Moreover, each freight train can take a large number of trucks off the roads, making them safer. Studies in this field can help to make railways more attractive to travelers by reducing operative cost, and increasing the number of services and their punctuality. To improve the transit system and service, it is necessary to build optimal train scheduling. There is an interest from the industry in automating the scheduling process. Fast computerized train scheduling, moreover, can be used to explore the effects of alternative draft timetables, operating policies, station layouts, and random delays or failures.Postprint (published version

How and Why Freight Trains Deviate from the Timetable : Evidence from Sweden

European infrastructure managers (IMs) create annual timetables for trains that will run during a year. Freight trains in Sweden often deviate from this by being added, cancelled, delayed or early, resulting in increased costs for IMs and railway undertakings (RUs). We investigate the frequency of and causes for these deviations, using one year of operational data for 48,000 trains, and 15 stakeholder interviews. We find that about 20% of freight trains are added once the timetable has been created, and that cancellations occur for about 35% of freight trains, mostly at the RUs’ initiative. Delays are common: some 40% of departures, 30% of runtimes, and 20% of dwell times are delayed. Running early is even more common: 80% are ready to depart early, and 60% do so, while 40% of runtimes and 75% of dwell times are shorter than scheduled. We find links and feedback loops between the root causes for these deviations and suggest that IMs reserve more of the capacity that is needed for freight trains and instead distribute it throughout the year. This could lead to more appropriate, attractive, and reliable timetables for freight trains, whilst greatly reducing the amount of planning effort

Identification of Timetable Attractiveness Parameters by an International Literature Review

Timetable attractiveness is influenced by a set of key parameters which are described in this article. Regarding the superior structure of the timetable, the trend in Europe goes towards periodic regular interval timetables. Regular departures and focus on optimal transfer possi- bilities make these timetables attractive. The travel time in the timetable depends on charac- teristics of the infrastructure and rolling stock, heterogeneity of the planned train traffic and the necessary number of transfers on the passenger’s journey. Planned interdependencies be- tween trains, such as transfers and heterogeneous traffic, add complexity to the timetable. The risk of spreading initial delays to other trains and parts of the network increases with the level of timetable complexity

Identification of Timetable Attractiveness Parameters by an International Literature Review

Timetable attractiveness is influenced by a set of key parameters which are described in this article. Regarding the superior structure of the timetable, the trend in Europe goes towards periodic regular interval timetables. Regular departures and focus on optimal transfer possi- bilities make these timetables attractive. The travel time in the timetable depends on charac- teristics of the infrastructure and rolling stock, heterogeneity of the planned train traffic and the necessary number of transfers on the passenger’s journey. Planned interdependencies be- tween trains, such as transfers and heterogeneous traffic, add complexity to the timetable. The risk of spreading initial delays to other trains and parts of the network increases with the level of timetable complexity