Railway Timetables Research Articles

A Railway Timetable Rescheduling Approach for Handling Large Scale Disruptions

A Railway Timetable Rescheduling Approach for Handling Large Scale Disruptions

Adjusting a railway timetable in case of partial or complete blockades

Unexpected events, such as accidents or track damages, can have a significant impact on the railway system so that trains need to be canceled and delayed. In case of a disruption it is important that dispatchers quickly present a good solution in order to minimize the nuisance for the passengers. In this paper, we focus on adjusting the timetable of a passenger railway operator in case of major disruptions. Both a partial and a complete blockade of a railway line are considered. Given a disrupted infrastructure situation and a forecast of the characteristics of the disruption, our goal is to determine a disposition timetable, specifying which trains will still be operated during the disruption and determining the timetable of these trains. Without explicitly taking the rolling stock rescheduling problem into account, we develop our models such that the probability that feasible solutions to this problem exist, is high. The main objective is to maximize the service level offered to the passengers. We present integer programming formulations and test our models using instances from Netherlands Railways.

Energy saving in railway timetabling: A bi-objective evolutionary approach for computing alternative running times

The timetabling step in railway planning is based on the estimation of the running times. Usually, they are estimated as the shortest running time increased of a short time supplement. Estimating the running time amounts to define the speed profile which indicates the speed that the train driver must hold at each position. The approach proposed in this paper produces a set of solutions optimizing both the running time and energy consumption. The approach is based on an original method of speed profiling performed by a multi-objective evolutionary algorithm. The speed profiles found by the evolutionary algorithm are all compromises between running time on the one hand and energy consumption on the other hand. A set of results obtained on two lines are analyzed and discussed to highlight the relevance of such an approach in a practical context.

A game theoretic model for re-optimizing a railway timetable

In the Nineties of the last century the European Commission decided to open the railway market to competition, allowing different railway companies to operate on the same network. Under this framework Infrastructure Managers have to allocate capacity in order to define the timetable, dealing with possible slot conflicts between competing Transport Operators. An efficient train scheduling requires collecting a lot of information from the Transport Operators, but it may not be in their interests to reveal their private information. Therefore, it may be useful for real-world applications to design methods that provide incentives to Transport Operators for cooperating with the aim of increasing their utility; moreover, this may result in an improvement of the efficiency even for the Infrastructure Managers, so they also have incentives for favouring the cooperation. In this paper we propose a game theoretical model in which the agents (Transport Operators) exchange information on their needs and are compensated by a possible increasing of their utility. This approach represents the situation as a coalition formation problem. In particular, we refer to the C-Solution proposed by Gerber (Rev Econ Design 5:149–175, 1), which is applied to some examples, each with different features. This model requires that information is revealed to a small number of competitors. This is rather important in a market currently still characterized by operator reluctance to an indiscriminate diffusion of information. Furthermore, the low dimension of the problem allows having a low computational complexity.

A Differential Evolution Algorithm With Dual Populations for Solving Periodic Railway Timetable Scheduling Problem

Railway timetable scheduling is a fundamental operational problem in the railway industry and has significant influence on the quality of service provided by the transport system. This paper explores the periodic railway timetable scheduling (PRTS) problem, with the objective to minimize the average waiting time of the transfer passengers. Unlike traditional PRTS models that only involve service lines with fixed cycles, this paper presents a more flexible model by allowing the cycle of service lines and the number of transfer passengers to vary with the time period. An enhanced differential evolution (DE) algorithm with dual populations, termed “dual-population DE” (DP-DE), was developed to solve the PRTS problem, yielding high-quality solutions. In the DP-DE, two populations cooperate during the evolution; the first focuses on global search by adopting parameter settings and operators that help maintain population diversity, while the second one focuses on speeding up convergence by adopting parameter settings and operators that are good for local fine tuning. A novel bidirectional migration operator is proposed to share the search experience between the two populations. The proposed DP-DE has been applied to optimize the timetable of the Guangzhou Metro system in Mainland China and six artificial periodic railway systems. Two conventional deterministic algorithms and seven highly regarded evolutionary algorithms are used for comparison. The comparison results reveal that the performance of DP-PE is very promising.

Mixed integer programming for minimizing the period of a cyclic railway timetable for a single track with two train types

In this paper we extend the work of Bergmann (1975) to investigate the capacity of a single track, unidirectional rail line that adheres to a cyclic timetable. A set of intermediate stations lies between an origin and destination with one siding at each station. Two types of trains—express and local—are dispatched from the origin in alternating fashion. The local stops at every intermediate station and the express stops at no intermediate stations. A mixed integer linear program is developed in order to minimize the length of the dispatching cycle and minimize the total stopping (dwell) time of the local train at all stations combined. Constraints include a minimum dwell time for the local train at each station, a maximum total dwell time for the local train, and headway considerations on the main line and in stations. Hundreds of randomly generated problem instances with up to 70 stations are considered and solved to optimality in a reasonable amount of time using IBM ILOG CPLEX.

A direct comparison of physical block occupancy versus timed block occupancy in train timetabling formulations

Two fundamental mathematical formulations for railway timetabling are compared on a common set of sample problems, representing both multiple track high density services in Europe and single track bidirectional operations in North America. One formulation, ACP, enforces against conflicts by constraining time intervals between trains, while the other formulation, RCHF, monitors physical occupation of controlled track segments. The results demonstrate that both ACP and RCHF return comparable solutions in the aggregate, with some significant differences in select instances, and a pattern of significant differences in performance and constraint enforcement overall.

Flexible Connections in PESP Models for Cyclic Passenger Railway Timetabling

In this paper we describe how rolling stock and passenger connections in a cyclic railway timetable can be modeled in a flexible way within the model for the Periodic Event-Scheduling Problem (PESP). Usually, PESP models assume that the constraints for rolling stock or passenger connections specify in detail which trains should connect with each other. However, the flexibility described in this paper allows the model to choose which trains should connect with each other in a rolling stock or passenger connection. We express the connection times in a minimum matching of arriving and departing trains in terms of certain process time variables. We also describe an abstract framework demonstrating that, under certain conditions, the extra flexibility can be modeled purely in terms of PESP constraints. The concept of flexible rolling stock and passenger connections is illustrated by an example based on three intercity lines of Netherlands Railways.

Incorporating transfer reliability into equilibrium analysis of railway passenger flow

Passenger’s transfer route choice behavior is one of the prominent research topics in the field of railway transportation. Existing traffic assignment approaches do not properly account for passenger’s expectation for transfer reliability. In this study, the transfer reliability is explicitly defined and a multi-class user equilibrium model is established, given which passengers choose the minimal-cost path based on their expected reliability thresholds. In particular, a path-based traffic assignment algorithm which combines a k-shortest path algorithm and the method of successive averages is proposed. The validity of the proposed approach is verified by an illustrative example. Using the proposed modeling approach, it is possible to determine the passenger’s collective route choice behavior based on the user equilibrium pattern. Moreover, the railway timetables can be evaluated and optimized based on the cost-based level of service estimation.

A Fuzzy Optimization Model for High‐Speed Railway Timetable Rescheduling

A fuzzy optimization model based on improved symmetric tolerance approach is introduced, which allows for rescheduling high‐speed railway timetable under unexpected interferences. The model nests different parameters of the soft constraints with uncertainty margin to describe their importance to the optimization purpose and treats the objective in the same manner. Thus a new optimal instrument is expected to achieve a new timetable subject to little slack of constraints. The section between Nanjing and Shanghai, which is the busiest, of Beijing‐Shanghai high‐speed rail line in China is used as the simulated measurement. The fuzzy optimization model provides an accurate approximation on train running time and headway time, and hence the results suggest that the number of seriously impacted trains and total delay time can be reduced significantly subject to little cost and risk.

Assessment of Advanced Dispatching Measures for Recovering Disrupted Railway Traffic Situations

Railway timetables are developed to make operations robust and resilient to small delays. However, disturbances perturb the daily plan, and dispatchers need to adjust the plan to keep operations feasible and to limit delay propagation. For large infrastructure disruptions, the available railway capacity is reduced, and the timetable could become infeasible. The paper studies how to support dispatchers in the management of traffic flow during disruptions. A set of disruption resolution scenarios to manage seriously disturbed traffic conditions in large networks is investigated. For instance, in the case of track blockage, train services can be canceled, rerouted in the disrupted dispatching area, or rerouted in other areas while still with the same origin and destination. Feasible and efficient operations schedules are found quickly by an advanced decision support system for dispatching known as ROMA (railway traffic optimization by means of alternative graphs), which is based on microscopic detail and can handle large areas by decomposition. Detailed performance indicators can be computed to let dispatchers choose a specific solution, for example, by minimizing train delays and reducing passengers' discomfort. In the computational experiments, an analysis is done of a blockage on a double track line, combined with multiple entrance delays on a large railway network with heavy traffic. Several disruption resolution scenarios involving cancellation of services, rerouting, and shuttle trains are considered, and each feasible plan is evaluated in relation to travel times, frequency of services, and delay propagation.

Railway Timetable Rescheduling Based on the Feedback of Train-set Circulation

This paper deals with the timetable rescheduling problem based on the feedback of train-set's circulation in highspeed railway transportation. Given the original timetable and the corresponding train-set circulation scheme, we describe an integer linear programming model based on the fixed departure/arrival order, which can tackle a static timetable rescheduling to optimize the train-set circulation, bring out more connections, especially without direction change in through station between train lines.Lingo11.0 is used in the case study.

Train service timetabling in railway open markets by particle swarm optimisation

Railway timetabling is an important process in train service provision as it matches the transportation demand with the infrastructure capacity while customer satisfaction is also considered. It is a multi-objective optimisation problem, in which a feasible solution, rather than the optimal one, is usually taken in practice because of the time constraint. The quality of services may suffer as a result. In a railway open market, timetabling usually involves rounds of negotiations amongst a number of self-interested and independent stakeholders and hence additional objectives and constraints are imposed on the timetabling problem. While the requirements of all stakeholders are taken into consideration simultaneously, the computation demand is inevitably immense. Intelligent solution-searching techniques provide a possible solution. This paper attempts to employ a particle swarm optimisation (PSO) approach to devise a railway timetable in an open market. The suitability and performance of PSO are studied on a multi-agent-based railway open-market negotiation simulation platform.

Time and Motion: Chronometry and the Railway Timetables of New South Wales, 1855-1906

Abstract Timetables are part of the textual infrastructure of travel and mobility. As a way of “envisioning information,” they came into being with the advent of rail. As an important document of quotidian life, important to navigating modern space, railway timetables encapsulate a modernist horology, ‘contemporality.’ They are an element of the culture of calculation that Georg Simmel describes in his essay on urban life. Yet timetables have not received the attention that is their due. In this paper I redress this and analyse the early timetables of New South Wales, Australia. I argue that as well as inducting the travelling public into the new horology, timetables also—because their contents were not limited to temporal matters—inducted them into the mobility and spatial practices associated with railway culture.

Periodic railway timetabling with event flexibility

AbstractThis article addresses the problem of generating conflict‐free periodic train timetables for large railway networks. We follow a two‐level approach, where a simplified track topology is used to obtain a macrolevel schedule, and the detailed topology is considered locally on the microlevel. To enlarge the solution space in the interface of the two levels, we propose an extension of the well‐known periodic event scheduling problem (PESP) such that it allows to generate flexible time slots for the departure and arrival times instead of exact times. This flexible periodic event scheduling problem (FPESP) formulation increases the chance to obtain feasible solutions (exact train routings) subsequently on the microlevel, in particular for stations with dense peak traffic. Total trip time and the time slot sizes are used as multiple objectives and weighted and/or constrained to allocate the flexibility where it is most useful. Tests on medium‐size instances of the Swiss Federal Railways' 2007 service intention demonstrate the advantage of the FPESP model, while it only moderately increases its solution time in most cases. A trade‐off analysis of the two conflicting objectives is presented and discussed for different scenarios. Finally, we present the Flexbox model, which generalizes the single event flexibilities of the FPESP to arbitrary subsets of events. These Flexboxes can make use of natural dependencies in the timetable and can considerably increase the total flexibility of the timetable. © 2010 Wiley Periodicals, Inc. NETWORKS, 2011

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.

A delay propagation algorithm for large-scale railway traffic networks

In scheduled railway traffic networks a single delayed train may cause a domino effect of secondary delays over the entire network, which is a main concern to planners and dispatchers. This paper presents a model and an algorithm to compute the propagation of initial delays over a periodic railway timetable. The railway system is modelled as a linear system in max-plus algebra including zero-order dynamics corresponding to delay propagation within a timetable period. A timed event graph representation is exploited in an effective graph algorithm that computes the propagation of train delays using a bucket implementation to store the propagated delays. The behaviour of the delay propagation and the convergence of the algorithm is analysed depending on timetable properties such as realisability and stability. Different types of delays and delay behaviour are discussed, including primary and secondary delays, structural delays, periodic delay regimes, and delay explosion. A decomposition method based on linearity is introduced to deal with structural and initial delays separately. The algorithm can be applied to large-scale scheduled railway traffic networks in real-time applications such as interactive timetable stability analysis and decision support systems to assist train dispatchers.

Charles Humphrey Jules Rey

Charles Humphrey Jules Rey was educated at Harrow School and Guy’s Hospital. He joined the Royal Army Medical Corps on qualifying, being posted to Burma in 1942 and attaining the...

Low frequency cultural noise

[1] Abnormal cultural seismic noise is observed in the frequency range of 0.01–0.05 Hz. Cultural noise generated by human activities is generally observed in frequencies above 1 Hz, and is greater in the daytime than at night. The low-frequency noise presented in this paper exhibits a characteristic amplitude variation and can be easily identified from time domain seismograms in the frequency range of interest. The amplitude variation is predominantly in the vertical component, but the horizontal components also show variations. Low-frequency noise is markedly periodic, which reinforces its interpretation as cultural noise. Such noise is observed world-wide, but is limited to areas in the vicinity of railways. The amplitude variation in seismograms correlates strongly with railway timetables, and the waveform shows a wavelength shift associated with the Doppler effect, which indicates that the origin of seismic background noise in the frequency range 0.01–0.05 Hz is railways.

Fast Approaches to Improve the Robustness of a Railway Timetable

The train timetabling problem (TTP) consists of finding a train schedule on a railway network that satisfies some operational constraints and maximizes some profit function that accounts for the efficiency of the infrastructure usage. In practical cases, however, the maximization of the objective function is not enough, and one calls for a robust solution that is capable of absorbing, as much as possible, delays/disturbances on the network. In this paper we propose and computationally analyze four different methods to improve the robustness of a given TTP solution for the aperiodic (noncyclic) case. The approaches combine linear programming (LP) and ad hoc stochastic programming/robust optimization techniques. We computationally compare the effectiveness and practical applicability of the four techniques under investigation on real-world test cases from the Italian railway company Trenitalia. The outcome is that two of the proposed techniques are very fast and provide robust solutions of comparable quality with respect to the standard (but very time consuming) stochastic programming approach.