Rolling Stock Circulation Research Articles

The Maintenance Location Choice Problem for railway rolling stock

Due to increasing railway use, the capacity at railway yards and maintenance locations is becoming limiting to accommodate existing rolling stock. To reduce capacity issues at maintenance locations during nighttime, railway undertakings consider performing more daytime maintenance, but the choice at which locations personnel needs to be stationed for daytime maintenance is not straightforward. Among other things, it depends on the planned rolling stock circulation and the maintenance activities that need to be performed. This paper presents the Maintenance Location Choice Problem (MLCP) and provides a Mixed Integer Linear Programming model for this problem. The model demonstrates that for a representative rolling stock circulation from The Netherlands Railways a substantial amount of maintenance activities can be performed during daytime. Also, it is shown that the location choice delivered by the model is robust under various time horizons and rolling stock circulations. Moreover, the running time for optimizing the model is considered acceptable for planning purposes.

Real-time integrated train rescheduling and rolling stock circulation planning for a metro line under disruptions

More and more unexpected events occur in metro systems, which may cause serious disturbances and even disruptions for the operation of trains. This paper studies an integrated train rescheduling and rolling stock circulation planning problem for the complete blockage situations in a metro line. We consider several key practical train operation constraints, including the maximum number of available rolling stocks, the turnaround constraints, the service connection constraints. This problem is viewed as a complex multi-objective mixed integer linear programming (MILP) formulation, where the objectives involve the deviations with respect to the timetable, the (partial) cancellations, and the headway deviations of train services. A two-stage approach is also developed to enhance the computational efficiency, where a smaller-size optimization problem is solved in the first stage, by considering a set of key turnaround stations only, while the original MILP problem is solved in the second stage by fixing some binary variables according to the first stage solution. In addition, we propose a heuristic technique that is based on introducing a new set of constraints to reduce the search space without eliminating potentially good solutions. Comprehensive experiments are investigated based on the practical data of Beijing Subway Lines, where the proposed integrated models and approaches yield much better solutions when compared with a widely used strategy, i.e., holding (waiting at station) strategy and the sequential approach. Moreover, the impacts of the complete blockage locations/durations and the effects of different weight settings in the multi-objective optimization are deeply analyzed.

Integrated Train Timetabling and Rolling Stock Circulation Planning for a Metro Line with Multiple Depots

With the expansion of metro networks, it is common that a metro line is equipped with multiple depots. The operation costs of rail operators and the passenger satisfaction are highly dependent on train timetables and rolling stock circulation plans, which are closely related to each other. Therefore, it is important to investigate the integrated train timetabling and rolling stock circulation planning problem for metro lines with multiple depots. A mixed integer linear programming formulation is proposed to generate train timetables and rolling stock circulation plans simultaneously for a metro line with multiple depots, in which the capacity of each depot and the rolling stock balances between depots are considered. Several numerical experiments based on real-world data of Beijing Subway Line 5 and Beijing Subway Line 6 are carried out to demonstrate the effectiveness of the presented model.

Energy-efficient timetabling and rolling stock circulation planning based on automatic train operation levels for metro lines

We investigate the energy-efficient train timetabling and rolling stock circulation planning problem for metro lines based on flexible selections of train operation levels, which involve running levels (various running times and speed profiles) and dwell levels (various dwell times at stations). The travel demand of passengers is involved in the energy-efficient train timetabling problem via service patterns, i.e., different operation headways are used in peak and off-peak hours to satisfy the passenger demand. A mixed integer nonlinear programming (MINLP) formulation is presented to optimize train timetables and circulation plans of rolling stocks simultaneously with the aim of minimizing the headway deviations relating to service patterns, the headway variations among neighboring train services, the needed depot movements for rolling stocks, and the overall energy consumption. To increase the regularity (i.e., the consistency of operation level selections of train services) of train timetables and to improve the computational efficiency, two extensions of the energy-efficient timetabling formulation are proposed, i.e. the energy-efficient train timetabling models with pre-fixed selections and optimal identical (or consistent) selections of the operation levels. The proposed MINLP formulations are transformed into mixed integer linear programming formulations, which could be effectively solved, e.g., by Cplex and Gurobi solvers. To investigate the effectiveness of the proposed models, we perform computational experiments based on the real-world data of the Beijing Yizhuang line. The numerical results illustrate that the energy consumption of the daily train timetable obtained by the proposed energy-efficient train timetabling model with flexible selection of operation levels is reduced by 9.90% when compared with that of the train timetables without operation level selections. Moreover, the energy savings of the energy-efficient train timetables with optimal identical selection and pre-fixed selection of operation levels are 7.67% and 5.75%, respectively. However, the computation time of the energy-efficient train timetabling models with operation level selections is significantly longer than that without operation level selections.

An integrated approach of train scheduling and rolling stock circulation with skip-stopping pattern for urban rail transit lines

Integrated planning for urban rail transit (URT) systems is a significant technique in URT operation to balance service level and operating cost. It is generally oriented towards transportation efficiency and solved in a sequential way due to the complexity, but ignores the service experiences among equitable passengers and the utilization balance among equal rolling stocks. This paper aims to study the integrated planning for an oversaturated URT line, incorporating the fairness in train scheduling and workload balance in rolling stock circulation that are measured by two defined min–max indexes. A mixed-integer nonlinear programming (MINLP) model is established to formulate the integrated planning of stop planning, train scheduling and rolling stock circulation, explicitly considering time-dependent origin–destination demand, first-come-first-serve principle and rigid capacity constraints. Due to the model complexity, an iterative searching approach (ISA) is proposed to solve the model, involving adjusting stop patterns, departure times and connections at the depot terminal. The performance of the ISA is evaluated by three cases with different time lengths based on the practical data from No.8 URT line in Guangzhou. The results are compared with the practical plans and the solutions solved by the two-stage approach respectively. It shows that the ISA can not only mitigate unfairness and balance workload, but also improve transportation efficiency. We also investigate the optimization effects and application conditions of different combinations of searching strategies in the ISA. Furthermore, the study on the typical case during peak hours shows more details about the optimization effects and mechanism of the ISA, which can reach a uniform state in both service level and resource utilization.

Dynamic railway timetable rescheduling for multiple connected disruptions

Unexpected disruptions occur in the railways on a daily basis, which are typically handled manually by experienced traffic controllers with the support of predefined contingency plans. When several disruptions occur simultaneously, it is rather hard for traffic controllers to make rescheduling decisions, because (1) the predefined contingency plans corresponding to these disruptions may conflict with each other and (2) no predefined contingency plan considering the combined effects of multiple disruptions is available. This paper proposes a Mixed Integer Linear Programming (MILP) model to reschedule the timetable in case of multiple disruptions that occur at different geographic locations but have overlapping periods and are pairwise connected by at least one train line. The dispatching measures of retiming, reordering, cancelling, adding stops and flexible short-turning are formulated in the MILP model that also considers the rolling stock circulations at terminal stations and platform capacity. We develop two approaches for rescheduling the timetable in a dynamic environment: the sequential approach and the combined approach. In the sequential approach, a single-disruption rescheduling model is applied to handle each new disruption with the last solution as reference. In the combined approach, the multiple-disruption rescheduling model is applied every time an extra disruption occurs by considering all ongoing disruptions. A rolling-horizon solution method to the multiple-disruption model has been developed to handle long multiple connected disruptions in a more efficient way. The sequential and combined approaches have been tested on real-life instances on a subnetwork of the Dutch railways with 38 stations and 10 train lines operating half-hourly in each direction. In a few cases, the sequential approach did not find feasible solutions, while the combined approach obtained the solutions for all considered cases. Besides, the combined approach was able to find solutions with less cancelled train services and/or train delays than the sequential approach. For long disruptions, the proposed rolling-horizon method was able to generate high-quality rescheduling solutions in an acceptable time.

An actor-critic deep reinforcement learning approach for metro train scheduling with rolling stock circulation under stochastic demand

This paper presents a novel actor-critic deep reinforcement learning approach for metro train scheduling with circulation of limited rolling stock. The scheduling problem is modeled as a Markov decision process driven by stochastic passenger demand. As in most dynamic optimization problems, the complexity of the scheduling process grows exponentially with the amount of states, decisions, and uncertainties involved. This study aims to address this ‘curses of dimensionality’ issue by adopting an actor-critic deep reinforcement learning solution framework. The framework simplifies the evaluation and searching process for potential optimal solutions by parameterizing the original state and decision spaces with the use of artificial neural networks. A deep deterministic policy gradient algorithm is developed for training the artificial neural networks via simulated system transitions before the actor-critic agent can be applied for online schedule control. The proposed approach is tested with a real-world scenario configured with data collected from the Victoria Line of London Underground, UK. Experiment results illustrate the advantages of the proposed method over a range of established meta-heuristics in terms of computing time, system efficiency, and robustness under different stochastic environments. This study innovates urban transit operations with state-of-the-art computer science and dynamic optimization techniques.

Integrated timetable rescheduling and passenger reassignment during railway disruptions

During railway disruptions, most passengers may not be able to find preferred alternative train services due to the current way of handling disruptions that does not take passenger responses into account. To offer better alternatives to passengers, this paper proposes a novel passenger-oriented timetable rescheduling model, which integrates timetable rescheduling and passenger reassignment into a Mixed Integer Linear Programming model with the objective of minimizing generalized travel times: in-vehicle times, waiting times at origin/transfer stations and the number of transfers. The model applies the dispatching measures of re-timing, re-ordering, cancelling, flexible stopping and flexible short-turning trains, handles rolling stock circulations at both short-turning and terminal stations of trains, and takes station capacity into account. To solve the model efficiently, an Adapted Fix-and-Optimize (AFaO) algorithm is developed. Numerical experiments were carried out to a part of the Dutch railways. The results show that the proposed passenger-oriented timetable rescheduling model is able to shorten generalized travel times significantly compared to an operator-oriented timetable rescheduling model that does not consider passenger responses. By allowing only 10 min more train delay than an optimal operator-oriented rescheduling solution, the passenger-oriented model is able to shorten the generalized travel times over all passengers by thousands of minutes in all considered disruption scenarios. With a passenger-oriented rescheduled timetable, more passengers continue their train travels after a disruption started, compared to a rescheduled timetable from the operator-oriented model. The AFaO algorithm obtains high-quality solutions to the passenger-oriented model in up to 300 s.

Role of Timetable, Rolling Stock Rescheduling, and Information Strategies to Passengers in Public Transport Disruptions

In the event of public transport disruption, operating companies produce disposition timetables depending on different rescheduling strategies, such as retiming or rerouting, with services fully/partially cancelled, and also taking into account more complex, adjusted, feasible rolling stock circulation. The aim is to reduce passengers’ delays, thereby limiting detriment to passengers’ activities and their related satisfaction. The key relation between the supply of operating companies and passengers’ satisfaction is information disseminated about running services. This paper innovatively combines an optimization model and an agent-based micro-simulation model (MATSim) to explore passengers’ (dis)satisfaction with different disposition timetables and information strategies, which is helpful for operating companies to offer better services to passengers in cases of public transport disruption. Activity-based agent behaviors in a multi-modal network are simulated and agents’ delays and scores for the city of Zürich, Switzerland, analyzed. Passengers’ (dis)satisfaction is indicated by their delays in the directly affected (i.e., disrupted) trip and utility for their whole trips and activities estimated by a score function. Disruption results in immediate delays for passengers whose planned services fail to run, plus delays for passengers on the line where extra services are planned to run (rerouted). The earlier information on the disposition timetable is disseminated to passengers, the higher their satisfaction during disruption. Compared with full cancellation of train services, computing a precise feasible rolling stock circulation able to handle partial train cancellations can significantly benefit passengers, especially those whose planned services are disrupted, against minor delays incurred by other group of passengers.

A Mixed Integer Linear Programming Model for Rolling Stock Deadhead Routing before the Operation Period in an Urban Rail Transit Line

In an urban rail transit line, train services are performed by the rolling stocks that are initially stored at depots. Before the start of the operation period, rolling stocks consecutively leave the depots and run without passengers (deadhead routing) to the origin station of their corresponding first departure train service in an operation day (first train service) using either direct or indirect routes. This paper investigates the rolling stock deadhead routing problem in an urban transit line with multiple circulation plans, depots, and rolling stock types. Given the rolling stock circulation plans, the problem is to identify a deadhead route for the rolling stock required by the train services to cover the initial operation. By pregenerating all direct and indirect candidate deadhead routes in a polynomial manner, the problem is then nicely formulated as a mixed integer linear programming (MILP) model to minimize the total deadhead mileages. A real-world case from the urban rail transit line 3 of Chongqing in China is adopted to test the proposed method. Computational results demonstrate that the problems of large-scale instances can be quickly solved to optimality by commercial optimization solvers on a personal computer. In addition, our optimization method is better than the empirical practices in terms of the solution quality. Meanwhile, alternative measures can further decrease the total deadhead mileages according to the proposed model, e.g., opening idle switch stations and prolonging the time that is used for the rolling stock departure. Finally, the model is further extended to consider operating costs, and more computation cases are tested for better adapting to the practical operating conditions.

Train punctuality analysis in a rolling stock perspective

This paper studies how time delays spread through the railway system. We evaluate timetable and rolling stock interaction in relation to medium size delays. In particular, we study the connection between arrival and departure delays for trains that are operated by the same rolling stock individual. We studied one year of data for trains circulating in the Oslo area.Research questions in this study are:What is the connection between arrival and departure delays for the same piece of rolling stock?How can delays be tracked through the route schedules and the rolling stock circulation plan?Punctuality analysis was performed to investigate if there is a connection between arrival and departure delays. A correlation analysis of the arrival delays and the corresponding departures was done in order to find the possible connection.There was a connection between the size of arrival delays and the size of the corresponding departure delays. We found a threshold at around 20 minutes. An arrival delay over this threshold is expected to cause departure delays. Below the threshold most of the arrival delays are absorbed.

Energy-Efficient Train Scheduling and Rolling Stock Circulation Planning in a Metro Line: A Linear Programming Approach

In metro systems, a tactical train schedule with the rolling stock circulation plan aims to determine the movements of all physical trains. To utilize the regenerative energy as much as possible, this paper proposes an integrated model to simultaneously generate the optimal train schedule and rolling stock circulation plan, in which the brake-traction overlapping time at stations is maximized. In particular, our model rigorously considers the train turn-around constraints, train circulation constraints, and dynamic passenger demands to tackle the train loading capacity constraints. To eliminate the effect of non-linear constraints, we reformulate the original model into its equivalent linear model that can be efficiently solved by linear programming solvers. Finally, the numerical experiments based on Beijing Yizhuang Metro Line are implemented to demonstrate the effectiveness of our proposed model.

Improvement of the technique of calculating operational parameters using an automated system

Impact of the existing operating conditions on terms of cargo delivery and compliance with the rolling stock circulation norms is studied. Planned and actual rolling stock circulation characteristics are analyzed. Deviations from the norms have been detected, which is indicative of non-compliance with technological processes. Nowadays the rolling stock circulation problem becomes more complex; for the service recipients, i.e. customers of the railway, it means delays in cargo deliveries, non-fulfillment of financial obligations before other participants in the railway transport process. A new approach to the methodology and principle of calculating anticipated key performance characteristics are proposed. The existing information technologies for railway management make it possible to monitor compliance with the rolling stock circulation norms and the terms of cargo deliveries and to further improve methods and techniques of performance parameters. This will enable establishing realistic rolling stock circulation norms and cargo delivery terms, thus ensuring compliance with technological requirements of the railway transport processes in order to provide good customer service.

Improvement of international rail transportation of benzene between Ukraine and the European Union countries

It is considered the possibility of improvement of the international railway transportation of benzene and other related cargoes between Ukraine and the European Union countries for the carriage of these cargoes in tank containers. The volume of chemical cargo transportation to the EU countries to the rolling stock types for 2018 has been analyzed. The research of the effectiveness of organization of international transportation according to the criterion of the total hours of downtime by wagons under accumulation. The mathematical model of chemical cargoes transportation by wagons, wagon groups and container trains with the accumulation to the technical standards on the cargo diversions was elaborated. The models take into account the unevenness of the wagon arrivals to the accumulation points and observance of the number of wagons to the established norm. A comparison of the effectiveness of the two models of the organization of the chemical cargo delivery and it was defined a more effective version of transportation. It has been established that for more efficient using of the rolling stock and for the rolling stock circulation decreasing is the cargo transportation by trains which consist of cisterns or/and tank container carriages. The influence of the components of the rolling stock circulation and its value are analyzed. The research of the cost of benzene transportation in cisterns and tank containers for the individual diversions was studied. According to the research results the cost of benzene transportation by platforms of the railways ownership is less than twice in comparison to private cisterns and tank-containers of the Ukrainian Railways fleet. These recommendations will improve the process of transportation and increase of volumes of international cargo by railroads between Ukraine and the EU countries.

Passenger demand oriented train scheduling and rolling stock circulation planning for an urban rail transit line

We study the integration of train scheduling and rolling stock circulation planning under time-varying passenger demand for an urban rail transit line, where the practical train operation constraints, e.g., the capacity of trains, the number of available rolling stocks, and the entering/exiting depot operations, are considered. Three solution approaches are proposed to solve the resulting multi-objective mixed-integer nonlinear programming (MINLP) problem to deliver both an irregular train schedule (i.e., departure and arrival times of all train services) and a rolling stock circulation plan (including entering/exiting depot operations of rolling stocks and connections between train services) simultaneously. We first present an iterative nonlinear programming (INP) approach, where the solutions of the original MINLP problem are obtained by solving a nonlinear programming problem and a mixed integer linear programming (MILP) problem iteratively. Moreover, an equivalent MILP formulation of the original MINLP model is developed and an approximated MILP approach is proposed to reduce the number of constraints introduced by passenger demand. A case study is conducted based on the practical data of the Beijing Yizhuang line, where the three proposed approaches are compared with a state-of-the-art approach and a practical method used by the traffic planners. This comparison shows the effectiveness and efficiency of the three proposed approaches.

Hybrid Demand‐Driven and Cyclic Timetabling Considering Rolling Stock Circulation for a Bidirectional Railway Line

AbstractFor dense railway lines, timetables are commonly designed periodically to provide regular services. However, such timetables may lead to many low‐occupancy departures and make it inefficient to a railway company. We combine the features of periodic timetabling with those of demand‐responsive timetabling design for a bidirectional rail transit line considering rolling stock circulation. A mixed‐integer programming model with the objective of minimizing total passenger waiting time and weighted total train travel time is formulated and a three‐phase heuristic algorithm is developed. Five performance indicators, namely, total train travel time, passenger average waiting time, event time deviation, event frequency deviation, and train connection time are introduced to evaluate the performance of the model. A case study on Jinshan railway corridor in Shanghai demonstrates that the proposed demand responsive periodic timetabling model can reduce passengers’ waiting time and keep periodicity in the meantime with short computational time

Разработка условий эксплуатации специальных вагонов по результатам комплексных испытаний

Objective: To develop the conditions of special cargo railway cars, multi-axis container cars and railway non-autonomous multiple unit trains circulation for transportation of special-purpose goods on public railways of OAO “RZhD”. The speeds of such trains can be higher in comparison with the speeds established by the existing normative documents of JSC “Russian Railways” for cargo trains. Special-purpose cars in nominal loading mode circulate in a train set with a unit locomotive. Methods: The assessment of conditions of the special-purpose rolling stock circulation was carried out by the results of tests on the line as well as the impact on the track and pointwork in the accredited centers, based on the regulations of GOST R 55050–2012. Results: The conditions for the fleet circulation consisting of 8–32-axle special-purpose railway cars, multiaxial container cars and non-autonomous multiple unit trains were established. Practical importance: A set of regulatory documents of JSC “Russian Railways” was developed in the form of regulations on technical conditions of special-purpose railway cars, conveyors and multiple unit trains designed for transportation of special purpose freight.

A Fix & Relax matheuristic for the Crew Scheduling Problem

Abstract This paper presents a crew scheduling model for rapid transit networks, where distances are not big but service frequency is very high. The crew scheduling problem has been traditionally modelled as a set covering/partitioning problem. Here, the presented approach faces the problem in a different way taking benefit from a linear payment policy and enabling an easier integration with other planning problems such as rolling stock circulations. For solving this new model, a Fix and Relax matheuristic is employed. Branch and Bound and commercial heuristics are also tested so as to compare the performance of the presented solution approach. In order to demonstrate the goodness of the results, experiments for real case studies drawn from the main Spanish train operator, RENFE, are presented showing a good balance between optimality and computational times. Compared to commercial software, computational times are reduced more than 94%, without sacrificing optimality GAP.

The integrated rolling stock circulation and depot location problem in railway rapid transit systems

Rolling stock management is one of the key operational issues for a railway transportation company. It constitutes the fourth phase of the classical Railway Planning Process, after Network design, Line Planning and Services Scheduling/Timetabling. Rolling stock circulation consists of defining individual train paths over the network accomplishing pre-defined services. Those services are previously designed in order to attend certain passengers’ demand, and fulfilling some design criteria. In this paper we propose, in the context of Railway Rapid Transit Systems, a general mixed integer programming model in order to design rolling stock circulation plans and simultaneously considering the problem of determining the number and location of rest facilities. The model yields then rolling stocks plans that facilitate the posterior design of rotating maintenance schemes. According to the problem structure, we propose a sequential solving approach. We first determine the minimum number of vehicles needed to perform the complete weekly train schedule. In a second phase, we obtain the set of daily routes that must be performed at each line every day. In a third stage, we deal with the problem of determining weekly circulations and depot locations by means of a Genetic Algorithm. The objective at this stage is to minimize empty movements and to equilibrate the number of kilometers covered by each unit. In order to illustrate the proposed approach, this is applied to design a rotating rolling stock plan for the RRT Network of Seville.

Maintenance Appointments in Railway Rolling Stock Rescheduling

This paper addresses the railway rolling stock rescheduling problem, while taking maintenance appointments into account. After a disruption, the rolling stock of the disrupted passenger trains has to be rescheduled to restore a feasible rolling stock circulation. Usually, a number of train units have a scheduled maintenance appointment during the day: these appointments must be taken into account while rescheduling the rolling stock. In this paper we propose three mixed-integer programming models for this purpose. All models are extensions of the composition model from the literature, which does not distinguish individual train units. The extra unit type model adds an additional rolling stock type for each train unit that requires maintenance. The shadow-account model keeps track of a shadow account for each train unit that requires maintenance. The job-composition model creates a path for each train unit such that the train units that require maintenance are on time for their maintenance appointments. All models are tested on instances of Netherlands Railways. The results show that especially the shadow-account model and the job-composition model are effectively able to take maintenance appointments into account during real-time rescheduling. It depends on the characteristics of an instance whether the shadow-account model or the job-composition model performs best.