Optimizing train stopping patterns and schedules for high-speed passenger rail corridors

High-speed railway (HSR) systems have been developing rapidly in China and various other countries throughout the past decade; as a result, the question of how to efficiently operate such large-scale systems is posing a new challenge to the railway industry. A high-quality train timetable should take full advantage of the system’s capacity to meet transportation demands. This paper presents a mathematical model for optimizing a train timetable for an HSR system. We propose an innovative methodology using a column-generation-based heuristic algorithm to simultaneously account for both passenger service demands and train scheduling. First, we transform a mathematical model into a simple linear programming problem using a Lagrangian relaxation method. Second, we search for the optimal solution by updating the restricted master problem (RMP) and the sub-problems in an iterative process using the column-generation-based algorithm. Finally, we consider the Beijing–Shanghai HSR line as a real-world application of the methodology; the results show that the optimization model and algorithm can improve the defined profit function by approximately 30% and increase the line capacity by approximately 27%. This methodology has the potential to improve the service level and capacity of HSR lines with no additional high-cost capital investment (e.g., the addition of new tracks, bridges and tunnels on the mainline and/or at stations).     

Towards a welfare enhancing process to manage railway infrastructure access

The European Commission has suggested that the use of scarce railway track capacity should be charged for on a marginal cost basis and that a welfare enhancing procedure to allocate capacity between competing operators is to be implemented. The present paper presents a practicable way to deal with these challenges. Two issues are at the analytical core of the problem. First, in order to prioritise, accurate information is required about the operators' willingness-to-pay for track access; to this end, an auctioning procedure has been developed. Secondly, an approach to handle the technically complex optimisation problem is needed so that `reasonably' optimal allocations, given the `accurate' information, can be established; dual optimisation is suggested as the remedy. Recent experiences from the US auctioning of radio-wave frequencies are cited as supporting evidence for the rationale of the approach.     

Perspectives of high speed rail transport in short-medium period

In this paper an analytic method to evaluate technical and economic conditions of convenience for new high speed lines in guided transport systems, is described. In particular it answers the following main questions: what are the conditions to construct a new high speed line; what is the optimal operational speed of a new line; which is the better between two systems, differing in costs structure and quality of performance? It is shown that a modern railway, able to reach a speed up to 300 km/h, is in short-medium period better than contactless systems so far tested. In the last part of the paper a hypothesis of a new generation contactless system is outlined. A comparison with high speed railway shows that, from a theoretical point of view, this new system called “synthesis solution,” could be in the future the real competitor of the railway.     

Integrating robust timetabling in line plan optimization for railway systems

We propose a heuristic algorithm to build a railway line plan from scratch that minimizes passenger travel time and operator cost and for which a feasible and robust timetable exists. A line planning module and a timetabling module work iteratively and interactively. The line planning module creates an initial line plan. The timetabling module evaluates the line plan and identifies a critical line based on minimum buffer times between train pairs. The line planning module proposes a new line plan in which the time length of the critical line is modified in order to provide more flexibility in the schedule. This flexibility is used during timetabling to improve the robustness of the railway system. The algorithm is validated on the DSB S-tog network of Copenhagen, which is a high frequency railway system, where overtakings are not allowed. This network has a rather simple structure, but is constrained by limited shunt capacity. While the operator and passenger cost remain close to those of the initially and (for these costs) optimally built line plan, the timetable corresponding to the finally developed robust line plan significantly improves the minimum buffer time, and thus the robustness, in eight out of ten studied cases.     

Analyzing the theoretical capacity of railway networks with a radial-backbone topology

In this work we propose a mechanism to optimize the capacity of the main corridor within a railway network with a radial-backbone or X-tree structure. The radial-backbone (or X-tree) structure is composed of two types of lines: the primary lines that travel exclusively on the common backbone (main corridor) and radial lines which, starting from the common backbone, branch out to individual locations. We define possible line configurations as binary strings and propose operators on them for their analysis, yielding an effective algorithm for generating an optimal design and train frequencies. We test our algorithm on real data for the high speed line Madrid–Seville. A frequency plan consistent with the optimal capacity is then proposed in order to eliminate the number of transfers between lines as well as to minimize the network fleet size, determining the minimum number of vehicles needed to serve all travel demand at maximum occupancy.     

A Heuristic Algorithm for the Allocation of Airport Runway System Capacity

Abstract

This paper develops a heuristic algorithm for the allocation of airport runway capacity to minimise the cost of arrival and departure aircraft/flight delays. The algorithm is developed as a potential alternative to optimisation models based on linear and integer programming. The algorithm is based on heuristic (‘greedy’) criteria that closely reflect the ‘rules of thumb’ used by air traffic controllers. Using inputs such as arrival and departure demand, airport runway system capacity envelopes and cost of aircraft/flight delays, the main output minimises the cost of arrival and departure delays as well as the corresponding interdependent airport runway system arrival and departure capacity allocation. The algorithm is applied to traffic scenarios at three busy US airports. The results are used to validate the performance of the proposed heuristic algorithm against results from selected benchmarking optimisation models.     

Formalizing a subset of ERTMS/ETCS specifications for verification purposes

ERTMS is the standard railway control-command and signaling system which aims to ensure railway interoperability throughout Europe while enhancing safety and competitiveness. ERTMS is composed of two main subsystems which include GSM-R, a radio system for enabling communication between the train and the traffic management center and ETCS, an automatic train protection system (ATP) to replace the existing national ATP systems. The ERTMS specifications are defined by means of standard documents which set out the requirements ensuring interoperability. These documents evolve regularly to give rise to successive versions. The ERTMS/ETCS standard defines different levels and operation modes according to various trackside and onboard setups and some operational conditions. Given the complexity and the high criticality of railway operation, verification and validation (V&V) are crucial tasks in railway application development.In this paper, after setting the background and the motivations, a mechanizable formalization of a subset of ERTMS/ETCS specifications relative to ETCS modes and transitions is developed. The present work aims to offer a readily available model for formal V&V. Using formal techniques to check SRS is highly recommended to tackle the complexity of the defined requirements and prevent specification errors. Model-checking technique, which is targeted here, offers exhaustive analysis of the system behavior based on its model and is highly automated, since it is supported by software tools. Based on the last available version of SRS specifications, a progressive process is undertaken to get a formal model which makes explicit the various modes characterized by their respective active functions, as well as the numerous combinations of conditions for switching between modes. The various steps guiding the translation of the SRS literal specifications into a formal model are explained. As will be shown through different examples, the obtained model is a convenient basis to check safety, interoperability and liveness properties.     

System energy optimisation strategies for metros with regeneration

Energy and environmental sustainability in transportation are becoming ever more important. In Europe, the transportation sector is responsible for about 30% of the final end use of energy. Electrified railway systems play an important role in contributing to the reduction of energy usage and CO₂ emissions compared with other transport modes. For metro-transit systems with frequently motoring and braking trains, the effective use of regenerated braking energy is a significant way to reduce the net energy consumption. Although eco-driving strategies have been studied for some time, a comprehensive understanding of how regeneration affects the overall system energy consumption has not been developed. This paper proposes a multi-train traction power network modelling method to determine the system energy flow of the railway system with regenerating braking trains. The initial results show that minimising traction energy use is not the same as minimising the system energy usage in a metro system. An integrated optimisation method is proposed to solve the system energy-saving problem, which takes train movement and electrical power flow into consideration. The results of a study of the Beijing Yizhuang metro line indicate that optimised operation could reduce the energy consumption at the substations by nearly 38.6% compared to that used with the existing ATO operation.     

Are railways really that bad? An evaluation of rail systems performance in Europe with a focus on passenger rail

With a large number of railway development projects in Europe and worldwide, which once completed will be serving rail passengers of the future, this paper aims to take a step back and evaluate current railway systems performance. The objectives are to compare statistical data on various passenger-related parameters of the railway system in a number of selected European countries and draw conclusions on the level of their performance when compared to the European average.Analyses of publically available statistical data, extracted from the Eurostat service at a European level will allow for a comparison of various indicators which influence the performance of the railway systems from an infrastructure and operational perspectives. The analyses will also allow identifying key performance indicators for the accurate assessment of the rail systems.The paper will highlight case studies for various parameters which are important to stakeholders of the railways, including infrastructure managers, rail operators, policy makers and the end users. This knowledge will be to the benefit of today’s railway industry as well as the rail systems of the future, as it will show trends drew upon existing data which might continue in the future.     

Guidance for new policy developments on railway noise and vibration

Noise and vibration are two of the main problems associated with railways in residential areas. To ensure quality of life and well-being of inhabitants living in the vicinity of railway paths, it is important to evaluate, understand, control and regulate railway noise and vibration. Much attention has been focused on the impact of noise from railway traffic but the consideration of railway-induced vibration has often been neglected. This paper aims to provide policy guidance based on results obtained from the analyses of relationships estimated from ordinal logit models between human response, railway noise exposure and railway vibration exposure. This was achieved using data from case studies comprised of face-to-face interviews (N = 931), internal vibration measurements (N = 755), and noise calculations (N = 688) collected within the study “Human Response to Vibration in Residential Environments” by the University of Salford, UK. Firstly, the implications of neglecting vibration in railway noise policies are investigated. The findings suggest that it is important to account for railway induced vibrations in future noise and transport policies, as neglecting vibrations results in an underestimation of people highly annoyed by noise. Secondly, implications of neglecting different types of railway sources are presented. It was found that the impact of noise and vibration form maintenance operations should be better understood and should be taken into account when assessing the environmental impact of railways in residential environments. Finally, factors that were found to influence railway vibration annoyance are presented and expressed as weightings. The data shows that factors specific to a particular residential area should also be taken into account in future vibration policies as the literature shows that attitudinal, socio-demographic and situational factors have a large influence on vibration annoyance responses. This work will be of interest to researchers and environmental health practitioners involved in the assessment of vibration complaints, as well as to policy makers, planners and consultants involved in the design of buildings and railways.     

Optimizing the demand captured by a railway system with a regular timetable

The railway systems in various European countries adopt regular timetables, in which the trains arrive and depart at constant intervals. In fact, their simple structure provides several advantages both to the passengers and to the management of the service. The design of such timetables has recently received a certain attention in the literature, but the standard model aims to optimize the service for a fixed demand. We relax this unrealistic assumption, taking into account the reciprocal influence between the quality of the timetable and the amount of transport demand captured by the railway. This results into a mixed-integer non linear model with a non-convex continuous relaxation. We solve it by a branch-and-bound algorithm based on a piecewise-linear overestimate of the objective function and a heuristic algorithm which iteratively applies the standard fixed-demand model and a demand-estimation model, feeding each one with data based on the solution obtained from the other one at the previous iteration. The computational results presented concern both random instances and a real-world regional network located in Northwestern Italy.     

Passenger Perspectives in Railway Timetabling: A Literature Review

When looking at railway planning, a discrepancy exists between planners who focus on the train operations and publish fixed railway schedules, and passengers who look not only at the schedules but also at the entirety of their trip, from access to waiting to on-board travel and egress. Looking into this discrepancy is essential, as assessing railway performances by merely measuring train punctuality would provide an unfair picture of the level of service experienced by passengers. Firstly, passengers’ delays are often significantly larger than the train delays responsible for the passengers to be late. Secondly, trains’ punctuality is often strictly related to too tight schedules that in turn might translate into knock-on delays for longer dwelling times at stations, trip delays for increased risk of missing transfer connections, and uncertain assessment of the level of service experienced, especially with fluctuating passenger demand. A key aspect is the robustness of railway timetables. Empirical evidence indicates that passengers give more importance to travel time certainty than travel time reductions, as passengers associate an inherent disutility with travel time uncertainty. This disutility may be broadly interpreted as an anxiety cost for the need for having contingency plans in case of disruptions, and may be looked at as the motivator for the need for delay-robust railway timetables. Interestingly, passenger-oriented optimisation studies considering robustness in railway planning typically limit their emphasis on passengers to the consideration of transfer maintenance. Clearly, passengers’ travel behaviour is far more complex and multi-faceted and thus several other aspects should be considered, as becoming more and more evident from passenger surveys. The current literature review starts by looking at the parameters that railway optimisation/planning studies are focused on and the key performance indicators that impact railway planning. The attention then turns to the parameters influencing passengers’ perceptions and travel experiences. Finally, the review proposes guidelines on how to reduce the gap between the operators’ railway planning and performance measurement on the one hand and the passengers’ perception of the railway performance on the other hand. Thereby, the conclusions create a foundation for a more passenger-oriented railway timetabling ensuring that passengers are provided with the best service possible with the resources available.     

Rail track infrastructure ownership: investment and operational issues

As privatisation of railway systems reach the political agendas in a number of countries, the separation of track infrastructure from train operations is seen as providing the vehicle which will improve profitability within the rail industry. This paper deals with three main issues related to such separation within a freight railway focus, namely: investment appraisal; track standards and maintenance; and train operating performance. The conflicts of interest between the owners of track and their client operators are discussed in detail. Costs related to track capacity and congestion need to be taken into account, given that additional trains are likely to lead to increased risk of delays to existing services. The paper discusses the use of a travel time reliability model to estimate the additional costs imposed on the system through the introduction of specific train services.It is concluded that investment in individual elements of railway infrastructure must be integrated with the overall financial and customer service strategies of both operators and owners. As an alternative to current practices, a hybrid model of track ownership is put forward here. Under such a model, a joint-venture company with equity from the main ÒplayersÓ would be owner of track. This would allow some of the benefits of vertical integration to be retained, whilst providing fair access to new operators.     

Balancing energy consumption and risk of delay in high speed trains: A three-objective real-time eco-driving algorithm with fuzzy parameters

Eco-driving is an energy efficient traffic operation measure that may lead to important energy savings in high speed railway lines. When a delay arises in real time, it is necessary to recalculate an optimal driving that must be energy efficient and computationally efficient.In addition, it is important that the algorithm includes the existing uncertainty associated with the manual execution of the driving parameters and with the possible future traffic disturbances that could lead to new delays.This paper proposes a new algorithm to be executed in real time, which models the uncertainty in manual driving by means of fuzzy numbers. It is a multi-objective optimization algorithm that includes the classical objectives in literature, running time and energy consumption, and as well a newly defined objective, the risk of delay in arrival. The risk of delay in arrival measure is based on the evolution of the time margin of the train up to destination.The proposed approach is a dynamic algorithm designed to improve the computational time. The optimal Pareto front is continuously tracked during the train travel, and a new set of driving commands is selected and presented to the driver when a delay is detected.The algorithm evaluates the 3 objectives of each solution using a detailed simulator of high speed trains to ensure that solutions are realistic, accurate and applicable by the driver. The use of this algorithm provides energy savings and, in addition, it permits railway operators to balance energy consumption and risk of delays in arrival. This way, the energy performance of the system is improved without degrading the quality of the service.     

Analysis on line capacity usage for China high speed railway with optimization approach

The purpose for the analysis of capacity usage is to utilize the rail infrastructure in a more efficient and practical way. The practical and theoretical challenge of the rail capacity is its dynamics and uncertainty, which are common in China and elsewhere. Based on the capacity balance, a train service-demand intention set (TSDIS) at High-Speed Rail (HSR) line (t@l-TSDIS) is defined, which takes the number of trains, the average speed, the heterogeneity and the stability as the core elements for the capacity usage. For dynamics and uncertainty, we update the norm for capacity measure as the time needed to fulfill the task list t@l-TSDIS. Then we develop the objectives and constraints for the Mathematical Program for Line Capacity (MPLC), which aims at minimization of heterogeneity and running time as well as maximization of reliability. For solving MPLC, the Pareto Archived Evolutionary Strategy (PAES) and fuzzy logic penalty function are introduced. Furthermore we propose a rolling optimization tactic oriented by the practical problem, which combines the improved Pareto Archived Evolutionary Strategy (iPAES) with an interactive technique. In a case study, we apply the proposed ideas and methodology to Beijing-Shanghai HSR (BS-HSR) line much closer to the railway practice. By using the computer language C# to compile the Console program, Pareto optimized results for MPLC are achieved, including the standard and practical values for the heterogeneity indices, reliability indices and running time indices. We also discuss the sensitivity of the heterogeneity index. This research demonstrates that it is useful to analyze the line capacity usage for China HSR with the proposed optimization approach.     

Regulatory reform and the congestion of urban railways

This paper examines various regulatory methods for congested urban railways. After building a closed spatial model with a congestible railway line, we conduct a numerical simulation of the impacts of the regulatory methods, using data on a typical railway firm in Japan. A closed spatial model in this paper enables us to evaluate the regulatory methods in terms of social welfare as well as to show a change in the typical performance of railways, such as the level of fares, railway capacity, and congestion. The simulation results show that implementing simple price-cap regulation, without properly addressing the congestion problem, makes railway firms operate efficiently, but substantially shrinks railway capacity and lowers social welfare. We then consider modified versions of price-cap regulation, which are consistent with relief of congestion.     

Resilience in railway transport systems: a literature review and research agenda

ABSTRACT

Critical infrastructure networks, such as transport and power networks, are essential for the functioning of a society and economy. The rising transport demand increases the congestion in railway networks and thus they become more interdependent and more complex to operate. Also, an increasing number of disruptions due to system failures as well as climate changes can be expected in the future. As a consequence, many trains are cancelled and excessively delayed, and thus, many passengers are not reaching their destinations which compromises customers need for mobility. Currently, there is a rising need to quantify impacts of disruptions and the evolution of system performance. This review paper aims to set-up a field-specific definition of resilience in railway transport and gives a comprehensive, up-to-date review of railway resilience papers. The focus is on quantitative approaches. The review analyses peer-reviewed papers in Web of Science and Scopus from January 2008 to August 2019. The results show a steady increase of the number of published papers in recent years. The review classifies resilience metrics and approaches. It has been recognised that system-based metrics tend to better capture effects on transport services and transport demand. Also, mathematical optimization shows a great potential to assess and improve resilience of railway systems. Alternatively, data-driven approaches could be potentially used for detailed ex-post analysis of past disruptions. Finally, several rising future scientific topics are identified, spanning from learning from historical data, to considering interdependent critical systems and community resilience. Practitioners can also benefit from the review to understand a common terminology, recognise possible applications for assessing and designing resilient railway transport systems.     

Development and Impact of the Modern High‐speed Train: A Review

Abstract

The inauguration of the Shinkansen high‐speed train service between Tokyo and Osaka, Japan, at 210 kph maximum operating speed some 40 years ago marked the comeback of the train as an important passenger mode of transport. Since then high‐speed train (HST) services have been introduced in many countries and are planned in many more, and the train has once more become the dominant mode of transport on many routes. This review summarizes the different elements of HST operation with the aim of characterizing HST operation and putting in context its impact in terms of what it is best designed for and what it can deliver. The review concludes that the HST is best designed to substitute conventional railway services on routes where much higher capacity is required and to reduce travel time, further improving the railway service, also against other modes, therefore leading to mode substitution. However, the high investment in HST infrastructure could not be justified based on its economic development benefits since these are not certain. Finally, the following definition for HST services is suggested: high capacity and frequency railway services achieving an average speed of over 200 kph.     

Multiple-phase train trajectory optimization with signalling and operational constraints

The train trajectory optimization problem aims at finding the optimal speed profiles and control regimes for a safe, punctual, comfortable, and energy-efficient train operation. This paper studies the train trajectory optimization problem with consideration of general operational constraints as well as signalling constraints. Operational constraints refer to time and speed restrictions from the actual timetable, while signalling constraints refer to the influences of signal aspects and automatic train protection on train operation. A railway timetable provides each train with a train path envelope, which consists of a set of positions on the route with a specified target time and speed point or window. The train trajectory optimization problem is formulated as a multiple-phase optimal control model and solved by a pseudospectral method. This model is able to capture varying gradients and speed limits, as well as time and speed constraints from the train path envelope. Train trajectory calculation methods under delay and no-delay situations are discussed. When the train follows the planned timetable, the train trajectory calculation aims at minimizing energy consumption, whereas in the case of delays the train trajectory is re-calculated to track the possibly adjusted timetable with the aim of minimizing delays as well as energy consumption. Moreover, the train operation could be affected by yellow or red signals, which is taken into account in the train speed regulation. For this purpose, two optimization policies are developed with either limited or full information of the train ahead. A local signal response policy ensures that the train makes correct and quick responses to different signalling aspects, while a global green wave policy aims at avoiding yellow signals and thus proceed with all green signals. The method is applied in a case study of two successive trains running on a corridor with various delays showing the benefit of accurate predictive information of the leading train on energy consumption and train delay of the following train.     

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.