A new approach for improving the performance of freight train timetabling of a single-track railway system

A new approach for improving the performance of freight train timetabling for single-track railways is proposed. Using the idea of a fixed-block signaling system, we develop a matrix representation to express the occupation of inter- and intra-station tracks by trains illustrating the train blocking time diagram in its entirety. Train departure times, dwell times, and unnecessary stopping are adjusted to reduce average train travel time and single train travel time. Conflicts between successive stations and within stations are identified and solved. A fuzzy logic system is further used to adjust the range of train departure times and checks are made to determine whether dwell times and time intervals can be adjusted for passenger and freight trains at congested stations to minimize train waiting times. By combining manual scheduling expertise with the fuzzy inference method, timetable efficiency is significantly improved and becomes more flexible.     

Stochastic prediction of train delays in real-time using Bayesian networks

In this paper we present a stochastic model for predicting the propagation of train delays based on Bayesian networks. This method can efficiently represent and compute the complex stochastic inference between random variables. Moreover, it allows updating the probability distributions and reducing the uncertainty of future train delays in real time under the assumption that more information continuously becomes available from the monitoring system. The dynamics of a train delay over time and space is presented as a stochastic process that describes the evolution of the time-dependent random variable. This approach is further extended by modelling the interdependence between trains that share the same infrastructure or have a scheduled passenger transfer. The model is applied on a set of historical traffic realisation data from the part of a busy corridor in Sweden. We present the results and analyse the accuracy of predictions as well as the evolution of probability distributions of event delays over time. The presented method is important for making better predictions for train traffic, that are not only based on static, offline collected data, but are able to positively include the dynamic characteristics of the continuously changing delays.     

Analyzing passenger train arrival delays with support vector regression

We propose machine learning models that capture the relation between passenger train arrival delays and various characteristics of a railway system. Such models can be used at the tactical level to evaluate effects of various changes in a railway system on train delays. We present the first application of support vector regression in the analysis of train delays and compare its performance with the artificial neural networks which have been commonly used for such problems. Statistical comparison of the two models indicates that the support vector regression outperforms the artificial neural networks. Data for this analysis are collected from Serbian Railways and include expert opinions about the influence of infrastructure along different routes on train arrival delays.     

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.     

Robust single-track train dispatching model under a dynamic and stochastic environment: A scenario-based rolling horizon solution approach

After a major service disruption on a single-track rail line, dispatchers need to generate a series of train meet-pass plans at different decision times of the rescheduling stage. The task is to recover the impacted train schedule from the current and future disturbances and minimize the expected additional delay under different forecasted operational conditions. Based on a stochastic programming with recourse framework, this paper incorporates different probabilistic scenarios in the rolling horizon decision process to recognize (1) the input data uncertainty associated with predicted segment running times and segment recovery times and (2) the possibilities of rescheduling decisions after receiving status updates. The proposed model periodically optimizes schedules for a relatively long rolling horizon, while selecting and disseminating a robust meet-pass plan for every roll period. A multi-layer branching solution procedure is developed to systematically generate and select meet-pass plans under different stochastic scenarios. Illustrative examples and numerical experiments are used to demonstrate the importance of robust disruption handling under a dynamic and stochastic environment. In terms of expected total train delay time, our experimental results show that the robust solutions are better than the expected value-based solutions by a range of 10-30%.     

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.     

Train scheduling simulation that minimises operational conflicts due to service constraints

This paper presents an attempt made to facilitate re‐scheduling of trains to minimize operational delays and accommodate uniform headways for off peak sub urban services subject to resource constraints such as locomotive availability, poor track conditions and stations without siding facilities. The paper describes the computer simulation model designed to optimize train schedules on single‐track rail lines. Using this simulation program it is possible to plan and optimize timetables for railway networks with train runs within short time periods for both single track and double track conditions. The paper describes the capabilities of presenting the results of the simulation runs. These include the time‐distance graph, the network with train movements, dialog boxes with information about selected trains. The programme is capable of changing the starting point, departure time, train destinations and adding or deleting a stop etc. from the user interface. Four objects of array variables are used in the simulation process to keep train and station data. Two object arrays are used for the train movements in up and down directions. The stations' data are stored in the other two object arrays. One of these arrays of stations contains all the stations of the line while the other one contains only the stations with siding facilities. A case study that covers a 61 km long single‐track line with 14 stations is presented to highlight the model capabilities.     

A practical capacity model of a single track line

The paper presents a model for determining the practical capacity of a single track line, i.e. the maximum number of trains which can be run along it in a time unit under the condition that each train enters its bottleneck segment with a definite delay.

The input data used in the model are: geometrical characteristics of the bottleneck segment of the line under study, the intensity and structure of demand expressed by a number of trains which are run over the line in a given time unit, the scenario of traffic running over the line under study and the operational tactics of individual train categories processing on the bottleneck segment.

(Two tactics can be applied in the train processing on the line under study; first, the trains of individual categories are given different priorities in the processing, and second, all the trains have the same priority).

The output results of the model are average delays of trains of each category occurring within the train processing performed on the bottleneck segment of the line under study in a given time unit.     

Scheduling heterogeneous train traffic on double tracks with efficient dispatching rules

To further improve the utilization rate of railway tracks and reduce train delays, this paper focuses on developing a high-efficiency train routing and timetabling approach for double-track railway corridors in condition that trains are allowable to travel on reverse direction tracks. We first design an improved switchable policy which is rooted in the approaches by Mu and Dessouky (2013), with the analysis of possible delays caused by different path choices. Then, three novel integrated train routing and timetabling approaches are proposed on the basis of a discrete event model and different dispatching rules, including no switchable policy (No-SP), Mu and Dessouky (2013)’s switchable policy (Original-SP) and improved switchable policy (Improved-SP). To demonstrate the performance of the proposed approaches, the heterogeneous trains on Beijing–Shanghai high speed railway are scheduled by aforementioned approaches. The case studies indicate that in comparison to No-SP and Original-SP approaches, respectively, the Improved-SP approach can reduce the total delay of trains up to 44.44% and 73.53% within a short computational time. Moreover, all of the performance criteria of the Improved-SP approach are usually better than those of other two approaches.     

Closing the loop in real-time railway control: Framework design and impacts on operations

Railway traffic is heavily affected by disturbances and/or disruptions, which are often cause of delays and low performance of train services. The impact and the propagation of such delays can be mitigated by relying on automatic tools for rescheduling traffic in real-time. These tools predict future track conflict based on current train information and provide suitable control measures (e.g. reordering, retiming and/or rerouting) by using advanced mathematical models. A growing literature is available on these tools, but their effects on real operations are blurry and not yet well known, due to the very scarce implementation of such systems in practice.In this paper we widen the knowledge on how automatic real-time rescheduling tools can influence train performance when interfaced with railway operations. To this purpose we build up a novel traffic control framework that couples the state-of-the art automatic rescheduling tool ROMA, with the realistic railway traffic simulation environment EGTRAIN, used as a surrogate of the real field. At regular times ROMA is fed with current traffic information measured from the field (i.e. EGTRAIN) in order to predict possible conflicts and compute (sub) optimal control measures that minimize the max consecutive delay on the network. We test the impact of the traffic control framework based on different types of interaction (i.e. open loop, multiple open loop, closed loop) between the rescheduling tool and the simulation environment as well as different combinations of parameter values (such as the rescheduling interval and prediction horizon). The influence of different traffic prediction models (assuming e.g. aggressive versus conservative driving behaviour) is also investigated together with the effects on traffic due to control delays of the dispatcher in implementing the control measures computed by the rescheduling tool.Results obtained for the Dutch railway corridor Utrecht–Den Bosch show that a closed loop interaction outperforms both the multiple open loop and the open loop approaches, especially with large control delays and limited information on train entrance delays and dwell times. A slow rescheduling frequency and a large prediction horizon improve the quality of the control measure. A limited control delay and a conservative prediction of train speed help filtering out uncertain traffic dynamics thereby increasing the effectiveness of the implemented measures.     

Service-cost tradeoffs for carload freight traffic in the U.S. rail industry

Railroad technology permits a single train to move a large number of individual freight cars. However, cars which are not in dedicated unit train or intermodal service experience considerable delay due to the consolidation and breakup of trains. Rail operations thus involve a tradeoff between the economies of shipment consolidation, and the resulting delays. More direct and/or more frequent train connections will increase costs, but reduce transit times. This article quantifies the cost of providing a range of transit times for general carload traffic for several representative U.S. rail systems. It shows that significant reductions in transit time will require a large increase in the number of train connections and operating cost. Changes in labor contracts to reduce train crew cost will provide some incentive for higher service levels, but reductions in crew cost alone cannot be expected to dramatically improve the performance of the carload segment of the industry.     

Individual freight effects,capacity utilization,and Amtrak service quality

This paper offers a new perspective on the post-deregulation rail industry. We hypothesize that a link exists between individual freight effects and Amtrak service quality. Specifically, we investigate the relationship between freight control of the infrastructure on which Amtrak trains operate and Amtrak train delays. Our sample consists of 1117 directional station-pairs for fiscal years 2002 through 2007 on 28 Amtrak non-Northeast Corridor passenger routes. We found that freight effects have a significant impact on Amtrak train delays after controlling for other important delay determinants such as the capacity utilization rate. The impact is higher on long-distance routes. We also observed significant differences between the effects of different freight railroads. For example, Amtrak operations on infrastructure controlled by several Class I railroads experienced significantly larger delays than baseline operations, while Amtrak train delays on Burlington Northern and Santa Fe’s tracks actually fell below baseline levels.     

Single track line capacity model

The objective of the research described in this paper was to develop a model for computation of an ultimate capacity of a single track line and to provide a sensitivity analysis of this capacity to the parameters which influence it. The model is based in a concept of mathematical expectation of capacity and can be applied under saturation conditions i.e. a constant demand for service. It can serve for planning purposes, computation of single track line capacity on the base of which estimations are possible concerning a single track line performance under given conditions, as well as commercial time‐tables planning, decisions about a partial or complete construction of the second parallel track along the line in service, intermediate stations locations planning and the necessary facilities along the line under construction.

In the sensitivity analysis, the model allows a change of parameters upon which the capacity depends. These are: the length of the line segment which is considered to be bottleneck for calculation of capacity, traffic distributions per directions, train mix, train velocities and train spacing rules applied by the dispatching service when regulating the traffic on a line.     

Integrated modeling of high performance passenger and freight train planning on shared-use corridors in the US

This paper studies strategic level train planning for high performance passenger and freight train operations on shared-use corridors in the US. We develop a hypergraph-based, two-level approach to sequentially minimize passenger and freight costs while scheduling train services. Passenger schedule delay and freight lost demand are explicitly modeled. We explore different solution strategies and conclude that a problem-tailored linearized reformulation yields superior computational performance. Using realistic parameter values, our numerical experiments show that passenger cost due to schedule delay is comparable to in-vehicle travel time cost and rail fare. In most cases, marginal freight cost increase from scheduling more passenger trains is higher than marginal reduction in passenger schedule delay cost. The heterogeneity of train speed reduces the number of freight trains that can run on a corridor. Greater tolerance for delays could reduce lost demand and overall cost on the freight side. The approach developed in the paper could be applied to other scenarios with different parameter values.     

Train delay and perceived-wait time: passengers' perspective

Abstract

Waiting time influences the overall perception of service quality. The passenger-perceived waiting time can determine their waiting experience. The concept of waiting time refers to the comparison between the passengers' inherent tolerance of waiting and the possible improvement scenarios. This study investigates the passengers' tolerance of waiting under various scenarios of train delays in order to improve their perceived waiting time. We propose the adoption of a modern psychometric method utilizing the Rasch model to measure a subjective latent construct known as ‘wait tolerance'. The Rasch measurement provides mathematical procedures for transforming scores from an ordinal to an interval scale to observe which scenarios can reduce certain passengers' perceived waiting time in the case of a delay. Empirical results show that ‘uncontrollable circumstances', ‘friendly staff attitudes', and ‘providing appropriate messages of apology' can improve the passenger-perceived waiting time during train delays. Likewise, distinct differences are found in the passengers' tolerance of waiting in terms of various personal characteristics, such as gender, age, and train riding frequency. The findings propose the implementation of strategies for improvement by rail system operators, as well as for regulators to define a reasonable service level in the case of train delays. The reviews show possible future innovative research orientations as well.     

On the use of “average delay” as a measure of train reliability

We investigate how passengers on long-distance trains value unexpected delays relative to scheduled travel time and travel cost. For scheduled services with high reliability and long headways, the value of delays is most commonly assumed to be proportional to the average delay. By exploring how the valuation of train delays depends on delay risk and delay length, using three different stated choice data sets, we find that the “average delay” approach does not hold: the disutility increases slower than linearly in the delay risk. This means that using the average delay as a performance indicator, a guide for operations planning or for investment appraisal will underestimate the value of small risks of long delays relative to large risks for short delays. It also means that estimated valuations of “average delay” will depend on the delay risk level: valuations will be higher the lower the risk levels in the study are.     

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.     

Integrating capacity analysis with high-speed railway timetabling: A minimum cycle time calculation model with flexible overtaking constraints and intelligent enumeration

Compared with most optimization methods for capacity evaluation, integrating capacity analysis with timetabling can reveal the types of train line plans and operating rules that have a positive influence on improving capacity utilization as well as yielding more accurate analyses. For most capacity analyses and cyclic timetabling methods, the cycle time is a constant (e.g., one or two hours). In this paper, we propose a minimum cycle time calculation (MCTC) model based on the periodic event scheduling problem (PESP) for a given train line plan, which is promising for macroscopic train timetabling and capacity analysis. In accordance with train operating rules, a non-collision constraint and a series of flexible overtaking constraints (FOCs) are constructed based on variations of the original binary variables in the PESP. Because of the complexity of the PESP, an iterative approximation (IA) method for integration with the CPLEX solver is proposed. Finally, two hypothetical cases are considered to analyze railway capacity, and several influencing factors are studied, including train regularity, train speed, line plan specifications (train stops), overtaking and train heterogeneity. The MCTC model and IA method are used to test a real-world case involving the timetable of the Beijing–Shanghai high-speed railway in China.     

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.     

A simulation model of train travel on a rail transit line

A simplified simulation model for the operational analysis of a rail rapid transit train is presented. The model simulates the movement of a train along a route, and develops the relationships of time—distance, time—speed and distance—speed. The inputs to the model are the profile of speed limits and the dynamic characteristics of the train. Without the information on the track geometry and tractive effort, the model determines the speed of the train at a location based on the previous and future speed limits relative to the location. It was found that the model can fairly accurately simulate the relationship between travel time and distance. A comparison of the train travel times between the actual and simulated runs is presented. Because of the simplicity of input and calculation method, the model can be a useful tool for the “desk-top” analysis of frequently occurring planning problems of a commuter rail or rail rapid transit line, such as the impacts of changes in speed limits, station locations, station stopping policy, addition/elimination of stations, and types of rail cars.