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.     

An integrated micro–macro approach to robust railway timetabling

With the increasing demand for railway transportation infrastructure managers need improved automatic timetabling tools that provide feasible timetables with enhanced performance in short computation times. This paper proposes a hierarchical framework for timetable design which combines a microscopic and a macroscopic model of the network. The framework performs an iterative adjustment of train running and minimum headway times until a feasible and stable timetable has been generated at the microscopic level. The macroscopic model optimizes a trade-off between minimal travel times and maximal robustness using an Integer Linear Programming formulation which includes a measure for delay recovery computed by an integrated delay propagation model in a Monte Carlo setting. The application to an area of the Dutch railway network shows the ability of the approach to automatically compute a feasible, stable and robust timetable. Practitioners can use this approach both for effective timetabling and post-evaluation of existing timetables.     

The status of German railway operations management in research and practice

The German railway operations management uses probabilistic and simulation methods in research and practice. The probabilistic methods are based on queuing theory. There are synchronous or asynchronous algorithms for the simulation of time tables, schedule, operation, and disposition. Models were also developed for the simulation of the operation in many parts of the network for the connection between the structure of the track and the capacity of lines and stations, for the evaluation of operating cost depending from the quality of service, and for the design of integrated timetables.     

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.     

Passenger centric train timetabling problem

The aim of this paper is to analyze and to improve the current planning process of the passenger railway service in light of the recent railway market changes. In order to do so, we introduce the Passenger Centric Train Timetabling Problem. The originality of our approach is that we account for the passenger satisfaction in the design of the timetable. We consider both types of timetable(s): cyclic and non-cyclic. The problem is modeled as a Mixed Integer Linear Programming (MILP) problem with an objective of maximizing the train operating company’s profit while maintaining ε level of passenger satisfaction. The model does not take into account conflicts between trains and does not adjust dwell times at stopping stations among the lines. By solving the model for various values of ε, the approximated Pareto frontier is constructed. The analysis, based on an experiment using realistic data, shows that an improvement of passenger satisfaction while maintaining a low profit loss for the railway company can be achieved. A sensitivity analysis on passenger congestion illustrates a quantitative evidence that the non-cyclic timetables can account better for high density demand in comparison to cyclic timetables.     

A hierarchical line planning approach for a large-scale high speed rail network: The China case

Planning a set of train lines in a large-scale high speed rail (HSR) network is typically influenced by issues of longer travel distance, high transport demand, track capacity constraints, and a non-periodic timetable. In this paper, we describe an integrated hierarchical approach to determine line plans by defining the stations and trains according to two classes. Based on a bi-level programming model, heuristics are developed for two consecutive stages corresponding to each classification. The approach determines day-period based train line frequencies as well as a combination of various stopping patterns for a mix of fast trunk line services between major stations and a variety of slower body lines that offer service to intermediate stations, so as to satisfy the predicted passenger transport demand. Efficiencies of the line plans described herein concern passenger travel times, train capacity occupancy, and the number of transfers. Moreover, our heuristics allow for combining many additional conflicting demand–supply factors to design a line plan with predominantly cost-oriented and/or customer-oriented objectives. A range of scenarios are developed to generate three line plans for a real-world example of the HSR network in China using a decision support system. The performance of potential train schedules is evaluated to further examine the feasibility of the obtained line plans through graphical timetables.     

An appraisal of a column-generation-based algorithm for centralized train-conflict resolution on a metropolitan railway network

In practice, a train-conflict resolution is decentralized around dispatchers each of whom controls a few segments in a global railway network with her rule-of-thumb to operational data. Conceptually, the global sub-optimality or infeasibility of the decentralized system is resolved by a network controller who coordinates the dispatchers and train operators at the lower layers on a real-time basis. However, such notion of a multi-layer system cannot be effectual unless the top layer is able to provide a global solution soon enough for the dynamic lower layers to adapt in a seamless manner. Unfortunately, a train-conflict resolution problem is NP-hard as formally established in this paper and an effective solution method traded off between computation time and solution quality has been lacking in literature. Thus, we propose a column-generation-based algorithm that exploits the separability of the problem. A key ingredient of the algorithm is an efficient heuristic for the pricing subproblem for column generation. Tested on the real data from the Seoul metropolitan railway network, the algorithm provides near-optimal conflict-free timetables in a few seconds for most cases. The performance of the proposed algorithm is compared to the ones of the previous MIP-based heuristic by Törnquist and Persson (2007) and the priority-based heuristic by Sahin (1999).     

Improving recovery-to-optimality robustness through efficiency-balanced design of timetable structure

To improve the service quality of the railway system (e.g., punctuality and travel times) and to enhance the robust timetabling methods further, this paper proposes an integrated two-stage approach to consider the recovery-to-optimality robustness into the optimized timetable design without predefined structure information (defined as flexible structure) such as initial departure times, overtaking stations, train order and buffer time. The first-stage timetabling model performs an iterative adjustment of all departure and arrival times to generate an optimal timetable with balanced efficiency and recovery-to-optimality robustness. The second-stage dispatching model evaluates the recovery-to-optimality robustness by simulating how each timetable generated from the first-stage could recover under a set of restricted scenarios of disturbances using the proposed dispatching algorithm. The concept of recovery-to-optimality is examined carefully for each timetable by selecting a set of optimally refined dispatching schedules with minimum recovery cost under each scenario of disturbance. The robustness evaluation process enables an updating of the timetable by using the generated dispatching schedules. Case studies were conducted in a railway corridor as a special case of a simple railway network to verify the effectiveness of the proposed approach. The results show that the proposed approach can effectively attain a good trade-off between the timetable efficiency and obtainable robustness for practical applications.     

Techniques for inserting additional trains into existing timetables

In this paper techniques for scheduling additional train services (SATS) are considered as is train scheduling involving general time window constraints, fixed operations, maintenance activities and periods of section unavailability. The SATS problem is important because additional services must often be given access to the railway and subsequently integrated into current timetables. The SATS problem therefore considers the competition for railway infrastructure between new services and existing services belonging to the same or different operators. The SATS problem is characterised as a hybrid job shop scheduling problem with time window constraints. To solve this problem constructive algorithm and meta-heuristic scheduling techniques that operate upon a disjunctive graph model of train operations are utilised. From numerical investigations the proposed framework and associated techniques are tested and shown to be effective.     

Conflict Resolution through Negotiation in a Railway Open Access Market: a Multi-agent System Approach

Abstract

Open access reforms to railway regulations allow multiple train operators to provide rail services on a common infrastructure. As railway operations are now independently managed by different stakeholders, conflicts in operations may arise, and there have been attempts to derive an effective access charge regime so that these conflicts may be resolved. One approach is by direct negotiation between the infrastructure manager and the train service providers. Despite the substantial literature on the topic, few consider the benefits of employing computer simulation as an evaluation tool for railway operational activities such as access pricing. This article proposes a multi-agent system (MAS) framework for the railway open market and demonstrates its feasibility by modelling the negotiation between an infrastructure provider and a train service operator. Empirical results show that the model is capable of resolving operational conflicts according to market demand.     

Macroscopic multiple-station short-turning model in case of complete railway blockages

In case of railway disruptions, traffic controllers are responsible for dealing with disrupted traffic and reduce the negative impact for the rest of the network. In case of a complete blockage when no train can use an entire track, a common practice is to short-turn trains. Trains approaching the blockage cannot proceed according to their original plans and have to short-turn at a station close to the disruption on both sides. This paper presents a Mixed Integer Linear Program that computes the optimal station and times for short-turning the affected train services during the three phases of a disruption. The proposed solution approach takes into account the interaction of the traffic between both sides of the blockage before and after the disruption. The model is applied to a busy corridor of the Dutch railway network. The computation time meets the real-time solution requirement. The case study gives insight into the importance of the disruption period in computing the optimal solution. It is concluded that different optimal short-turning solutions may exist depending on the start time of the disruption and the disruption length. For periodic timetables, the optimal short-turning choices repeat due to the periodicity of the timetable. In addition, it is observed that a minor extension of the disruption length may result in less delay propagation at the cost of more cancellations.     

Equity-oriented skip-stopping schedule optimization in an oversaturated urban rail transit network

In this study, we focus on improving system-wide equity performance in an oversaturated urban rail transit network based on multi-commodity flow formulation. From the system perspective, an urban rail transit network is a distributed system, where a set of resources (i.e., train capacity) is shared by a number of users (i.e., passengers), and equitable individuals and groups should receive equal shares of resources. However, when oversaturation occurs in an urban rail transit network during peak hours, passengers waiting at different stations may receive varying shares of train capacity leading to the inequity problem under train all-stopping pattern. Train skip-stopping pattern is an effective operational approach, which holds back some passengers at stations and re-routes their journeys in the time dimension based on the available capacity of each train. In this study, the inequity problem in an oversaturated urban rail transit network is analyzed using a multi-commodity flow modeling framework. In detail, first, discretized states, corresponding to the number of missed trains for passengers, are constructed in a space-time-state three-dimensional network, so that the system-wide equity performance can be viewed as a distribution of all passengers in different states. Different from existing flow-based optimization models, we formulate individual passenger and train stopping pattern as commodity and network structure in the multi-commodity flow-modeling framework, respectively. Then, we aim to find an optimal commodity flow and well-designed network structure through the proposed multi-commodity flow model and simultaneously achieve the equitable distribution of all passengers and the optimal train skip-stopping pattern. To quickly solve the proposed model and find an optimal train skip-stopping pattern with preferable system-wide equity performance, the proposed linear programming model can be effectively decomposed to a least-cost sub-problem with positive arc costs for each individual passenger and a least-cost sub-problem with negative arc costs for each individual train under a Lagrangian relaxation framework. For application and implementation, the proposed train skip-stopping optimization model is applied to a simple case and a real-world case based on Batong Line in the Beijing Subway Network. The simple case demonstrates that our proposed Lagrangian relaxation framework can obtain the approximate optimal solution with a small-gap lower bound and a lot of computing time saved compared with CPLEX solver. The real-world case based on Batong Line in the Beijing Subway Network compares the equity and efficiency indices under the operational approach of train skip-stopping pattern with those under the train all-stopping pattern to state the advantage of the train skip-stopping operational approach.     

Strategic assessment of capacity consumption in railway networks: Framework and model

In this paper, we develop a new framework for strategic planning purposes to calculate railway infrastructure occupation and capacity consumption in networks, independent of a timetable. Furthermore, a model implementing the framework is presented. In this model different train sequences are generated and assessed to obtain timetable independence. A stochastic simulation of delays is used to obtain the capacity consumption. The model is tested on a case network where four different infrastructure scenarios are considered. Both infrastructure occupation and capacity consumption results are obtained efficiently with little input. The case illustrates the model’s ability to quantify the capacity gain from infrastructure scenario to infrastructure scenario which can be used to increase the number of trains or improve the robustness of the system.     

A constraint generation algorithm for the construction of periodic railway timetables

This paper addresses the problem of constructing periodic timetables for train operations. We use a mathematical model consisting of periodic time window constraints by means of which arrival and departure times can be related pairwise on a clock, rather than on a linear time axis. Constructing a timetable, then, means solving a set of such constraints. This problem is known to be hard, i.e. it is NP-complete. We describe a new algorithm to solve the problem based on constraint generation and work out a real-life example. It appears that, for problem instances of modest, yet non-trivial, size, the algorithm performs very well, which opens a way to thorough performance analysis of railway systems by studying a large number of possible future timetables.     

Train routing and timetabling problem for heterogeneous train traffic with switchable scheduling rules

This paper proposes a mathematical model for the train routing and timetabling problem that allows a train to occasionally switch to the opposite track when it is not occupied, which we define it as switchable scheduling rule. The layouts of stations are taken into account in the proposed mathematical model to avoid head-on and rear-end collisions in stations. In this paper, train timetable could be scheduled by three different scheduling rules, i.e., no switchable scheduling rule (No-SSR) which allows trains switching track neither at stations and segments, incomplete switchable scheduling rule (In-SSR) which allows trains switching track at stations but not at segments, and complete switchable scheduling rule (Co-SSR) which allows trains switching track both at stations and segments. Numerical experiments are carried out on a small-scale railway corridor and a large-scale railway corridor based on Beijing–Shanghai high-speed railway (HSR) corridor respectively. The results of case studies indicate that Co-SSR outperforms the other two scheduling rules. It is also found that the proposed model can improve train operational efficiency.     

Estimation method for railway passengers’ train choice behavior with smart card transaction data

Smart card systems have become the predominant method of collecting public transport fares in Japan. Transaction data obtained through smart cards have resulted in a large amount of archived information on how passengers use public transportation. The data have the potential to be used for modeling passenger behavior and demand for public transportation. This study focused on train choices made by railway passengers. If each passenger’s train choice can be identified over a long period of time, this information would be useful for improving the customer relationship management of the railway company and for improving train timetables. The aim of this study was to develop a methodology for estimating which train is boarded by each smart card holder. This paper presents a methodology and an algorithm for estimation using long-term transaction data. To validate the computation time and accuracy of the estimation, an empirical analysis is carried out using actual transaction data provided by a railway company in Japan. The results show that the proposed method is capable of estimating passenger usage patterns from smart card transaction data collected over a long time period.     

Integrated operations planning and revenue management for rail freight transportation

In the rail industry, profit maximization relies heavily on the integration of logistics activities with an improved management of revenues. The operational policies chosen by the carrier have an important impact on the network yield and thus on global profitability. This paper bridges the gap between railroad operations planning and revenue management. We propose a new bilevel mathematical formulation which encompasses pricing decisions and network planning policies such as car blocking and routing as well as train make-up and scheduling. An exact solution approach based on a mixed integer formulation adapted to the problem structure is presented, and computational results are reported on randomly generated instances.     

Designing an integrated distribution system for catering services for high-speed railways: A three-echelon location routing model with tight time windows and time deadlines

An emerging task in catering services for high-speed railways (CSHR) is to design a distribution system for the delivery of high-quality perishable food products to trains in need. This paper proposes a novel model for integrating location decision making with daily rail catering operations, which are affected by various aspects of rail planning, to meet time-sensitive passenger demands. A three-echelon location routing problem with time windows and time budget constraints (3E-LRPTWTBC) is thus proposed toward formulating this integrated distribution system design problem. This model attempts to determine the capacities/locations of distribution centers and to optimize the number of meals delivered to stations. The model also attempts to generate a schedule for refrigerated cars traveling from distribution centers to rail stations for train loading whereby meals can be catered to trains within tight time windows and sold before a specified time deadline. By relaxing the time-window constraints, a relaxation model that can be solved using an off-the-shelf mixed integer programming (MIP) solver is obtained to provide a lower bound on the 3E-LRPTWTBC. A hybrid cross entropy algorithm (HCEA) is proposed to solve the 3E-LRPTWTBC. A small-scale case study is implemented, which reveals a 9.3% gap between the solution obtained using the HCEA and that obtained using the relaxation model (RM). A comparative analysis of the HCEA and an exhaustive enumeration algorithm indicates that the HCEA shows good performance in terms of computation time. Finally, a case study considering 156 trains on the Beijing-Shanghai high-speed corridor and a large-scale case study considering 1130 trains on the Chinese railway network are addressed in a comprehensive study to demonstrate the applicability of the proposed models and algorithm.     

Optimizing the freight train connection service network of a large-scale rail system

This paper presents a formulation and solution for the train connection services (TCSs) problem in a large-scale rail network in order to determine the optimal freight train services, the frequency of services, and the distribution of classification workload among yards. TCS problem is modeled as a bi-level programming problem. The upper-level is intended to find an optimal train connection service, and the lower-level is used for assigning each shipment to a sequence of train services and determining the frequency of services.Our model solves the TCS problem of the China railway system, which is one of the largest railway systems in the world. The system consists of 5544 stations, and over 520,000 shipments using this system for a year period. A subnetwork is defined with 127 yards having some minimum level of reclassification resources and 14,440 demands obtained by aggregating 520,000 shipments to the subnetwork. We apply a simulated annealing algorithm to the data for optimal computation after pre-processing and get an excellent result. Comparing our optimal solution with the existing plan result, there are improvements of about 20.8% in the total cost.     

A tabu search algorithm to solve the integrated planning of container on an inter-terminal network connected with a hinterland rail network

Transport demand for containers has been increasing for decades, which places pressure on road transport. As a result, rail transport is stimulated to provide better intermodal freight transport services. This paper investigates mathematical models for the planning of container movements in a port area, integrating the inter-terminal transport of containers (ITT, within the port area) with the rail freight formation and transport process (towards the hinterland). An integer linear programming model is used to formulate the container transport across operations at container terminals, the network interconnecting them, railway yards and the railway networks towards the hinterland. A tabu search algorithm is proposed to solve the problem. The practical applicability of the algorithm is tested in a realistic infrastructure case and different demand scenarios. Our results show the degree by which internal (ITT) and external (hinterland) transport processes interact, and the potential for improvement of overall operations when the integrated optimization proposed is used. Instead, if the planning of containers in the ITT system is optimized as a stand-alone problem, the railway terminals may suffer from longer delay times or additional train cancellations. When planning the transport of 4060 TEU containers within one day, the benefits of the ITT planning without considering railway operations account for 17% ITT cost reduction but 93% railway operational cost growth, while the benefits of integrating ITT and railway account for a reduction of 20% in ITT cost and 44% in railway operational costs.