Modelling single line train operations (original) (raw)

Modeling Single-Line Train Operations

Transportation Research Record, 1995

Scheduling of trains on a single line involves the use of train priorities for the resolution of conflicts. First, a mathematical programming model is described. The model schedules trains over a single line of track when the priority of each train in a conflict depends on an estimate of the remaining crossing and overtaking delay. This priority is used in a branch-and-bound procedure to allow the determination of optimal solutions quickly. This is demonstrated with the use of an example. Rail operations over a single-line track require the existence of a set of sidings at which trains can cross or overtake each other. Investment decisions on upgrading the numbers and locations of these sidings can have a significant impact on both customer service and rail profitability. Sidings located at insufficient positions may lead to high operating costs and congestion. Second, a model to determine the optimal position of a set of sidings on a single-track rail corridor is described. The sid...

Optimal scheduling of trains on a single line track

Transportation Research Part B-methodological, 1996

This paper describes the development and use of a model designed to optimise train schedules on single line rail corridors. The model has been developed with two major applications in mind, namely: as a decision support tool for train dispatchers to schedule trains in real time in an optimal way; and as a planning tool to evaluate the impact of timetable changes, as well as railroad infrastructure changes. The mathematical programming model described here schedules trains over a single line track. The priority of each train in a conflict depends on an estimate of the remaining crossing and overtaking delay, as well as the current delay. This priority is used in a branch and bound procedure to allow and optimal solution to reasonable size train scheduling problems to be determined efficiently. The use of the model in an application to a "real life" problem is discussed. The impacts of changing demand by increasing the number of trains, and reducing the number of sidings for a 150 km section of single line track are discussed. It is concluded that the model is able to produce useful results in terms of optimal schedules in a reasonable time for the test applications shown here.

An exact solution procedure to determine the optimal dispatching times for complex rail networks

IIE Transactions, 2006

Trains operating in densely populated metropolitan areas typically encounter complex trackage configurations. To make optimal use of the available rail capacity, some portions of the rail network may consist of single-track lines while other locations may consist of double-or triple-track lines. This paper develops a branch-and-bound procedure for determining the optimal dispatching times for trains traveling in complex rail networks. We demonstrate the efficiency of our branch-and-bound algorithm by comparing it to CPLEX, a commercially available integer program solver, on an actual rail network in Los Angeles County. meets and overtakes that minimizes train delays from the scheduled timetables while satisfying all the operational constrains. Recently, the train dispatching problem has received attention in the research community. The reason is partially due to the fact that faster trains, increasing traffic density, and the availability of real-time information on train position and velocity have made the tasks of the dispatchers too complex and demanding to perform manually. A deficient dispatching strategy may cause a decrease of the railroad line capacity and service reliability and the increase of energy consumption and pollution to the environment, or in the most severe case lead to deadlock. Therefore, building a robust methodology to handle train dispatching in an optimal way is an important research issue in rail freight transportation. In this paper, we propose a new optimization approach to dispatch trains for a general railway trackage configuration, commonly found in urban networks.

Timetabling optimization of a mixed double- and single-tracked railway network

Applied Mathematical Modelling, 2011

The paper deals with the timetabling problem of a mixed multiple-and single-tracked railway network. Out of all the solutions minimizing the maximum relative travel time, the one minimizing the sum of the relative travel times is selected. User preferences are taken into account in the optimization problems, that is, the desired departure times of travellers are used instead of artificially planned departure times. To find the global optimum of the optimization problem, an algorithm based on the bisection rule is used to provide sharp upper bounds of the objective function together with one trick that allows us to drastically reduce the number of binary variables to be evaluated by considering only those which really matter. These two strategies together permit the memory requirements and the computation time to be reduced, the latter exponentially with the number of trains (several orders of magnitude for existing networks), when compared with other methods. Several examples of applications are presented to illustrate the possibilities and excellences of the proposed method. The model is applied to the case of the existing Madrid-Sevilla high-speed line (double track), together with several extensions to Toledo, Valencia, Albacete, and Málaga, which are contemplated in the future plans of the high-speed train Spanish network. The results show that the computation time is reduced drastically, and that in some corridors single-tracked lines would suffice instead of double-tracked lines.

Train Scheduling in Public Rail Transport

2000

This thesis deals with train scheduling problems with an emphasis on public rail transport. In particular, we assume a periodic schedule and a fixed railroad track network, which is common for public rail transport. A train schedule consists of arrival and departure times for the lines at certain points of the traffic network, e.g. railroad stations. The minimization of operational cost for the realization of a schedule forms a central part of this thesis. We introduce a mixed integer linear programming model for this objective. A direct solution of instances of real-world size is not possible with today's hard- and software. With the help of a decomposition idea, we are able to find solutions of acceptable quality for those instances in a reasonable amount of time. Therefore, we split the instance into an optimization component and a feasibility component. Both subproblems are integrated into a branch-and-bound algorithm. With these methods, we can produce solutions of practica...

Discrete optimization in public rail transport

Mathematical Programming, 1997

Many problems arising in traffic planning can be modelled and solved using discrete optimization. We will focus on recent developments which were applied to large scale real world instances.

A Constraint-Based Scheduling Model for Optimal Train Dispatching

2010 Joint Rail Conference, Volume 2, 2010

Railway networks are faced to an increase demand of new services. This situation leads to train schedules close to the maximum capacity of the infrastructure. As the extension of the infrastructure is too expensive, an alternative solution is to improve traffic management in congested areas. In heavy traffic areas of rail networks, conflicts and subsequent train delays can cause considerable chain reactions during operations. A disturbance can quickly lead to many other delays called secondary delays or knock-on delays.

Development of hybrid optimization of train schedules model for N-track rail corridors

Transportation Research Part C: Emerging Technologies, 2016

From a capacity perspective, efficient utilization of a railway corridor has two main objectives; avoidance of schedule conflicts, and finding a proper balance between capacity utilization and level of service (LOS). There are several timetable tools and commercial rail simulation packages available to assist in reaching these objectives, but few of them offer both automatic train conflict resolution and automatic timetable management features for the different types of corridor configurations. This research presents a new rescheduling model to address some of the current limitations. The multi-objective linear programming (LP) model is called ''Hybrid Optimization of Train Schedules" (HOTS), and it works together with commercial rail simulation tools to improve capacity utilization or LOS metrics. The HOTS model uses both conflict resolution and timetable compression techniques and is applicable to single-, double-, and multiple-track corridors (N-track networks), using both directional and bi-directional operations. This paper presents the approach, formulation and data requirements for the HOTS model. Single and multi-track case studies test and demonstrate the model's train conflict resolution and timetable compression capabilities, and the model's results are validated by using RailSys simulation package. The HOTS model performs well in each tested scenario, providing comparable results (either improved or similar) to the commercial packages.

Confrontation of Different Objectives in the determination of train scheduling

Procedia - Social and Behavioral Sciences, 2011

In the railway networks management context, the determination of train schedules is a topic which affects both the level of satisfaction amongst the users and the network performance and profitability. This double influence makes it a widely studied topic in the literature, where nowadays the main lines of research tend to improve the solving methods of the corresponding integer programming problems. However, literature about methods that take both user and service provider point of view jointly into account is sparse. In this work, we tackle the problem of scheduling in middle and long distances networks by means of a non-linear integer programming model which fits the schedules to a dynamic behavior of demand and represents a trade-off between some measures of quality of the service offered and aspects related to the network profitability. The confrontation of different objective selection policies is analyzed in depth in the core part of this study, with the intention of both improving the insight into the proposed model and adding the flexibility of choosing different objectives by knowing in advance their influence on the resulting schedule plan.