Modelling single line train operations

Scheduling of trains on a single line involves using train priorities for the resolution of conflicts. The mathematical programming model described in the first part of this paper schedules trains over a single line 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 and/ or overtake each other. Investment decisions on upgrading the number and location 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. The second part of this paper puts forward a model to determine the optimal position of a set of sidings on a single track rail corridor. The sidings are positioned to minimise the total delay and train operating costs of a given cyclic train schedule. The key feature of the model is the allowance of non-constant train velocities and non-uniform departure times

Optimal Scheduling of Trains on a Single Line Track

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 kilometre 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

Analytical Models in Rail Transportation: An Annotated Bibliography

Not AvailableThis research has been supported, in part, by the U.S. Department of Transportation under contract DOT-TSC-1058, Transportation Advanced Research Program (TARP)

A Dynamic Row/Column Management Algorithm for Freight Train Scheduling

We propose a new dynamic row/column management algorithm for freight train scheduling in a single track railway system. While many papers have already been devoted to train scheduling, previously published optimization models still suffer from scalability issues, even for single track railway systems. Moreover, very few of them take into account the capacity constraints, i.e., the number of alternate tracks in the railway stations/sidings in order for the trains to meet/bypass. We propose an optimization model which takes such constraints into account, while still handling efficiently the other meaningful constraints. We design an original solution scheme with iterative additions/removals of constraints/variables in order to remain with a manageable sized mixed integer linear program at each iteration, without threatening to reach the optimal solution. Numerical results are presented on several data instances of CPR (Canadian Pacific Railway) on the Vancouver-Calgary corridor, one of the most busy corridor in their railway system. Therein, the proposed model and algorithm are used as a planning tool to evaluate the network capacity, i.e., how much the number of trains can be increased without impacting significantly the average travel times between the source and destination stations of the various trains in the corridor. Larger data instances than those previously published are solved accurately (epsilon-optimal solutions) for the schedule of freight trains

Coal by rail: historic trends and transhipment modelling

This paper presents an account of the historic trends of coal transportation by rail in Great Britain over the last 50 years. The Re-shaping Britain’s Railways report by the British Railways Board in 1963 highlighted the need to improve the efficiency of rail freight transportation to compete with road haulage. More recently, coal is imported to the UK to coastal ports from Europe and the rest of the World. The movement of trains on the network has changed since the report in 1963. Research has shown that it is not the amount that has increased, only the distance (Vanek and Smith, 2004). Historic data and research has been collated using national sources and statistics, and a Transhipment Model has been used to determine the optimisation of the coal locations. The data and the model have supported the statement that coal now accounts for more freight train journeys than ever before although the demise of the coal mines in the North East and the increase of power stations and ports in Yorkshire has altered the pattern of movements. The UK still requires coal for its power stations but has sourced it increasingly from abroad

Capacity evaluation and infrastructure planning techniques for heterogeneous railway traffic under structured, mixed, and flexible operation

North American railroads have a strong business incentive to match rail line capacity to traffic demand. Since insufficient capacity reduces level of service and excess capacity represents inefficient use of capital, either one of these situations is undesirable. Various processes, models, and tools have been developed to assist the railroads in determining appropriate infrastructure projects and operational plans to balance network capacity. In North America, these approaches have typically been tailored to operating conditions on rail corridors that are dominated by freight trains that do not run according to a precise schedule. Changes in the composition of rail traffic have resulted in new operating conditions that require new approaches to rail capacity evaluation. The long-term growth of freight rail traffic (with particular increases in premium intermodal traffic) and recent interest in the expansion of passenger service on freight corridors have increased rail traffic volume and heterogeneity, while altering the level of randomness involved in train departure and trip times. The single-track lines that comprise the majority of the North American rail network have limited capacity and can frequently become congested under these new rail traffic demands. The combined impact of traffic volume, heterogeneity, and level of randomness in train plans has not always been fully considered by previous approaches to the study of rail line capacity. This dissertation develops new capacity evaluation and infrastructure planning techniques for single-track lines that consider the impact of relationships between infrastructure layout, train operating plans including train-specific levels of service, and train characteristics on line capacity. In this study, the randomness involved in a train operating plan is described by “schedule flexibility” and “operating style”. In chapter 1, the concepts of operating style and schedule flexibility are proposed and defined. In chapters 2 and 3, a capacity evaluation and alternative comparison process are proposed to assist the capacity evaluation and planning of single-track lines under mixed or flexible operation. In chapter 4, an optimization model is developed to determine the optimal number and locations of passing sidings for single-track lines under structured operation. In chapter 5, the concept of traffic conflict analysis is introduced as a research direction to address rail infrastructure and operational planning problems. The methods developed in this dissertation can help to better assess mainline capacity under current operating conditions and determine more effective infrastructure expansion projects or changes in operational strategy for railroads and passenger rail agencies in North America. Use of these methods can help railroads improve their service quality and maximize returns to their stakeholders

FERRMED global study: FERRMED great axis rail freight network and its area of influence: Scandinavia - Rhein - Rhone - Western Mediterranean: feasibility, conclusions and recommendations

Postprint (published version

Model metadata report for Manchester and Salford, NW England

This report describes the creation of a 3D geological model of natural and artificial superficial deposits in Manchester and Salford, NW England. The Manchester and Salford model forms part of the Lower Mersey Corridor, NW England. The Lower Mersey Corridor includes models within the region comprising: Manchester-Salford Warrington Liverpool Irlam The location of the geological models is shown in Figure 1 and the spacing of cross-sections is shown in Figure 2. Figure 1 Location of Manchester and Salford 3D geological model and its relationship to others in the Lower Mersey Corridor area of NW England. The 3D models include natural and artificial superficial deposits. Cross-sections for Manchester and Salford include schematic bedrock correlations for illustration only. Bedrock is not included in the calculated mode

A Category Classification Based Safety Risk Assessment Method for Railway Wagon Loading Status

The identification and control of safety risks in the loading state of goods wagon is one of the important tasks to ensure the safety of goods in transit. In view of the problem that the current risk assessment of transportation schemes is mainly based on manual experience and cannot be quantified, which makes it difficult to accurately determine the safety risk of transportation on the way, a risk assessment method for loading status of goods wagon based on scenario classification was proposed. Firstly, based on a detailed analysis of the safety risk points in various stages of railway freight operations, a SHEL influencing factor model based on scenario classification was constructed. Then, considering the characteristics of railway freight transportation, a fuzzy accident tree model (FTA) of goods wagon loading state risk was constructed, and the fault tree was transformed into a Bayesian network structure according to the mapping algorithm of fuzzy fault tree and Bayesian. Furthermore, a triangular fuzzy membership function was introduced to describe the fault probability of nodes, and a BN based fuzzy fault tree inference algorithm was proposed. Finally, taking a railway station and route transporting coil steel goods in China as an example, this paper explained how to integrate expert knowledge through fault tree and Bayesian network to support railway freight scheme designers in conducting risk quantification assessment of freight wagon loading status