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.     

A railway capacity determination model and rail access charging methodologies

This article discusses approaches to the determination of railway capacity and the significance of the following factors on capacity: mix of trains, length and weight of trains, direction of train travel, acceleration and deceleration, stopping protocols of trains, location and length of crossing loops, location of signals, length of sections, dwell times and sectional running times. A more accurate method to calculate railway capacity is developed using previously unaddressed aspects for capacity determination. Capacity and pricing are two key issues for organizations involved with open track access regimes. A train access charging methodology is therefore developed and incorporated into a railway capacity determination model.     

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.     

High-Speed Rail Operations on an Existing Network: An Assessment Model for China

High-speed rail operations have the potential to reduce the long-term decline in rail passenger travel demand for the medium to long distance inter-urban markets. Such decline has been evident through most of the industrialized countries where air and road transport tend to be the dominant modes. In China, the operations of long distance high-speed rail on fully dedicated track is not very easy to implement, due to the high proportion of passengers who travel between high-speed and conventional railways. An alternative approach would be to allow for mixed operations with trains of various speeds on the same track. This article puts forward a simulation model designed to allow an evaluation of the most efficient distance for high-speed rail operations under mixed train speed scenarios. The model takes into account the main operating parameters such as passenger volumes, train speeds, capital and maintenance costs, train operating costs and energy consumption. The distance of high-speed train running on conventional rail that will yield the most economic benefit can be estimated using the model. The article includes the results of using the model for a specific example. It is concluded that large-scale high-speed trains have the potential to be successfully operated on conventional rail networks.     

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.     

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.     

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 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.     

Passenger rail in North America in the light of developments in Western Europe and Japan

Because of different geo‐demographic and economic conditions, the impact of the new passenger modes (road and air) on rail travel was much larger in North America than in Europe. In 1960s and 1970s, as the railway share of intercity traffic in North America shrunk to a negligible one or two percent, the passenger trains were abandoned by private railway companies and taken over by state organizations, which have continued to operate traditional trains and generate mounting losses. On the technology side, no attempts have been made to improve competitiveness of trains vis‐a‐vis automobiles and airplanes.

In Europe and Japan, the railways responded to the challenge by (i) upgrading the performance (speed) and comfort of traditional trains operating on existing tracks and (ii) developing trains which could, on short and intermediate range distances, compete successfully, in terms of speed and economy, with the road and air modes. The Japanese (Shinkansen trains) and French (TGV trains) experience clearly shows that trains operating on dedicated lines at average speeds of 150 to 200 km/hr provide a superior transportation service and economy on high‐traffic intercity routes of up to about 500 km length. In this paper the factors responsible for the present status of passenger rail in North America are analysed, the current policies in the U.S. and Canada are evaluated in the light of experience to date and developments abroad, and suggestions for a long‐term passenger rail policy are made. This includes examination of (i) the viability of continued subsidization of traditional train services, (ii) the viability of operation of faster trains on existing tracks, (iii) the scope for introduction of modern, fast trains on dedicated lines in high‐density, intercity corridors, (iv) the application of fast trains as access to major airports and integration of airports with fast intercity lines, and (v) the impact of energy (oil) consumption in transportation.

     

The measurement of train noise: a case study in northern Italy

This paper analyses the interactions between vehicles, infrastructure and environment for rail traffic. It identifies variables having a significant influence on sound levels, defines a standard procedure for measuring noise, and develops a database for setting up and calibrating train noise models. A pilot study looks at two railway lines passing through Vercelli, a medium sized town in the north-west of Italy. Four main conclusions were drawn. First, in certain conditions, variables that normally influence noise production can be neglected (e.g. when surrounding environmental conditions are constant, different types of train do not cause a significant variation in noise level). Secondly, when diesel trains are travelling at less than 70 km/h, a speed change of 30–40 km/h significantly affects the maximum noise level (Lmax). However, for electrified lines, when speed is below 80 km/h, a change of 20–30 km/h does not cause significant variations in Lmax. Thirdly, for diesel trains transiting at low speeds––e.g. near stations––noise emissions are strongly affected by acceleration/deceleration. Lastly, an approach based on ‘sites types’ is able to produce useful results because site configuration and the presence of building significantly affect Lmax. High buildings along the line can increase noise levels and may nullify the advantages derived from technological advance in the vehicles.     

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.     

Own and cross-price elasticities of demand for domestic flights and intercity trains in the U.S.

In 2009, the U.S. Federal Government announced its plan to invest in the expansion of the passenger rail system, instead of adding to the freeway or aviation systems. On the other hand, environmental studies show that passenger rails have a lower polluting impact than flights or cars. In order to evaluate whether consumers would switch from flights to trains and use the new rail system, this paper estimates the own and cross-price elasticities of demand for domestic flights and passenger trains using the methodology described in Berry (1994). Specifically, the changes in demand for domestic flights and trains with respect to their prices are evaluated. The static model in this study suggests that the substitutability between these two modes of transport is minimal, in other words, travelers will to change their choices is very small given the configuration of the transportation system when the notice was made. In particular, train trips are substituted more easily.     

A bi-level model for single-line rail timetable design with consideration of demand and capacity

This paper proposes a bi-level model to solve the timetable design problem for an urban rail line. The upper level model aims at determining the headways between trains to minimize total passenger cost, which includes not only the usual perceived travel time cost, but also penalties during travel. With the headways given by the upper level model, passengers’ arrival times at their origin stops are determined by the lower level model, in which the cost-minimizing behavior of each passenger is taken into account. To make the model more realistic, explicit capacity constraints of individual trains are considered. With these constraints, passengers cannot board a full train, but wait in queues for the next coming train. A two-stage genetic algorithm incorporating the method of successive averages is introduced to solve the bi-level model. Two hypothetical examples and a real world case are employed to evaluate the effectiveness of the proposed bi-level model and algorithm. Results show that the bi-level model performs well in reducing total passenger cost, especially in reducing waiting time cost and penalties. And the section loading-rates of trains in the optimized timetable are more balanced than the even-headway timetable. The sensitivity analyses show that passenger’s desired arrival time interval at destination and crowding penalty factor have a high influence on the optimal solution. And with the dispersing of passengers' desired arrival time intervals or the increase of crowding penalty factor, the section loading-rates of trains become more balanced.     

Efficient dispatching rules on double tracks with heterogeneous train traffic

The most natural and popular dispatching rule for double-track segments is to dedicate one track for trains traveling in one direction. However, sometimes passenger trains have to share some portions of the railway with freight trains and passenger trains are traveling faster and faster nowadays. The major drawback of this dedicated rule is that a fast train can be caught behind a slow train and experience significant knock-on delay. In this paper, we propose a switchable dispatching policy for a double-track segment. The new dispatching rule enables the fast train to pass the slow train by using the track traveled by trains in the opposite direction if the track is empty. We use queueing theory techniques to derive the delay functions of this policy. The numerical experiments show that a switchable policy can reduce the fast train knock-on delay by as high as 30% compared to a dedicated policy. When there are crossovers at the middle of the double-track segment, our proposed switchable policy can reduce the delay of the fast trains by as high as 65%.     

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.     

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.     

Reinforcement learning approach for train rescheduling on a single-track railway

Optimal rail network infrastructure and rolling stock utilization can be achieved with use of different scheduling tools by extensive planning a long time before actual operations. The initial train timetable takes into account possible smaller disturbances, which can be compensated within the schedule. Bigger disruptions, such as accidents, rolling stock breakdown, prolonged passenger boarding, and changed speed limit cause delays that require train rescheduling. In this paper, we introduce a train rescheduling method based on reinforcement learning, and more specifically, Q-learning. We present here the Q-learning principles for train rescheduling, which consist of a learning agent and its actions, environment and its states, as well as rewards. The use of the proposed approach is first illustrated on a simple rescheduling problem comprising a single-lane track with three trains. The evaluation of the approach is performed on extensive set of experiments carried out on a real-world railway network in Slovenia. The empirical results show that Q-learning lead to rescheduling solutions that are at least equivalent and often superior to those of several basic rescheduling methods that do not rely on learning agents. The solutions are learned within reasonable computational time, a crucial factor for real-time applications.     

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.     

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.     

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.