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.     

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.     

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.     

A study of train dwelling time at the hong kong mass transit railway system

This paper investigates the relationship between the dwelling time of trains and the crowding situations at Mass Transit Railway (MTR) stations in Hong Kong. Regression models were established for the dwelling delays of trains due to congestion at stations, and a simulation model making use of the Monte-Carlo technique is developed to assess the reliability of the estimated train dwelling time. Therefore, the distribution and the confidence interval of the train dwelling time can be predicted on the basis of observed boarding and alighting distributions.     

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.     

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.     

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.     

A heuristic for the train pathing and timetabling problem

In a railroad system, train pathing is concerned with the assignment of trains to links and tracks, and train timetabling allocates time slots to trains. These important tasks were traditionally done manually, but there is an increasing move toward automated software based on mathematical models and algorithms. Most published models in the literature either focus on train timetabling only, or are too complicated to solve when facing large instances. In this paper, we present an optimization heuristic that includes both train pathing and train timetabling, and has the ability to solve real-sized instances. This heuristic allows the operation time of trains to depend on the assigned track, and also lets the minimum headway between the trains to depend on the trains’ relative status. It generates an initial solution with a simple rule, and then uses a four-step process to derive the solution iteratively. Each iteration starts by altering the order the trains travel between stations, then it assigns the services to the tracks in the stations with a binary integer program, determines the order they pass through the stations with a linear program, and uses another linear program to produce a timetable. After these four steps, the heuristic accepts or rejects the new solution according to a Threshold Accepting rule. By decomposing the original complex problem into four parts, and by attacking each part with simpler neighborhood-search processes or mathematical programs, the heuristic is able to solve realistic instances. When tested with two real-world examples, one from a 159.3 km, 29-station railroad that offers 44 daily services, and another from a 345 km, eight-station high-speed rail with 128 services, the heuristic obtained timetables that are at least as good as real schedules.     

Estimation of train dwell time at short stops based on track occupation event data: A study at a Dutch railway station

Train dwell time is one of the most unpredictable components of railway operations, mainly because of the varying volumes of alighting and boarding passengers. However, for reliable estimations of train running times and route conflicts on main lines, it is necessary to obtain accurate estimations of dwell times at the intermediate stops on the main line, the so‐called short stops. This is a great challenge for a more reliable, efficient and robust train operation. Previous research has shown that the dwell time is highly dependent on the number of boarding and alighting passengers. However, these numbers are usually not available in real time. This paper discusses the possibility of a dwell time estimation model at short stops without passenger demand information by means of a statistical analysis of track occupation data from the Netherlands. The analysis showed that the dwell times are best estimated for peak and off‐peak hours separately. The peak‐hour dwell times are estimated using a linear regression model of train length, dwell times at previous stops and dwell times of the preceding trains. The off‐peak‐hour dwell times are estimated using a non‐parametric regression model, in particular, the k‐nearest neighbor model. There are two major advantages of the proposed estimation models. First, the models do not need passenger flow data, which is usually impossible to obtain in real time in practice. Second, detailed parameters of rolling stock configuration and platform layout are not required, which makes the model more generic and eases implementation. A case study at Dutch railway stations shows that the estimation accuracy is 85.8%–88.5% during peak hours and 80.1% during off‐peak hours, which is relatively high. We conclude that the estimation of dwell times at short stop stations without passenger data is possible. Copyright © 2016 John Wiley & Sons, Ltd.     

Coordinated cruise control for high-speed train movements based on a multi-agent model

This paper investigates the coordinated cruise control strategy for multiple high-speed trains’ movement. The motion of an ordered set of high-speed trains running on a railway line is modeled by a multi-agent system, in which each train communicates with its neighboring trains to adjust its speed. By using the potential fields and LaSalles invariance principle, we design a new coordinated cruise control strategy for each train based on the neighboring trains’ information, under which each train can track the desired speed, and the headway distances between any two neighboring trains are stabilized in a safety range. Numerical examples are given to illustrate the effectiveness of the proposed methods.     

Train boarding and alighting rates at high passenger loads

Line capacity in metro and high‐frequency suburban railways is as much determined by station stop times as by factors such as line speed or train acceleration. This paper applies the method developed by London Underground to estimate the time that trains spend at stations, as a function of the physical characteristics of the situation (e.g. train door width) and the numbers of passengers involved. Analysis was carried out on a number of alternative designs for refurbishment of South West Trains' Class 455 inner‐suburban rolling stock. Whilst there is indeed an interaction between boarding and alighting passengers, this paper demonstrates that the LUL relationship breaks down at the highest passenger loads. Moreover, results indicate that passenger flow is not equal between different parts of the same group of boarders or alighters.     

Standardization of capacity unit for headway-based rail capacity analysis

Determining the required capacity upgrades to accommodate future demand is a critical process in assisting public and private financing of capacity investments. Conventional railway systems usually operate multiple types of trains on the same track. These different types of trains can exert substantially different capacity impact, and can cause serious operational conflicts. In the past, rail line capacity is commonly defined as the maximum number of trains that can be operated on a section of track within a given time period. However, a specific unit (trains/hr or trains/day) does not reflect the heterogeneity of train types. According to the concept of base train equivalents (BTE) and base train unit (BTU), this study developed headway-based models to determine BTE for transforming different train types into a standard unit (i.e., BTU). An approximate method for lines with three and more types of trains was also proposed to compute BTEs for non-base trains. Results from the case studies demonstrate that this method enables the standardization of rail capacity unit, facilitates assessment of the impact from heterogeneous trains, and allows comparison and evaluation of the capacity measurements from different lines and systems.     

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%.     

Performability evaluation of the ERTMS/ETCS – Level 3

Level 3 of the ERTMS/ETCS improves the capacity of railways by replacing fixed-block signalling, which prevents a train to enter a block occupied by another train, with moving block signalling, which allows a train to proceed as long as it receives radio messages ensuring that the track ahead is clear of other trains. If messages are lost, a train must stop for safety reasons within a given deadline, even though the track ahead is clear, making the availability of the communication link crucial for successful operation.We combine analytic evaluation of failures due to burst noise and connection losses with numerical solution of a non-Markovian model representing also failures due to handovers between radio stations. In so doing, we show that handovers experienced by a pair of chasing trains periodically affect the availability of the radio link, making behavior of the overall communication system recurrent over the hyper-period of periodic message releases and periodic arrivals at cell borders. As a notable aspect, non-Markovian transient analysis within two hyper-periods is sufficient to derive an upper bound on the first-passage time distribution to an emergency brake, permitting to achieve a trade-off between railway throughput and stop probability. A sensitivity analysis is performed with respect to train speed and headway distance, permitting to gain insight into the consequences of system-level design choices.     

Comparing rail fuel efficiency with truck and waterway

This paper presents a railroad energy efficiency model used to estimate the fuel economies for classes of trains transporting various commodities. Comparable procedures are used to estimate truck and waterway fuel consumption. The results show that coal unit trains are 4.5–5.0 times more energy efficient than movements in the largest trucks allowed in the eastern and western regions of the US, unit grain train movements in the central US are 4.6 times more fuel efficient, soda ash unit train and non-unit train shipments are 4.9 and 3.2 times more efficient, and ethanol unit train and non-unit train movements are 4.8 and 3.0 times more efficient. In terms of barge traffic, coal unit train and non-unit train are 1.3 and 0.9 times as energy efficient in the eastern US, grain unit train and non-unit train movements are 1.7 and 1.0 times more efficient from Minneapolis to the Gulf of Mexico, and grain unit train and non-unit train movements are 1.0 and 0.7 times more fuel efficient from the Upper Ohio River to the Gulf of Mexico.     

Integrated optimization on train scheduling and preventive maintenance time slots planning

We address the problem of simultaneously scheduling trains and planning preventive maintenance time slots (PMTSs) on a general railway network. Based on network cumulative flow variables, a novel integrated mixed-integer linear programming (MILP) model is proposed to simultaneously optimize train routes, orders and passing times at each station, as well as work-time of preventive maintenance tasks (PMTSs). In order to provide an easy decomposition mechanism, the limited capacity of complex tracks is modelled as side constraints and a PMTS is modelled as a virtual train. A Lagrangian relaxation solution framework is proposed, in which the difficult track capacity constraints are relaxed, to decompose the original complex integrated train scheduling and PMTSs planning problem into a sequence of single train-based sub-problems. For each sub-problem, a standard label correcting algorithm is employed for finding the time-dependent least cost path on a time-space network. The resulting dual solutions can be transformed to feasible solutions through priority rules. Numerical experiments are conducted on a small artificial network and a real-world network adapted from a Chinese railway network, to evaluate the effectiveness and computational efficiency of the integrated optimization model and the proposed Lagrangian relaxation solution framework. The benefits of simultaneously scheduling trains and planning PMTSs are demonstrated, compared with a commonly-used sequential scheduling method.     

Nonlinear programming methods based on closed-form expressions for optimal train control

This paper proposes a novel approach to solve the complex optimal train control problems that so far cannot be perfectly tackled by the existing methods, including the optimal control of a fleet of interacting trains, and the optimal train control involving scheduling. By dividing the track into subsections with constant speed limit and constant gradient, and assuming the train’s running resistance to be a quadratic function of speed, two different methods are proposed to solve the problems of interest. The first method assumes an operation sequence of maximum traction – speedholding – coasting – maximum braking on each subsection of the track. To maintain the mathematical tractability, the maximum tractive and maximum braking functions are restricted to be decreasing and piecewise-quadratic, based on which the terminal speed, travel distance and energy consumption of each operation can be calculated in a closed-form, given the initial speed and time duration of that operation. With these closed-form expressions, the optimal train control problem is formulated and solved as a nonlinear programming problem. To allow more flexible forms of maximum tractive and maximum braking forces, the second method applies a constant force on each subsection. Performance of these two methods is compared through a case study of the classic single-train control on a single journey. The proposed methods are further utilised to formulate more complex optimal train control problems, including scheduling a subway line while taking train control into account, and simultaneously optimising the control of a leader-follower train pair under fixed- and moving-block signalling systems.     

关于上海轨道交通12号线停车线长度的探讨

对上海轨道交通12号线配线车站设置的停车线长度,包括1列位、1列位＋1节车和2列位进行了探讨,对这几种停车线长度进行了比较,并对具体车站停车线长度进行了详细设计和计算。     

An investigation of passenger interchange and train standing time at LRT stations: (ii) Estimation of standing time

The standing-time of trains at urban rail stations is pertinent to determining the line capacity and fleet size. The assumption of uniform boarding and alighting leads to under-estimation of the standing time. It is shown that the train standing-time is related to the fraction of boarders and the maximum demand for boarding and alighting at a door. It is further shown that the probability distribution of passengers at a door depends on the platform entrance locations. A methodology that takes into account the above factors is proposed for estimating the train standing-time.     

Assessing the usage and level-of-service of pedestrian facilities in train stations: A Swiss case study

A framework for assessing the usage and level-of-service of rail access facilities is presented. It consists of two parts. A dynamic demand estimator allows to obtain time-dependent pedestrian origin–destination demand within walking facilities. Using that demand, a traffic assignment model describes the propagation of pedestrians through the station, providing an estimate of prevalent traffic conditions in terms of flow, walking times, speed and density. The corresponding level-of-service of the facilities can be directly obtained. The framework is discussed at the example of Lausanne railway station. For this train station, a rich set of data sources including travel surveys, pedestrian counts and trajectories has been collected in collaboration with the Swiss Federal Railways. Results show a good performance of the framework. To underline its practical applicability, a six-step planning guideline is presented that can be used to design and optimize rail access facilities for new or existing train stations. In the long term, the framework may also be used for crowd management, involving real-time monitoring and control of pedestrian flows.