Online distributed cooperative model predictive control of energy-saving trajectory planning for multiple high-speed train movements

The cooperative energy-efficient trajectory planning for multiple high-speed train movements is considered in this paper. We model all the high-speed trains as the agents that can communicate with others and propose a local trajectory planning control model using the Model Predictive Control (MPC) theory. After that we design an online distributed cooperative optimization algorithm for multiple train trajectories planning, under which each train agent can regulate the trajectory planning procedure to save energy using redundancy trip time through tuning ACO’s heuristic information parameter. Compared to the existing literature, the vital distinctions of our work lies not only on the online cooperative trajectory planning but also on the distributed mechanism for multiple high-speed trains. Experimental studies are given to illustrate the effectiveness of the proposed methods with the practical operational data of Wuhan-Guangzhou High-speed Railway in China.     

动卧客运与快递货运的高速铁路夜间能力利用模式

目前我国高速铁路的日间行车能力已得到了较为充分的利用,而如何组织好高铁夜间垂直天窗与夜行列车之间的耦合关系、用好高铁夜间能力,是适应多样化市场需求的需要,也是进一步提升高铁经营效益的有效途径。对此,本文提出了动卧列车和货运动车组两种相对可行的高铁夜间运输产品,分别对其产品特征进行了分析,充分考虑高铁夜间天窗制约下两种列车的开行模式,基于市场需求提出了列车开行策略,并在充分对比两种产品的经济效益、客(货)源组织、能力分配等因素的基础上,给出了高铁夜间能力发展建议。     

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.     

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.     

Multiple-phase train trajectory optimization with signalling and operational constraints

The train trajectory optimization problem aims at finding the optimal speed profiles and control regimes for a safe, punctual, comfortable, and energy-efficient train operation. This paper studies the train trajectory optimization problem with consideration of general operational constraints as well as signalling constraints. Operational constraints refer to time and speed restrictions from the actual timetable, while signalling constraints refer to the influences of signal aspects and automatic train protection on train operation. A railway timetable provides each train with a train path envelope, which consists of a set of positions on the route with a specified target time and speed point or window. The train trajectory optimization problem is formulated as a multiple-phase optimal control model and solved by a pseudospectral method. This model is able to capture varying gradients and speed limits, as well as time and speed constraints from the train path envelope. Train trajectory calculation methods under delay and no-delay situations are discussed. When the train follows the planned timetable, the train trajectory calculation aims at minimizing energy consumption, whereas in the case of delays the train trajectory is re-calculated to track the possibly adjusted timetable with the aim of minimizing delays as well as energy consumption. Moreover, the train operation could be affected by yellow or red signals, which is taken into account in the train speed regulation. For this purpose, two optimization policies are developed with either limited or full information of the train ahead. A local signal response policy ensures that the train makes correct and quick responses to different signalling aspects, while a global green wave policy aims at avoiding yellow signals and thus proceed with all green signals. The method is applied in a case study of two successive trains running on a corridor with various delays showing the benefit of accurate predictive information of the leading train on energy consumption and train delay of the following train.     

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.     

Scheduling heterogeneous train traffic on double tracks with efficient dispatching rules

To further improve the utilization rate of railway tracks and reduce train delays, this paper focuses on developing a high-efficiency train routing and timetabling approach for double-track railway corridors in condition that trains are allowable to travel on reverse direction tracks. We first design an improved switchable policy which is rooted in the approaches by Mu and Dessouky (2013), with the analysis of possible delays caused by different path choices. Then, three novel integrated train routing and timetabling approaches are proposed on the basis of a discrete event model and different dispatching rules, including no switchable policy (No-SP), Mu and Dessouky (2013)’s switchable policy (Original-SP) and improved switchable policy (Improved-SP). To demonstrate the performance of the proposed approaches, the heterogeneous trains on Beijing–Shanghai high speed railway are scheduled by aforementioned approaches. The case studies indicate that in comparison to No-SP and Original-SP approaches, respectively, the Improved-SP approach can reduce the total delay of trains up to 44.44% and 73.53% within a short computational time. Moreover, all of the performance criteria of the Improved-SP approach are usually better than those of other two approaches.     

Multi-objective optimization of train routing problem combined with train scheduling on a high-speed railway network

Based on train scheduling, this paper puts forward a multi-objective optimization model for train routing on high-speed railway network, which can offer an important reference for train plan to provide a better service. The model does not only consider the average travel time of trains, but also take the energy consumption and the user satisfaction into account. Based on this model, an improved GA is designed to solve the train routing problem. The simulation results demonstrate that the accurate algorithm is suitable for a small-scale network, while the improved genetic algorithm based on train control (GATC) applies to a large-scale network. Finally, a sensitivity analysis of the parameters is performed to obtain the ideal parameters; a perturbation analysis shows that the proposed method can quickly handle the train disturbance.     

A comparison of modelled and real-life driving profiles for the simulation of railway vehicle operation

A key factor in determining the performance of a railway system is the speed profile of the trains within the network. There can be significant variation in this speed profile for identical trains on identical routes, depending on how the train is driven. A better understanding and control of speed profiles can therefore offer significant potential for improvements in the performance of railway systems. This paper develops a model to allow the variability of real-life driving profiles of railway vehicles to be quantitatively described and predicted, in order to better account for the effects on the speed profile of the train and hence the performance of the railway network as a whole. The model is validated against data from the Tyne and Wear Metro, and replicates the measured data to a good degree of accuracy.     

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 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.     

Design of single-track rail line for high-speed trains

This paper presents a method for designing a single-track rail line for a reliable high-speed passenger train service. We first consider deterministic train performance and describe a general method for finding the best location and length of the passing tracks. The design is then modified to include slack, which is necessary to ensure on-time performance for trains encountering unexpected delay. An analysis of the robustness of the system to small delays is presented. Robustness to large train delays and slower traffic is incorporated through the provision of additional sidings. Finally, simulation results are presented which compare the performance of a single-track line to a fully double-tracked equivalent.     

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.     

Express guideway transit: A case for further development in transit automation

Safe and reliable coupling and decoupling of cars from a moving train is feasible with further developments in linear motor propulsion and control of transit vehicles. This allows the last car of a train to decouple and stop at a station for a relative long dwell time, before it accelerates and is coupled to a following train. Controlled doors in front and rear of the transit vehicle permit passengers to walk through the train to the car which stops at their destination. A proposed transit system using these features is described and compared to Bombardier's Advanced Rapid Transit. Potential advantages are high schedule speed, uncrowded trains, smaller and more stations, low energy requirements and a smaller vehicle fleet.     

Real-time energy consumption minimization in railway networks

A new timetable must be calculated in real-time when train operations are perturbed. Although energy consumption is becoming a central issue both from the environmental and economic perspective, it is usually neglected in the timetable recalculation. In this paper, we formalize the real-time Energy Consumption Minimization Problem (rtECMP). It finds in real-time the driving regime combination for each train that minimizes energy consumption, respecting given routing and precedences between trains. In the possible driving regime combinations, train routes are split in subsections for which one of the regimes resulting from the Pontryagin’s Maximum Principle is to be chosen. We model the trade-off between minimizing energy consumption and total delay by considering as objective function their weighted sum. We propose an algorithm to solve the rtECMP, based on the solution of a mixed-integer linear programming model. We test this algorithm on the Pierrefitte-Gonesse control area, which is a critical area in France with dense mixed traffic. The results show that the problem is tractable and an optimal solution of the model tackled can often be found in real-time for most 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.     

高速铁路桥上无缝线路制动附加力研究

制动荷载是高速铁路桥梁的重要荷载，但高速列车在双线高速铁路桥梁上单向或双线对向制动时，制动荷载并不具有对称性，而双线高速铁路整孔箱形梁具有很强的空间性，平面力学模型不能很好反映上述工况，有着很大的局限性。本文在吸收专家研究成果的基础上，建立了梁轨相互作用三维有限元空间力学模型，并用该模型对高速列车在桥上不同制动工况下引...     

The train platforming problem: The infrastructure management company perspective

If railway companies ask for station capacity numbers, their underlying question is in fact one about the platformability of extra trains. Train platformability depends not only on the infrastructure, buffer times, and the desired departure and arrival times of the trains, but also on route durations, which depend on train speeds and lengths, as well as on conflicts between routes at any given time. We consider all these factors in this paper. We assume a current train set and a future one, where the second is based on the expected traffic increase through the station considered. The platforming problem is about assigning a platform to each train, together with suitable in- and out-routes. Route choices lead to different route durations and imply different in-route-begin and out-route-end times. Our module platforms the maximum possible weighted sum of trains in the current and future train set. The resulting number of trains can be seen as the realistic capacity consumption of the schedule. Our goal function allows for current trains to be preferably allocated to their current platforms.Our module is able to deal with real stations and train sets in a few seconds and has been fully integrated by Infrabel, the Belgian Infrastructure Management Company, in their application called Ocapi, which is now used to platform existing and projected train sets and to determine the capacity consumption.     

The variation in the value of travel-time savings and the dilemma of high-speed rail in China

This paper examines the variation in the value of travel-time savings (VTTS), a fundamental element determining the market demand for high-speed rail. Following a review of time allocation theories, a time allocation model for general travel behavior is proposed as a further elaboration of Evans’ (1972) activities analysis. There are relationships among activities that can be expressed using a linear inequality to show the constraints on the arrangement of activities. This model indicates that two or more activities can be simultaneously rearranged to improve time management, which may be a source of variation in VTTS. This time allocation model can explain why large-scale high-speed rail construction in China faces significant market risks and a high likelihood of economic loss. Data from a new ticket sales and booking system for railway passengers indicate that passengers prefer conventional overnight sleeper trains, rather than high-speed trains, for long-distance travel, which supports the analysis of the time allocation model.