Large-scale Railway Networks Research Articles

Train rescheduling for large-scale disruptions in a large-scale railway network

This paper studies the problem of rescheduling trains in a large-scale railway network with the characteristics of long distance, long time horizon and a large number of trains, where a disruption causes the paralysis of a significant part of the network for a long duration. As rescheduling measures we consider train reordering and retiming as well as the option of rerouting trains along alternative paths in the railway network. Although rerouting was not previously employed in large-scale long-distance networks, we show its benefit in reducing passenger delays. We formulate the problem as an integer linear programming (ILP) model on a space–time network with the goal of minimizing the total passenger delay and the number of passengers that could not reach their destination. In order to effectively solve the ILP model for real-world instances, we propose a heuristic algorithm (LR-H), based on the Lagrangian relaxation (LR) of a subset of constraints in the ILP model. LR allows decomposing the problem into a series of independent train-based subproblems which are easy to solve. Due to the large number of constraints and to cope with the real-time requirement, LR-H employs dynamic constraint-generation.We tested LR-H on railway networks of different sizes under several disruption scenarios: first, we compared the results obtained by LR-H on a small-size instance with those found by the general-purpose ILP solver GUROBI, showing that LR-H can find near-optimal solutions in significantly shorter computing times. Then, we applied LR-H to a real-world instance of a railway network in China with 350 trains in different disruption scenarios. The experimental results show that, LR-H can obtain near-optimal solutions with an average optimality gap of 2.27% in an average computing time of about 300 s.

Railway Network Development and the «Big Economic Breakthrough» in Russia

Rail transport has a very significant impact on development of the economy and society. The objective of the study described in the article is to identify, using the methods of historical and statistical analysis, the relationship between development of the Russian railway network and the «big economic breakthrough» that took place from 1885 to 1914 and brought the country to a fundamentally higher level of development.The analysis begins with a review of the previous period of 1861–1884, during which cardinal institutional changes were carried out and a large-scale railway network was created that connected all the main economic regions of the European part of Russia. Due to this, even then high rates of industrial growth were ensured, but the growth was very volatile.It has been revealed that during the period of the «big economic breakthrough» it was possible not only to accelerate, but also to increase sustainability of economic development. These results were based on a significant level of availability of railway infrastructure for population already reached by the beginning of the «big economic breakthrough», allowing continuing dynamic development of railway transport and achieving growing intensity of employment of the railway network. The synergy of institutional and transport infrastructure development was of great importance. Due to this, the Russian economy during the period of the «big economic breakthrough» became the world record holder in terms of growth in industrial production and labour productivity, while a significant increase in the human development index was also achieved.Thus, the study of the relationship between development of the railway network and the «big economic breakthrough» in Russia at the end of 19th – the beginning of 20th century has shown the importance of the synergy of institutional and infrastructural and transport development for successful economic and social modernisation and demonstrated the key role that railway transport in this process.

Data-Driven Empty Container Repositioning for Large Scale Railway Network With Fuzzy Demands

The Chinese rail network has a fast-growing number of containers in service to promote intermodal transport service and to attract more freight demand to the railway for a sustainable transport system. The repositioning of empty containers induces a significant problem for the large-scale rail network, due to the spatial imbalance between freight supply and demand. Traditionally, the empty container repositioning (ECR) problem is solved with the estimated parameters of a given demand distribution, which may difficult known to decision maker. This article develops a data-driven framework for the ECR problem based on the large datasets available. This framework employs machine-learning algorithms to forecast the supply/demand of empty containers, and to draw parameters identifying the factors that can be hardly integrated into optimization models. Based on those parameters, two optimization models for different ECR modes are then proposed to explore the optimal ECR plan. An integrated weight coefficient is introduced into the objective functions, which minimizes the total kilometers that empty containers transported. The models are solved by CPLEX after constraints conversion based on triangular fuzzy supply/demand. The numerical results based on a real-world case show that the proposed solution method can yield the optimal empty container repositioning plan. The total container-kilometer may increase after data-driven parameters are introduced, as some of the empty container repositioning may no longer follow the shortest path, while the final plan becomes more practicable and executable.

A logic-based Benders decomposition for microscopic railway timetable planning

Railway timetable planning is one of the key factors in the successful operation of a railway network. The timetable must satisfy all operational restrictions at a microscopic representation of the railway network, while maximizing transportation capacity for passengers and freight. The microscopic planning of a railway timetable is an NP-Hard problem, difficult to solve for large-scale railway networks, such as those of entire countries. In this work, we propose a logic Benders decomposition approach to solve the problem of microscopic railway timetable planning. Our decomposition exploits the typical structure of a railway with dense networks around major hubs and sparse connections in-between hubs. A logic Benders cut is designed, which we are able to compute effectively for all decomposed problems within our considered structure, using a SAT based algorithm we developed. Moreover, an aggregation scheme for Benders cuts is proposed to speed up the iterative process. Experiments on real-world cases of the Swiss Federal Railways show a clear improvement in scalability compared to a variety of benchmarks including centralized approaches.

Scalable Rail Planning and Replanning: Winning the 2020 Flatland Challenge

Multi-Agent Path Finding (MAPF) is the combinatorial problem of finding collision-free paths for multiple agents on a graph. This paper describes MAPF-based software for solving train planning and replanning problems on large-scale railway networks under uncertainty. The software recently won the 2020 Flatland Challenge, a NeurIPS competition trying to determine how to efficiently manage dense traffic on rail networks. The software incorporates many state-of-the-art MAPF, or in general, optimization technologies, such as prioritized planning, large neighborhood search, safe interval path planning, minimum communication policies, parallel computing, and simulated annealing. It can plan collision-free paths for thousands of trains within a few minutes and deliver deadlock-free actions in real-time during execution.

An MPC-Based Rescheduling Algorithm for Disruptions and Disturbances in Large-Scale Railway Networks

Railways are a well-recognized sustainable transportation mode that helps to satisfy the continuously growing mobility demand. However, the management of railway traffic in large-scale networks is a challenging task, especially when both a major disruption and various disturbances occur simultaneously. We propose an automatic rescheduling algorithm for real-time control of railway traffic that aims at minimizing the delays induced by the disruption and disturbances, as well as the resulting cancellations of train runs and turn-backs (or short-turns) and shuntings of trains in stations. The real-time control is based on the Model Predictive Control (MPC) scheme where the rescheduling problem is solved by mixed integer linear programming using macroscopic and mesoscopic models. The proposed resolution algorithm combines a distributed optimization method and bi-level heuristics to provide feasible control actions for the whole network in short computation time, without neglecting physical limitations nor operations at disrupted stations. A realistic simulation test is performed on the complete Dutch railway network. The results highlight the effectiveness of the method in properly minimizing the delays and rapidly providing feasible feedback control actions for the whole network. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article aims at contributing to the enhancement of the core functionalities of Automatic Train Control (ATC) systems and, in particular, of the Automatic Train Supervision (ATS) module, which is included in ATC systems. In general, the ATS module allows to automate the train traffic supervision and consequently the rescheduling of the railway traffic in case of unexpected events. However, the implementation of an efficient rescheduling technique that automatically and rapidly provides the control actions necessary to restore the railway traffic operations to the nominal schedule is still an open issue. Most literature contributions fail in providing rescheduling methods that successfully determine high-quality solutions in less than one minute and include real-time information regarding the large-scale railway system state. This research proposes a semi-heuristic control algorithm based on MPC that, on the one hand, overcomes the limitations of manual rescheduling (i.e., suboptimal, stressful, and delayed decisions) and, on the other hand, offers the advantages of online and closed-loop control of railway traffic based on continuous monitoring of the traffic state to rapidly restore railway traffic operations to the nominal schedule. The semi-heuristic procedure permits to significantly reduce the computation time necessary to solve the rescheduling problem compared with an exact procedure; moreover, the use of a distributed optimization approach permits the application of the algorithm to large instances of the rescheduling problem, and the inclusion of both the traffic and rolling stock constraints related to the disrupted area. The method is tested on a realistic simulation environment, thus still requires further refinements for the integration into a real ATS system. Further developments will also consider the occurrence of various simultaneous disruptions in the network.

Decomposition and distributed optimization of real-time traffic management for large-scale railway networks

This paper introduces decomposition and distributed optimization approaches for the real-time railway traffic management problem considering microscopic infrastructure characteristics, aiming at an improved computational efficiency when tackling large-scale railway networks.Based on the nature of the railway traffic management problem, we consider three decomposition methods, namely a geography-based (GEO) decomposition, a train-based (TRA) decomposition, and a time-interval-based (TIN) decomposition, in order to partition the large railway traffic management optimization problem into several subproblems. In particular, an integer linear programming (ILP) model is developed to generate the optimal GEO solution, with the objectives of minimizing the number of interconnections among regions and of balancing the size of regions. The decomposition creates couplings among the subproblems, in terms of either capacity usage or transit time consistency; therefore the whole problem gets a non-separable structure. To handle the couplings, we introduce three distributed optimization approaches, namely an Alternating Direction Method of Multipliers (ADMM) algorithm, a priority-rule-based (PR) algorithm, and a Cooperative Distributed Robust Safe But Knowledgeable (CDRSBK) algorithm, which operate iteratively.We test all combinations of the three decomposition methods and the three distributed optimization algorithms on a large-scale railway network in the South-East of the Netherlands, in terms of feasibility, computational efficiency, and optimality. Overall the CDRSBK algorithm with the TRA decomposition performs best, where high-quality (optimal or near-optimal) solutions can be found within 10 s of computation time.

Optimizing train frequencies and train routing with simultaneous passenger assignment in high-speed railway network

In a high speed railway line plan (LP), train frequencies, train routing and passenger assignment problems are usually solved sequentially, which may lower the quality of the line plan. To bridge the gap, a bi-level multi-objective mixed integer nonlinear programming model for simultaneously obtaining the optimal plan of passenger assignment and train routing is developed in this paper. The upper level model is an integer programming (IP) model with an objective of minimizing both the total train travel time and the average capacity utilization rate, while the lower level one is a model with an objective of minimizing the total travel time of passengers and maximizing the average train attendance rate for all sections. In order to obtain the solution in relatively short time, a particle swarm approach is adopted to solve the model in a large scale railway network. As a case study, the model is applied to a high speed railway network in China. The results show that the total travel time of passengers and trains obtained from the simultaneous optimization model can be reduced by 0.9% in comparison with the two problems solved sequentially, which indicates that the model and the solution algorithms could be useful in practice.

Risk of increasing temperature due to climate change on high-speed rail network in Spain

With more than 3,200 km of track, the Spanish high-speed rail network is the longest network in Europe and the second largest in the world after China. Due to its geographical location in southern Europe, the entire network is exposed to periods of elevated temperatures that can cause disturbances and severe disruptions such as rail deformation, or in the worst case, lateral track buckling. In this study, the vulnerability of the current Spanish high-speed rail network is analysed in terms of track buckling failures with a Monte Carlo simulation. Downscaled temperature projections from a range of Global Climate Models (GCMs), under three Representative Concentration Pathways (RCP4.5, RCP6.0 and RCP8.5), were forced in a buckling model and particularized for different segments of the network. With that, the proposed methodology provides the number of rail buckles expected per year by assuming current maintenance standards and procedures. The result reveals significant increase in the occurrence of buckling events for future years, mainly in the central and southern areas of mainland Spain. However, relevant variations are found in different climates and time horizon scenarios in Spain. The anticipated buckling occurrences highlight the vulnerability of the Spanish rail network in the context of global warming scenarios. Overall, the proposed methodology is designed to be applicable in large-scale railway networks to identify potential buckling sites for the purpose of understanding and predicting their behaviour.

A dynamic, interpretable, and robust hybrid data analytics system for train movements in large-scale railway networks

We investigate the problem of analysing the train movements in large-scale railway networks for the purpose of understanding and predicting their behaviour. We focus on different important aspects: the Running Time of a train between two stations, the Dwell Time of a train in a station, the Train Delay, the Penalty Costs associated to a delay, and the Train Overtaking between two trains which are in the wrong relative position on the railway network. Two main approaches exist in the literature to address these problems. One is based on the knowledge of the network and the experience of the operators. The other one is based on the analysis of the historical data about the network with advanced data analytics methods. In this paper, we will propose a hybrid approach in order to address the limitations of the current solutions. In fact, experience-based models are interpretable and robust but not really able to take into account all the factors which influence train movements resulting in low accuracy. From the other side, data-driven models are usually not easy to interpret nor robust to infrequent events and require a representative amount of data which is not always available if the phenomenon under examination changes too fast. Results on real-world data coming from the Italian railway network will show that the proposed solution outperforms both state-of-the-art experience-based and data-driven systems in terms of interpretability, robustness, ability to handle nonrecurring events and changes in the behaviour of the network, and ability to consider complex and exogenous information.

An Algorithm to Create Test Data for Large-Scale Railway Network Revenue Management Models with Customer Choice

An Algorithm to Create Test Data for Large-Scale Railway Network Revenue Management Models with Customer Choice

A Passenger Flow Routing Model for High-speed Railway Network in Different Transportation Organization Modes

Reasonable selection of passenger flow routes consideringdifferent transportation organization modes can meetthe demands of adapting to large-scale high-speed railwaynetworks and improving network efficiency. Passenger flowrouting models are developed to find and optimize a setof passenger flow routes for a high-speed railway network considering different transportation organization modes. In this paper, we presented a new approach minimizing the operating costs, including traveling cost, cost of travel time differences between different lines, and penalties for the inter-line. The network was reconstructed to solve the directed graph with four nodes (node-in-up, node-in-down, nodes-outup, and nodes-out-down) indicating one station. To tackle our problem, we presented an integer non-linear programming model, and direct passenger demand was guaranteed owing to volume constraints. Binary variables were introduced to simplify the model, and the algorithm process was optimized. We suggested a global optimal algorithm by Lingo 11.0. Finally, the model was applied to a sub-network of the Northeast China railway system. Passenger flow routes were optimized and the transportation organization mode was discussed based on passenger volume, traveling distance, and infrastructure.

One-block train formation in large-scale railway networks: An exact model and a tree-based decomposition algorithm

We investigate the one-block train formation problem (TFP) in the railway freight transportation industry. The input to this problem is a railway network and a set of demands for transportation. Each demand is a request for shipping a number of rail cars from one station to another. The one-block TFP now addresses two subproblems in the tactical level: Which pairs of stations are directly connected via a block (or: train service); and which demands are transported by each block. The aim is to service all demands against minimal costs. Moving beyond current researches on service network design, the unitary rule and the intree rule are taken into account in this study based on the Chinese railway background. We develop a linear binary programming formulation to minimize the total sum of train accumulation costs and car classification costs, subject to limitations on the classification capacity and the number of sort tracks at each station. Furthermore, we propose a novel solution methodology that applies a tree-based decomposition algorithm. Here, we first decompose the whole network into a series of rooted trees for each destination separately. Then, we divide the trees further into sufficiently small subtrees, whose size is regulated by a node size parameter. Finally, we construct a restricted linear binary model for each subtree and solve these models sequentially to find their optimal solutions. The algorithm ensures that an overall feasible solution is obtained if one exists. Our computational results on a realistic network from the Chinese railway system with 83 stations, 158 links and 5700 randomly generated demands show that the proposed algorithm can derive high-quality solutions within a few hours of computation time. These solutions are on average 48.05% better than those obtained after solving the linear binary program with a commercial solver for 1 day.

Distributed optimization for real-time railway traffic management

We introduce a distributed optimization method for improving the computational efficiency of real-time traffic management approaches for large-scale railway networks. We first decompose the whole network into a pre-defined number of regions by using an integer linear optimization approach. For each resulting region, a mixed-integer linear programming approach is used to address the traffic management problem, with micro details of the network and incorporated with the train control problem. For handling the interactions among regions, an alternating direction method of multipliers (ADMM) algorithm based solution approach is developed to solve the subproblem of each region through coordination with the other regions in an iterative manner. A priority rule based solution approach is proposed to generate feasible suboptimal solutions, in case of lack of convergence. Numerical experiments are conducted based on the Dutch railway network to show the performance of the proposed solution approaches, in terms of effectiveness and efficiency. We also show the trade-off between solution quality and computational efficiency.

Dynamic Delay Predictions for Large-Scale Railway Networks: Deep and Shallow Extreme Learning Machines Tuned via Thresholdout

Current train delay (TD) prediction systems do not take advantage of state-of-the-art tools and techniques for handling and extracting useful and actionable information from the large amount of endogenous (i.e., generated by the railway system itself) and exogenous (i.e., related to railway operation but generated by external phenomena) data available. Additionally, they are not designed in order to deal with the intrinsic time varying nature of the problem (e.g., regular changes in the nominal timetable, etc.). The purpose of this paper is to build a dynamic data-driven TD prediction system that exploits the most recent tools and techniques in the field of time varying big data analysis. In particular, we map the TD prediction problem into a time varying multivariate regression problem that allows exploiting both historical data about the train movements and exogenous data about the weather provided by the national weather services. The performance of these methods have been tuned through the state-of-the-art thresholdout technique, a very powerful procedure which relies on the differential privacy theory. Finally, the performance of two efficient implementations of shallow and deep extreme learning machines that fully exploit the recent in-memory large-scale data processing technologies have been compared with the current state-of-the-art TD prediction systems. Results on real-world data coming from the Italian railway network show that the proposal of this paper is able to remarkably improve the state-of-the-art systems.

Train Delay Prediction Systems: A Big Data Analytics Perspective

Abstract Current train delay prediction systems do not take advantage of state-of-the-art tools and techniques for handling and extracting useful and actionable information from the large amount of historical train movements data collected by the railway information systems. Instead, they rely on static rules built by experts of the railway infrastructure based on classical univariate statistic. The purpose of this paper is to build a data-driven Train Delay Prediction System (TDPS) for large-scale railway networks which exploits the most recent big data technologies, learning algorithms, and statistical tools. In particular, we propose a fast learning algorithm for Shallow and Deep Extreme Learning Machines that fully exploits the recent in-memory large-scale data processing technologies for predicting train delays. Proposal has been compared with the current state-of-the-art TDPSs. Results on real world data coming from the Italian railway network show that our proposal is able to improve over the current state-of-the-art TDPSs.

Multi-route railroad blocking problem by improved model and ant colony algorithm in real world

In rail freight transportation, general merchandise freight cars may pass through many classification stations on their route from origin to destination. The Railroad Blocking Problem (RBP) is to reclassify inbound traffic from various origins in the classification stations and put them on outbound trains with the same or close destinations, the objective of the RBP is to minimize the total operating costs of delivering all traffic on the railway network while satisfying the resource and capacity constraints at the stations and the priority constraints for shipments. In this paper, we introduce a new mathematic model which can comprehensively describe the blocking strategy and various combinations of multi-route O–D pairs in large scale railway network. Furthermore, we propose an improved Ant Colony (AC) algorithm for RPB, and a computational experiment derived from the real life instances of coal heavy haul rail network in north China is given. Experimental results verified the validation of the model and effectiveness of the algorithm.

A delay propagation algorithm for large-scale railway traffic networks

In scheduled railway traffic networks a single delayed train may cause a domino effect of secondary delays over the entire network, which is a main concern to planners and dispatchers. This paper presents a model and an algorithm to compute the propagation of initial delays over a periodic railway timetable. The railway system is modelled as a linear system in max-plus algebra including zero-order dynamics corresponding to delay propagation within a timetable period. A timed event graph representation is exploited in an effective graph algorithm that computes the propagation of train delays using a bucket implementation to store the propagated delays. The behaviour of the delay propagation and the convergence of the algorithm is analysed depending on timetable properties such as realisability and stability. Different types of delays and delay behaviour are discussed, including primary and secondary delays, structural delays, periodic delay regimes, and delay explosion. A decomposition method based on linearity is introduced to deal with structural and initial delays separately. The algorithm can be applied to large-scale scheduled railway traffic networks in real-time applications such as interactive timetable stability analysis and decision support systems to assist train dispatchers.

Performance Study of a Mobile Multi-hop 802.11a/b Railway Network Using Passive Measurement

In this paper, we study the performance of IEEE 802.11a/b in a large-scale mobile railway networks and introduce our developed passive measurement approach. To provide a comprehensive evaluation, we built an outdoor multi-hop multi-interface railroad testbed (UNL-FRA Testbed), which consists of eight access points deployed along 3.5 mile of railroad track. We propose a novel large-scale passive measurement approach that synchronizes the system clocks of our monitoring systems, merges packet traces collected from multiple wireless channels across a multi-hop network, and enables a global performance view for the entire monitored network and across multiple layers. Based on the testing data collected from 15 field experiments carried out using BNSF locomotives and HyRail vehicles over a period of 18 months we conclude that in typical outdoor 802.11 railway environments the wireless link quality, the channel assignment scheme, and the handoff latency have much more significant impacts on the performance than the velocity. Furthermore, we discuss the implications of our conclusions on guaranteeing the quality of mobile services. We believe this is the first analysis on such a scale for 802.11-family railway networks.

Dynamic Benefit Analysis of Large Scale Railway Network by a System of Cities Model

Dynamic Benefit Analysis of Large Scale Railway Network by a System of Cities Model