Integer programming based solution approaches for the train dispatching problem

Railroads face the challenge of competing with the trucking industry in a fastpaced environment. In this respect, they are working toward running freight trains on schedule and reducing travel times. The planned train schedules consist of departure and arrival times at main stations on the rail network. A detailed timetable, on the other hand, consists of the departure and arrival times of each train in each track section of its route. The train dispatching problem aims to determine detailed timetables over a rail network in order to minimize deviations from the planned schedule. We provide a new integer programming formulation for this problem based on a spacetime network; we propose heuristic algorithms to solve it and present computational results of these algorithms. Our approach includes some realistic constraints that have not been previously considered as well as all the assumptions and practical issues considered by the earlier works

Susceptibility of optimal train schedules to stochastic disturbances of process times

This work focuses on the stochastic evaluation of train schedules computed by a microscopic scheduler of railway operations based on deterministic information. The research question is to assess the degree of sensitivity of various rescheduling algorithms to variations in process times (running and dwell times). In fact, the objective of railway traffic management is to reduce delay propagation and to increase disturbance robustness of train schedules at a network scale. We present a quantitative study of traffic disturbances and their effects on the schedules computed by simple and advanced rescheduling algorithms. Computational results are based on a complex and densely occupied Dutch railway area; train delays are computed based on accepted statistical distributions, and dwell and running times of trains are subject to additional stochastic variations. From the results obtained on a real case study, an advanced branch and bound algorithm, on average, outperforms a First In First Out scheduling rule both in deterministic and stochastic traffic scenarios. However, the characteristic of the stochastic processes and the way a stochastic instance is handled turn out to have a serious impact on the scheduler performance

Stochastic Improvement of Cyclic Railway Timetables

Real-time railway operations are subject to stochastic disturbances. However, a railway timetable is a deterministic plan. Thus a timetable should be designed in such a way that it can cope with the stochastic disturbances as well as possible. For that purpose, a timetable usually contains time supplements in several process times and buffer times between pairs of consecutive trains. This paper describes a Stochastic Optimization Model that can be used to allocate the time supplements and the buffer times in a given timetable in such a way that the timetable becomes maximally robust against stochastic disturbances. The Stochastic Optimization Model was tested on several instances of NS Reizigers, the main operator of passenger trains in the Netherlands. Moreover, a timetable that was computed by the model was operated in practice in a timetable experiment on the so-called “Zaanlijn”. The results show that the average delays of trains can often be reduced significantly by applying relatively small modifications to a given timetable

Improved stochastic optimization of railway timetables

We present a general model to find the best allocation of a limited amount of supplements (extra minutes added to a timetable in order to reduce delays) on a set of interfering railway lines. By the best allocation, we mean the solution under which the weighted sum of expected delays is minimal. Our aim is to finely adjust an already existing and well-functioning timetable. We model this inherently stochastic optimization problem by using two-stage recourse models from stochastic programming, building upon earlier research from the literature. We present an improved formulation, allowing for an efficient solution using a standard algorithm for recourse models. We show that our model may be solved using any of the following theoretical frameworks: linear programming, stochastic programming and convex non-linear programming, and present a comparison of these approaches based on a real-life case study. Finally, we introduce stochastic dependency into the model, and present a statistical technique to estimate the model parameters from empirical data

Issues on simulation of the railway rolling stock operation process – a system and literature review

Railway traffic simulation, taking into account operation and maintenance conditions, is not a new issue in the literature. External effects in such networks (eg. level crossings) were not taken into account in studies. The used models do not take into account sufficiently the process of degradation and recovery of the network. From the technical side, currently carried out simulations are made using similar approaches and techniques as in the initial stage of research. Well-established work in this area could be the basis for evaluation of new solutions. However, the progress in simulation tools during the last years, especially in performance and programming architecture, attempt to create a modern simulation tool. In the paper were presented the main assumptions for the evaluated event-based simulation method, with application to stiff-track transportation network

Railway Capacity Enhancement with Modern Signalling Systems – A Literature Review

In times of ever stronger awareness of environmental protection and potentiation of a beneficial modal split, the railway sector with efficient asset utilization and proper investment planning has the highest chance of meeting customer expectations and attracting new users more effectively. Continuous increase in railway demand leads to an increase in the utilization of railway infrastructure, and the inevitable lack of capacity, a burning problem that many national railways are continually facing. To address it more effectively, this paper reviews available methodologies for railway capacity determination and techniques for its enhancement in the recent scientific literature. Particular focus is given to the possibility of increasing railway capacity through signalling systems and installing the European Train Control System (ETCS). The most important relationships with segments of existing research have been identified, and in line with this, the directions for a potential continuation of research are suggested

A mixed-integer linear program for real-time train platforming management

Unexpected events may perturb operations and generate conflicts that must be addressed promptly to limit delay propagation and other negative impacts on the network. The real-time railway traffic management problem deals with disruptions in railway networks, including tracks, junctions and stations. When they happen in station areas, new decisions involving train platforming, rerouting, ordering and timing must be made in real time. This paper explores a mesoscopic approach to deal with disruptions at rail stations. A mathematical programming-based model is proposed to determine re-routing and re-scheduling decisions for railway traffic in a station area. The key steps of the approach, which simulate what happens in real-time traffic management, are: i) an initial off-line preprocessing stage of the set of feasible routes originally planned, ii) a second preprocessing stage which analyses the disruption and sets the necessary parameters for the last step iii), which consists of an integer programming model that seeks solutions which minimise deviations from planned train schedules and assigns new and appropriate platforms (if necessary). Computational experiments show that realistic instances can be solved near to optimality using CPLEX in very short times. This allows to consider this methodology for solving real time traffic management problems.Peer ReviewedPostprint (published version

Adaptive Railway Traffic Control using Approximate Dynamic Programming

Railway networks around the world have become challenging to operate in recent decades, with a mixture of track layouts running several different classes of trains with varying operational speeds. This complexity has come about as a result of the sustained increase in passenger numbers where in many countries railways are now more popular than ever before as means of commuting to cities. To address operational challenges, governments and railway undertakings are encouraging development of intelligent and digital transport systems to regulate and optimise train operations in real-time to increase capacity and customer satisfaction by improved usage of existing railway infrastructure. Accordingly, this thesis presents an adaptive railway traffic control system for realtime operations based on a data-based approximate dynamic programming (ADP) approach with integrated reinforcement learning (RL). By assessing requirements and opportunities, the controller aims to reduce delays resulting from trains that entered a control area behind schedule by re-scheduling control plans in real-time at critical locations in a timely manner. The present data-based approach depends on an approximation to the value function of dynamic programming after optimisation from a specified state, which is estimated dynamically from operational experience using RL techniques. By using this approximation, ADP avoids extensive explicit evaluation of performance and so reduces the computational burden substantially. In this thesis, formulations of the approximation function and variants of the RL learning techniques used to estimate it are explored. Evaluation of this controller shows considerable improvements in delays by comparison with current industry practices

Combining robustness and recovery in rapid transit network design

When designing a transport network, decisions are made according to an expected value for network state variables, such as infrastructure and vehicle conditions, which are uncertain at a planning horizon of up to decades. Because disruptions, such as infrastructure breakdowns, will arise and affect the network on the day of operations, actions must be taken from the network design. Robust network designs may be implemented but they are extremely expensive if disruptions do not realise. In this paper, we propose a novel approach to the network design problem where robustness and recovery are combined. We look for the trade-off between efficiency and robustness accounting for the possibility of recovering from disruptions: recoverable robust network design. Computational experiments drawn from fictitious and realistic networks show how the presented approach reduces the price of robustness and recovery costs as compared to traditional robust and non-robust rapid transit network design approaches