Stochastic optimization model and solution algorithm for robust double-track train-timetabling problem

Journal ArticleAbstract-By considering various stochastic disturbances unfolding in a real-time dispatching environment, this paper develops a stochastic optimization formulation for incorporating segment travel-time uncertainty and dispatching policies into a medium-term train-timetabling process that aims to minimize the total trip time in a published timetable and reduce the expected schedule delay. Based on a heuristic sequential solution framework, this study decomposes the robust timetabling problem into a series of subproblems that optimize the slack-time allocation for individual trains. A number of illustrative examples are provided to demonstrate the proposed model and solution algorithms using data collected from a Beijing-Shanghai high-speed rail corridor in China

On the delivery robustness of train timetables with respect to production replanning possibilities

Measuring timetable robustness is a complex task. Previous efforts have mainly been focused on simulation studies or measurements of time supplements. However, these measurements don't capture the production flexibility of a timetable, which is essential for measuring the robustness with regard to the trains' commercial activity commitments, and also for merging the goals of robustness and efficiency. In this article we differentiate between production timetables and delivery timetables. A production timetable contains all stops, meetings and switch crossings, while a delivery timetable only contains stops for commercial activities. If a production timetable is constructed such that it can easily be replanned to cope with delays without breaking any commercial activity commitments it provides delivery robustness without compromising travel efficiency. Changing meeting locations is one of the replanning tools available during operation, and this paper presents a new framework for heuristically optimising a given production timetable with regard to the number of alternative meeting locations. Mixed integer programming is used to find two delivery feasible production solutions, one early and one late. The area between the two solutions represents alternative meeting locations and therefore also the replanning enabled robustness. A case study from Sweden demonstrates how the method can be used to develop better production timetables

An Overview and Categorization of Approaches for Train Timetable Generation

A train timetable is a crucial component of railway transportation systems as it directly impacts the system’s performance and the customer satisfaction. Various approaches can be found in the literature that deal with timetable generation. However, the approaches proposed in the literature differ significantly in terms of the use case for which they are in tended. Differences in objective function, timetable periodicity, and solution methods have led to a confusing number of works on this topic. Therefore, this paper presents a com pact literature review of approaches to train timetable generation. The reviewed papers are briefly summarized and categorized by objective function and periodicity. Special emphasis is given to approaches that have been applied to real-world railway data

Operations research in passenger railway transportation

In this paper, we give an overview of state-of-the-art OperationsResearch models and techniques used in passenger railwaytransportation. For each planning phase (strategic, tactical andoperational), we describe the planning problems arising there anddiscuss some models and algorithms to solve them. We do not onlyconsider classical, well-known topics such as timetabling, rollingstock scheduling and crew scheduling, but we also discuss somerecently developed topics as shunting and reliability oftimetables.Finally, we focus on several practical aspects for each of theseproblems at the largest Dutch railway operator, NS Reizigers.passenger railway transportation;operation research;planning problems

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

Dispatching and Rescheduling Tasks and Their Interactions with Travel Demand and the Energy Domain: Models and Algorithms

Abstract The paper aims to provide an overview of the key factors to consider when performing reliable modelling of rail services. Given our underlying belief that to build a robust simulation environment a rail service cannot be considered an isolated system, also the connected systems, which influence and, in turn, are influenced by such services, must be properly modelled. For this purpose, an extensive overview of the rail simulation and optimisation models proposed in the literature is first provided. Rail simulation models are classified according to the level of detail implemented (microscopic, mesoscopic and macroscopic), the variables involved (deterministic and stochastic) and the processing techniques adopted (synchronous and asynchronous). By contrast, within rail optimisation models, both planning (timetabling) and management (rescheduling) phases are discussed. The main issues concerning the interaction of rail services with travel demand flows and the energy domain are also described. Finally, in an attempt to provide a comprehensive framework an overview of the main metaheuristic resolution techniques used in the planning and management phases is shown

Robustness for a single railway line: Analytical and simulation methods

[EN] Railway scheduling has been a significant issue in the railway industry. Over the last few years, numerous approaches and tools have been developed to compute railway scheduling. However, robust solutions are necessary to absorb short disruptions. In this paper, we present the robustness problem from the point of view of railway operators and we propose analytical and simulation methods to measure robustness in a single railway line. In the analytical approach, we have developed some formulas to measure robustness based on the study of railway line infrastructure topology and buffer times. In the simulation approach, we have developed a software tool to assess the robustness for a given schedule. These methods have been inserted in MOM (More information can be found at the MOM web page http://www.dsic.upv.es/users/ia/gps/MOM), which is a project in collaboration with the Spanish Railway Infrastructure Manager (ADIF). © 2012 Elsevier Ltd. All rights reserved.This work has been partially supported by the research project TIN2010-20976-C02-01 (Min. de Economia y Competitividad, Spain) and project PIRSES-GA-2011-294931 (FP7-PEOPLE-2011-IRSES).Salido Gregorio, MA.; Barber Sanchís, F.; Ingolotti Hetter, LP. (2012). Robustness for a single railway line: Analytical and simulation methods. Expert Systems with Applications. 39(18):13305-13327. https://doi.org/10.1016/j.eswa.2012.05.071S1330513327391

An approximate dynamic programming approach for designing train timetables

Traditional approaches to solving the train timetabling problem—the optimal allocation of when each train arrives and departs each station—have relied on Mixed-Integer Programming (MIP) approaches. We propose an alternative formulation for this problem based on the modeling and algorithmic framework of approximate dynamic programming. We present a Q-learning algorithm in order to tractably solve the high-dimensional problem. We compare the performance of several variants of this approach, including discretizing the state and the action spaces, and continuous function approximation with global basis functions. We demonstrate the algorithms on two railway system cases, one minimizing energy consumption subject to punctuality constraints, and one maximizing capacity subject to safety constraints. We demonstrate that the ADP algorithm converges rapidly to an optimal solution, and that the number of iterations required increases linearly in the size of the rail system, in contrast with MIP approaches whose computation time grows exponentially. We also show that an additional benefit to the ADP approach is the intuition gained from visualizing the Q-factor functions, which graphically capture the intuitive tradeoffs between efficiency and constraints in both examples