A game theoretic model for re-optimizing a railway timetable

The Setting In the Nineties of the last century the European Commission decided to open the railway market to competition, allowing different railway companies to operate on the same network. Under this framework Infrastructure Managers have to allocate capacity in order to define the timetable, dealing with possible slot conflicts between competing Transport Operators. The Problem An efficient train scheduling requires collecting a lot of information from the Transport Operators, but it may not be in their interests to reveal their private information. Therefore, it may be useful for real-world applications to design methods that provide incentives to Transport Operators for cooperating with the aim of increasing their utility; moreover, this may result in an improvement of the efficiency even for the Infrastructure Managers, so they also have incentives for favouring the cooperation. The Proposal In this paper we propose a game theoretical model in which the agents (Transport Operators) exchange information on their needs and are compensated by a possible increasing of their utility. This approach represents the situation as a coalition formation problem. In particular, we refer to the C-Solution proposed by Gerber (Rev Econ Design 5:149–175, 1), which is applied to some examples, each with different features. This model requires that information is revealed to a small number of competitors. This is rather important in a market currently still characterized by operator reluctance to an indiscriminate diffusion of information. Furthermore, the low dimension of the problem allows having a low computational complexity

An optimization model for line planning and timetabling in automated urban metro subway networks

In this paper we present a Mixed Integer Nonlinear Programming model that we developed as part of a pilot study requested by the R&D company Metrolab in order to design tools for finding solutions for line planning and timetable situations in automated urban metro subway networks. Our model incorporates important factors in public transportation systems from both, a cost-oriented and a passenger-oriented perspective, as time-dependent demands, interchange stations, short-turns and technical features of the trains in use. The incoming flows of passengers are modeled by means of piecewise linear demand functions which are parameterized in terms of arrival rates and bulk arrivals. Decisions about frequencies, train capacities, short-turning and timetables for a given planning horizon are jointly integrated to be optimized in our model. Finally, a novel Math-Heuristic approach is proposed to solve the problem. The results of extensive computational experiments are reported to show its applicability and effectiveness to handle real-world subway networksComment: 30 pages, 6 figures, 9 table

Exploratory Analysis of Demand Interaction in the Planning of Passenger Railway Service

With the new EU legislature, the track management and the Train Operating Companies (TOCs) have to be separated subjects and hence allowing the private sector to enter the market (also called as liberalization of railways). Up to this point, the market was ruled by one TOC (usually the national carrier) subsidized by local government. Its purpose was to provide accessibility and mobility to the general public. However with a new competition entering the industry, the traditional business model has to be adapted to reflect the demand on profitable lines and at the same time provide the basic accessibility and mobility on lines, that are not profitable (subsidized by government). In this paper, we analyze the current planning process of the passenger railway service in the context of demand interaction, including references to the fundamental literature on the topic. Our study shows that the current Train Timetabling Problem (TTP) in the literature does not reflect the actual demand and hence we propose a new problem to be inserted in the planning process: the Ideal Train Timetabling Problem. Such a problem would find the most profitable timetable for each train and would serve as an input to the TTP, in which the feasibility of such timetables would be secured

The Ideal Train Timetabling Problem

The aim of this paper is to analyze and to improve the current planning process of the passenger railway service. At first, the state-of-the-art in research is presented. However, given the recent changes in legislature allowing competitors in the railway industry, the current way of planning is not sufficient anymore. The original planning is based on the accessibility/mobility concept provided by one carrier, whereas the competitive market consists of several carriers that are driven by the profit. Moreover, the current practice does not define the ideal timetables and thus it is assumed that they evolve incrementally, based on a historical data (train occupation, ticket sales, etc.). And thus, we introduce a definition of an ideal timetable that is expressed using the passenger cost. In order to create the timetables itself, we propose to insert the Ideal Train Timetabling Problem (ITTP) that is solved for each Train Operating Company (TOC) separately, into the planning process. The ITTP approach incorporates the passenger demand in the planning and its aim is to minimize the passenger cost(s). The outcome of the ITTP is the ideal timetables (including connections between the trains and weighted by the demand), which then serve as an input for the traditional Train Timetabling Problem (TTP). The TTP takes into account wishes of each TOC (the ideal timetables) and creates global feasible timetable for the given railway network, while minimizing the changes of the TOCs wishes. The ITTP is in line with the new market structure and it can produce both: non-cyclic and cyclic timetables. The model is tested on the data provided by the Israeli Railways (IR). The instance consists of a full demand OD Matrix of an average working day in Israel during 2008. The results are compared to the current timetable of IR. Due to the large complexity of the model, it is solved using the Column Generation methodology

Railway Passenger Service Timetable Design

The aim of this paper is to analyze and to improve the current planning process of the passenger railway service. At first, the state-of-the-art in research is presented. Given the recent changes in legislature allowing competitors to enter the railway industry in Europe, also known as liberalization of railways, the current way of planning does not reflect the situation anymore. The original planning is based on the accessibility/mobility concept provided by one carrier, whereas the competitive market consists of several carriers that are driven by the profit. Moreover, the current practice does not define the ideal timetables (the initial most profitable timetables) and thus it is assumed that the Train Operating Companies (TOCs) use their historical data (train occupation, ticket sales, etc.) in order to construct the ideal timetables. For the first time in this field, we tackle the problem of ideal timetables in railway industry from the both points of view: TOCs’ and passengers’. We propose the Ideal Train Timetabling Problem (ITTP) to create a list of train timetables for each TOC separately. The ITTP approach incorporates the passenger demand in the planning and its aim is to maximize TOCs’ profits while keeping the passengers’ costs at a certain level. The outcome of the ITTP is the ideal timetables (including connections between the trains), which then serve as inputs for the traditional Train Timetabling Problem (TTP). We test our approach on the S-train network of Canton Vaud, Switzerland