Flexible Connections in PESP Models for Cyclic Passenger Railway Timetabling

In this paper we describe how rolling stock and passenger connections in a cyclic railway timetable can be modeled in a flexible way within the model for the Periodic Event Scheduling Problem (PESP). The PESP model was introduced by Serani and Ukovich (1989). Usually, PESP-models assume that the constraints for rolling stock or passenger connections specify in detail which trains should connect with each other. However, the flexibility described in this paper allows the model to choose which trains should connect with each other in a rolling stock or passenger connection. We express the required number of train compositions in terms of the integer cycle variables of the constraint graph. We also describe an abstract framework, demonstrating that, under certain conditions, the extra flexibility can be modeled purely in terms of PESP constraints. The concept of flexible rolling stock and passenger connections is illustrated by an example based on three intercity lines of Netherlands Railways

Solving the Periodic Scheduling Problem: An Assignment Approach in Non-Periodic Networks

The periodic event scheduling problem (PESP) is a well researched problem used for finding good periodic timetables in public transport. While it is based on a periodic network consisting of events and activities which are repeated every period, we propose a new periodic timetabling model using a non-periodic network. This is a first step towards the goal of integrating periodic timetabling with other planning steps taking place in the aperiodic network, e.g. passenger assignment or delay management. In this paper, we develop the new model, show how we can reduce its size and prove its equivalence to PESP. We also conduct computational experiments on close-to real-world data from Lower Saxony, a region in northern Germany, and see that the model can be solved in a reasonable amount of time

Towards Improved Robustness of Public Transport by a Machine-Learned Oracle

The design and optimization of public transport systems is a highly complex and challenging process. Here, we focus on the trade-off between two criteria which shall make the transport system attractive for passengers: their travel time and the robustness of the system. The latter is time-consuming to evaluate. A passenger-based evaluation of robustness requires a performance simulation with respect to a large number of possible delay scenarios, making this step computationally very expensive. For optimizing the robustness, we hence apply a machine-learned oracle from previous work which approximates the robustness of a public transport system. We apply this oracle to bi-criteria optimization of integrated public transport planning (timetabling and vehicle scheduling) in two ways: First, we explore a local search based framework studying several variants of neighborhoods. Second, we evaluate a genetic algorithm. Computational experiments with artificial and close to real-word benchmark datasets yield promising results. In all cases, an existing pool of solutions (i.e., public transport plans) can be significantly improved by finding a number of new non-dominated solutions, providing better and different trade-offs between robustness and travel time

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

How (not) to Evaluate Passenger Routes, Timetables and Line Plans

Accurate evaluation of the service quality of public transport is imperative for public transport operators, providers of competing mobility services and policy makers. However, there is no consensus on how public transport should be evaluated. We fill this research gap by presenting a structural approach to evaluate three common manifestations of public transport (route sets, timetables and line plans), considering the two predominant route choice models (shortest path routing and logit routing). The measures for service quality that we derive are consistent with the underlying routing models, are easy to interpret, and can be computed efficiently, providing a ready-to-use framework for evaluating public transport. As a byproduct, our analysis reveals multiple managerial insights

Using information engineering to understand the impact of train positioning uncertainties on railway subsystems

Many studies propose new advanced railway subsystems, such as Driver Advisory System (DAS), Automatic Door Operation (ADO) and Traffic Management System (TMS), designed to improve the overall performance of current railway systems. Real time train positioning information is one of the key pieces of input data for most of these new subsystems. Many studies presenting and examining the effectiveness of such subsystems assume the availability of very accurate train positioning data in real time. However, providing and using high accuracy positioning data may not always be the most cost-effective solution, nor is it always available. The accuracy of train position information is varied, based on the technological complexity of the positioning systems and the methods that are used. In reality, different subsystems, henceforth referred to as ‘applications’, need different minimum resolutions of train positioning data to work effectively, and uncertainty or inaccuracy in this data may reduce the effectiveness of the new applications. However, the trade-off between the accuracy of the positioning data and the required effectiveness of the proposed applications is so far not clear. A framework for assessing the impact of uncertainties in train positions against application performance has been developed. The required performance of the application is assessed based on the characteristics of the railway system, consisting of the infrastructure, rolling stock and operational data. The uncertainty in the train positioning data is considered based on the characteristics of the positioning system. The framework is applied to determine the impact of the positioning uncertainty on the application’s outcome. So, in that way, the desired position resolution associated with acceptable application performance can be characterised. In this thesis, the framework described above is implemented for DAS and TMS applications to understand the influence of positioning uncertainty on their fundamental functions compared to base case with high accuracy (actual position). A DAS system is modelled and implemented with uncertainty characteristic of a Global Navigation Satellite System (GNSS). The train energy consumption and journey time are used as performance measures to evaluate the impact of these uncertainties compared to a base case. A TMS is modelled and implemented with the uncertainties of an on-board low-cost low-accuracy positioning system. The impact of positioning uncertainty on the modelled TMS is evaluated in terms of arrival punctuality for different levels of capacity consumption. The implementation of the framework for DAS and TMS applications determines the following: • which of the application functions are influenced by positioning uncertainty; • how positioning uncertainty influences the application output variables; • how the impact of positioning uncertainties can be identified, through the application output variables, whilst considering the impact of other railway uncertainties; • what is the impact of the underperforming application, due to positioning uncertainty, on the whole railway system in terms of energy, punctuality and capacity