Phase Synchronization in Railway Timetables

Timetable construction belongs to the most important optimization problems in public transport. Finding optimal or near-optimal timetables under the subsidiary conditions of minimizing travel times and other criteria is a targeted contribution to the functioning of public transport. In addition to efficiency (given, e.g., by minimal average travel times), a significant feature of a timetable is its robustness against delay propagation. Here we study the balance of efficiency and robustness in long-distance railway timetables (in particular the current long-distance railway timetable in Germany) from the perspective of synchronization, exploiting the fact that a major part of the trains run nearly periodically. We find that synchronization is highest at intermediate-sized stations. We argue that this synchronization perspective opens a new avenue towards an understanding of railway timetables by representing them as spatio-temporal phase patterns. Robustness and efficiency can then be viewed as properties of this phase pattern

Розробка методу моделювання розповсюдження затримок поїздів в залізничних мережах за допомогою епідеміологічних SIR-моделей

A method has been developed to simulate propagation of train delays in branched railroad ranges using modified epidemiological SIR models. These models take into account the mutual influence of trains with different priorities in the flow. This makes it possible to study the heterogeneous dynamics in the propagation of delays among trains of different priorities. To consider the propagation of the primary delay in space and time, it is proposed to represent the topology of the railway network in the form of an undirected graph with reference to the edge of the graph in the mathematical system of differential equations of the SIR model. This unifies the process of constructing SIR models for each edge (section) of the network graph and reduces the dimension of the problem. To take into account the influence of the “network effect”, it is proposed to determine the transit coefficient for each station of the section. This coefficient helps calculate the number of delayed trains for adjacent sections. To set SIR models, it is proposed to use empirical data on the propagation of the average delay in the standard traffic schedule in the corresponding section. For the sequential solution of SIR models corresponding to interconnected network sections, an algorithm is applied to turn the network graph into a directed tree the root of which is the station where the delay occurs. Tests on modelling the propagation of train delays in the railway network are carried out taking into account the mutual influence of different categories of trains in the flow and the built-in time reserves for the restoration of movement. The obtained simulation results have confirmed the adequacy of the solutions and helped quantify the influence of primary delays and the amount of time reserve in the schedules of trains of various categories on the reliability of the standard train schedule Разработан метод моделирования распространения задержек поездов на разветвленных железнодорожных полигонах с помощью модифицированных эпидемиологических SIR-моделей. Данные модели учитывают взаимовлияние поездов с разным приоритетом в потоке. Это позволяет учесть гетерогенную динамику при распространении задержек между поездопотоками разной приоритетности. Для учета распространения первичной задержки в пространстве и времени предложено представить топологию железнодорожной сети в виде неориентированного графа с привязкой к ребру графа математической системы дифференциальных уравнений SIR-модели. Это позволило унифицировать процесс построения SIR-моделей для каждого ребра (участка) графа сети и уменьшить размерность задачи. Для учета влияния "сетевого эффекта" предложено определять транзитный коэффициент по каждой станции участка. Данный коэффициент позволяет вычислить количество задержанных поездов на смежные участки. Для настройки SIR-моделей предложено использовать эмпирические данные о распространении средней задержки в нормативном графике движения на соответствующем участке. Для последовательного решения SIR-моделей, отвечающих взаимосвязанным участкам сети, применен алгоритм, который превращает граф сети в направленное дерево, корнем которого является станция возникновения задержки. Проведены исследования моделирования распространения задержек поездов на железнодорожном полигоне с учетом взаимовлияния разных категорий поездов в потоке и заложенных резервов времени на восстановление движения. Полученные результаты моделирования подтвердили адекватность решений и позволяют количественно оценить влияние первичных задержек и величин резерва времени в расписаниях движения поездов различных категорий на надежность нормативного графика движения поездовРозроблено метод моделювання розповсюдження затримок поїздів на розгалужених залізничних полігонах за допомогою модифікованих епідеміологічних SIR-моделей. Дані моделі враховують взаємовплив поїздів з різним пріоритетом в потоці. Це дозволяє врахувати гетерогенну динаміку при поширенні затримок між поїздопотоками різної пріоритетності. Для врахування поширення первинної затримки у просторі і часі запропоновано представити топологію залізничної мережі у вигляді неорієнтованого графу з прив’язкою до ребра графу математичної системи диференційних рівнянь SIR-моделі. Це дозволило уніфікувати процес побудови SIR-моделей для кожного ребра (дільниці) графу мережі та зменшити розмірність задачі. Для обліку впливу “мережевого ефекту” запропоновано визначати транзитний коефіцієнт за кожною станцією дільниці. Даний коефіцієнт дозволяє вирахувати кількість затриманих поїздів на суміжні дільниці. Для настроювання SIR-моделей запропоновано використати емпіричні дані щодо розповсюдження середньої затримки в нормативному графіку руху на відповідній дільниці. Для послідовного розв’язку SIR-моделей, що відповідають взаємопов’язаним дільницям мережі, застосовано алгоритм, який перетворює граф мережі на спрямоване дерево, коренем якого є станція виникнення затримки. Проведені дослідження моделювання поширення затримок поїздів на залізничному полігоні з врахуванням взаємовпливу різних категорій поїздів в потоці та закладених резервів часу на відновлення руху. Отримані результати моделювання підтвердили адекватність рішень та дозволяють кількісно оцінити вплив первинних затримок та величин резерву часу в розкладах руху поїздів різних категорій на надійність нормативного графіка руху поїзді

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

Robust routing in urban public transportation: How to find reliable journeys based on past observations.

Abstract We study the problem of robust routing in urban public transportation networks. In order to propose solutions that are robust for typical delays, we assume that we have past observations of real traffic situations available. In particular, we assume that we have "daily records" containing the observed travel times in the whole network for a few past days. We introduce a new concept to express a solution that is feasible in any record of a given public transportation network. We adapt the method of Buhmann et al. ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems, G.2.2 Graph Theory (Graph algorithms, Network problems), I.2.6 Learning Keywords and phrases Introduction We study the problem of routing in urban public transportation networks, such as tram and bus networks in large cities, focusing on the omnipresent uncertain situations when (typical) delays occur. In particular, we search for robust routes that allow reliable yet quick passenger transportation. We think of a "dense" tram network in a large city containing many tram lines, where each tram line is a sequence of stops that is served repeatedly during the day, and where there are several options to get from one location to another. Such a network usually does not contain clear hierarchical structure (as opposed to train networks), and each line is served with high frequency. Given two tram stops a and b together with a latest arrival time t A , our goal is to provide a simple yet robust description of how to travel in the

Sustainability in passenger transport: the relevance of punctuality in rail and modal choice in commuting

The overall purpose of this PhD research is the analysis of the sustainable passenger mobility, both on long and short-distance trips. Mobility plays a central role in the social system and it is a key driving force for socio-economic, global and local development, but it produces also negative externalities on the territory. The thesis has the aim to explain the main elements of sustainable mobility from a theoretical point of view and, successively, to apply these concepts to two empirical cases with the use of Italian real data. These empirical analyses can help in underling the importance of sustainable mobility and of the efforts to improve it, influencing the transport modal choices of the commuter journeys. The first case regards the most sustainable mode of transport for medium-long distance trips, the train, and particularly the problem of delay that strongly affects the performance of the train, influencing the modal choices of commuters. The analysis is based on data collected in the period 2013-2016 on the railway line from Milano to Genoa. The second case concerns medium-short trips, focusing on the issue of home-work commuting of a medium Italian university located in two different cities (Varese and Como) in the north of Italy. The data come from a survey performed in November 2017. Finally, the last chapter draws some conclusions and mentions some upcoming evolutions of mobility that could give a strong contribution in achieving sustainability

Sustainability in passenger transport: the relevance of punctuality in rail and modal choice in commuting

The overall purpose of this PhD research is the analysis of the sustainable passenger mobility, both on long and short-distance trips. Mobility plays a central role in the social system and it is a key driving force for socio-economic, global and local development, but it produces also negative externalities on the territory. The thesis has the aim to explain the main elements of sustainable mobility from a theoretical point of view and, successively, to apply these concepts to two empirical cases with the use of Italian real data. These empirical analyses can help in underling the importance of sustainable mobility and of the efforts to improve it, influencing the transport modal choices of the commuter journeys. The first case regards the most sustainable mode of transport for medium-long distance trips, the train, and particularly the problem of delay that strongly affects the performance of the train, influencing the modal choices of commuters. The analysis is based on data collected in the period 2013-2016 on the railway line from Milano to Genoa. The second case concerns medium-short trips, focusing on the issue of home-work commuting of a medium Italian university located in two different cities (Varese and Como) in the north of Italy. The data come from a survey performed in November 2017. Finally, the last chapter draws some conclusions and mentions some upcoming evolutions of mobility that could give a strong contribution in achieving sustainability

Algorithm Engineering for Realistic Journey Planning in Transportation Networks

Diese Dissertation beschäftigt sich mit der Routenplanung in Transportnetzen. Es werden neue, effiziente algorithmische Ansätze zur Berechnung optimaler Verbindungen in öffentlichen Verkehrsnetzen, Straßennetzen und multimodalen Netzen, die verschiedene Transportmodi miteinander verknüpfen, eingeführt. Im Fokus der Arbeit steht dabei die Praktikabilität der Ansätze, was durch eine ausführliche experimentelle Evaluation belegt wird