Timetable-based determination of the capacity of railroad networks under consideration of the service quality

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Strategic planning of railway traffic in Europe’s densely operated railway network is developing towards timetable-driven planning approaches, where infrastructure is designed to meet the requirements and to reflect the structure of the network timetable. With shifting planning paradigms, fundamental challenges are arising, which require detailed analysis of the mutual dependencies of timetable and infrastructure. To this end, a new methodology for capacity and infrastructure planning in railway networks is developed that reflects the changing conditions in timetabling and capacity allocation and accounts for temporally and spatially coherent train paths on the network level. The core of the developed methodology is formed by the connection of mathematical optimization and a stochastic (max,+)-approach. While the optimization is used for train scheduling and train-path assignment, the (max,+)-system allows to assess the operational quality associated with a specific timetable. By combining these two components, a macroscopic traffic assignment model is achieved, which allows to assess the infrastructures capabilities to accommodate a specific demand, as well as the number of trains that can be operated at a specific service quality. The assignment model forms the base of the network capacity planning procedure. Based on a microscopic infrastructure, train path segments are constructed. These segments are the spatial building blocks for pre-arranged system train paths, which are the foundation of capacity allocation. The demand structure is transformed into network-based traffic flow relations which are routed on the macroscopic infrastructure using pre-arranged system train paths. A mixed-integer program is used for determining the individual, complete and optimal train paths based on a selection of pre-arranged train paths. As a result, the capacity-optimal path assignment, as well as the residual capacity is determined. Iteratively adjusting pre-arranged system train paths and solving the optimization model for system train path assignment allows for the simultaneous, network-wide determination of capacity-optimal train paths. Service quality and robustness are incorporated using a stochastic (max,+)-approach which allows to model delay propagation and punctuality based on the identification of arrival, departure and train running times in the previous deterministic capacity-optimal solution with random variables. Individual train runs are described in terms of a sequence of activities. The mutual dependencies between trains yield connections between trains, which allows to recursively capture delay propagation between different trains. As a result, the service quality associated with a specific timetable and train demand can be assessed both locally, and on the network level, such that a coherent model for capacity assessment accounting for timetable connections and relating to the service quality is achieved.