For over a century, the railway system has been gradually designed and adapted to serve the corresponding demands under variations of given budgets. However, recent developments indicate that the railway systems of many European countries gradually come to their limits, as the national infrastructure managers declare an increasing share of their network tracks as congested. Consequently, the capabilities of each railway system are getting more into focus, to adequately serve the recent intention of shifting more demand to rail to encounter climate change. The system’s capacity is thereby of particular interest, i. e. whether the system already has the ability to serve increasing traffic loads by leveraging existing reserves, or otherwise needs significant extensions to serve the increasing demand. We thus need to quantify the current capacity of the railway system to identify its current capabilities and to deduct corresponding measures to leverage capacity reserves and relieve saturated network parts. Only the appropriate measure selection, i.e. deciding where to apply traffic reorganization and optimization or infrastructural extensions and restructuring, allows to achieve the goal of shifting more demand to rail under limited resource constraints. The main contributions of this thesis are in the design, optimization and application of a network capacity assessment approach for large-scale railway networks, which incorporates the perspectives of infrastructure, operations and demand by using the number of trains per time window and scheduled waiting times as capacity metric. Hence, this thesis provides a new definition of network capacity, and develops petri net (PN)-based capacity assessment models for railway networks with the use of mixed integer program (MIP) and row generation. The capacity is then determined by assessing the maximum utilization and the scheduled waiting times of the railway network with respect to infrastructure, railway operations and demand. We first introduce the definition of railway network capacity, which extends the concept of railway capacity from stations and corridors to entire networks. This new utilization-based and demand-centric definition of practical railway network capacity defines railway network capacity as the maximum number of departing trains in the network over a given time period, regarding the given infrastructure, operations and demand. This definition allows to accurately determine the interplay of infrastructure, operations and demand, with a combined measure of traffic flow and scheduled waiting times. In the context of this new definition on network capacity, different assessment approaches for the capacity of railway stations, corridors and networks are reviewed with regard to their spatial scope, the used approach and the applied capacity metric. Second we propose the railway network utilization model (RNUM), which extends an existing PN based approach from single line to entire network operations. This model builds upon individual lines, which are then connected to more complex structures. The analysis of the maximum utilization is based on the network’s elementary circuits. Furthermore, token modifications are introduced to characterize relevant process circuits and introduce interline separation places to model and assess complex networks. By additionally considering rolling stock circulations and imposed train orders, the utilization is determined for given operation scenarios of a line system, which operates at heterogeneous frequencies. The resulting timetable independent approach allows to fully characterize the utilization of the network. To assess the network capacity, an enumeration-based railway network capacity (RNC) framework is further introduced, which evaluates the maximum utilization over diverse operation scenarios to represent possible network demands. The resulting train flows as well as the average scheduled waiting times per train, the capacity and the corresponding network effects were finally quantified and determined in network-specific macroscopic fundamental diagram for the railway network (MFD-R). Third, we introduce the railway network utilization MIP model (MIP-RNUM) to determine the optimal capacity utilization by combining PNs with mathematical linear programming. The presented model is enabled to simultaneously assess different train locations and line orders to provide the network’s utilization, capacity-optimal train locations and line orders for given operation scenarios. The MIP-RNUM is further improved to provide the demand-centered capacity utilization, by incorporating extended demand structures, which capture the demanded flows and magnitudes as fixed proportions of trains per line. The additional incorporation of local routing and thus optimal line orders in the utilization assessment, extend the model further to provide the optimal and demand-centered capacity utilization without the correspondingly required enumeration of different line orders. The resulting fully extended MIP-RNUM comprehensively captures the interplay of infrastructure, railway operations and demand; and the resulting effects on the network capacity. Fourth, we propose the row generation MIP-RNUM (MIP-RNUM-RG) to assess the capacity of large-scale instances. The proposed approach tackles the computationally intensive enumeration of the network’s cycles of the RNUM by applying lazy-constraint generation i.e. iteratively adding violated constraints of previous solutions to the problem in a row generating manner. To assess the solution quality of intermediate solutions during the capacity assessment of large instances, a lower-bound method is presented, which combines a higher order max-plus system and a binary search algorithm. The lower-bound method allows to check the feasibility of a given solution and to quantify the optimality gap of the current results while solving the MIP-RNUM-RG. In summary, this thesis provides multiple scientific contributions to efficiently assess the capacity of complex railway networks by developing several assessment models and frameworks. By integrating the different perspectives of infrastructure, operations and demand, this thesis supports network design towards the development of demand-centric railway systems. Regarding the intended growth of the railway demand in the near future, this thesis can guide practitioners to assess the capabilities of our present railway systems and derive the necessary actions to transform them into the transport systems of our future.