Optimizing periodic stability in railway timetables: A microscopic model for networks with a macroscopic comparison

We present a novel microscopic model for railway timetabling designed to maximize periodic stability in mixed single- and multi-track networks. Unlike conventional approaches based on the Periodic Event Scheduling Problem (PESP), our model provides a detailed infrastructure representation with flexible routing and nuanced conflict resolution, enhancing adaptability to real-world constraints and facilitating practical implementation by operators. To ensure scalability, we integrate a Satisfiability Modulo Theories (SMT)-based approach, which efficiently narrows feasible cycle time bounds, enabling the model to handle large-scale networks. Validated on operational data from the Rhätische Bahn network—a Swiss railway with complex infrastructure—the microscopic model consistently yields lower minimal cycle times than its macroscopic counterpart. The comparative analysis also offers insights into the trade-offs between model detail, computational efficiency, and achievable cycle times across diverse operational scenarios. These findings underscore the importance of infrastructure abstraction and the careful consideration of operational and commercial interdependencies for optimal stability in complex railway networks.