Modelling periodic operations on single track lines: Timetable design and stability evaluation

The paper analyses the application of high-frequency periodic timetables on single track railways. A mesoscopic approach is first of all presented, in order to provide a simple but rather complete model. On this basis, a mathematical and deterministic evaluation formula is presented, as well as a simulation tool able to evaluate the effects of traffic perturbations. All the main parameters which characterise railway operations (with a special focus on single track infrastructure) are taken into consideration and their influence is pointed out, as regards the possibility to realise high frequency periodic timetables. The analysis is subsequently extended for assessing how these timetables can behave in case of traffic perturbations, in order to provide also in these circumstances a sufficient service quality. The influence of the abovementioned parameters on buffer times and hence on timetable stability and robustness is therefore outlined, highlighting the benefits that an effective rescheduling algorithm could play. The presented calculation method is then applied to a real case, i.e. to a part of the railway network of Piedmont, Italy. This case study provides some considerations about the elements that can actually play a determinant role and what measures can be planned for achieving certain service targets. Finally, conclusions are drawn together with some considerations for future work about the possible implementation of effective rescheduling logics within advanced driver advisory systems as well as modern signalling and control systems.