<p>Finding optimal train scheduling is one of the most important challenges in railway logistics. Providing a pre-defined timetable is a prevalent response to manage this challenge in many developing countries. Single line track is widely used in these countries where old infrastructures may cause unforeseen delays. Such train delays can affect the fixed timetables and postpone destination arrival times, which bring economical side effects. Delay propagation may influence other trains in both directions of a track. To minimize the total propagated delays in a single-track railway network and maximize its performance, optimal timetabling should be provided. In this paper, we rely on the stochastic nature of train failures and propose a new framework to approximate the expected propagated delays in a railway network for a given timetable. Our approach is to reduce the problem of minimizing the total expected propagated delays to a probabilistic model checking of the corresponding MDP model. We apply the PRISM modeling language to provide a high-level description of a given railway system and apply the PRISM model checker engines to analyze the related problem. To overcome the state and time complexities of computing the problem for complex railway systems we utilize the statistical methods to approximate optimal solutions. Using this framework, we follow two approaches for computing a near-optimal timetable. These approaches include the lightweight smart sampling and genetic algorithm and in both cases statistical model checking is used to analyse the proposed timetable solutions. The north-west part of Iranian railways is considered as an empirical benchmark. The proposed approach reduces the total delays for this case study to less than half.</p>