Computing the supplementary times and the number of required trains in operation plan studies under stochastic perturbations

In the urban railway systems, the perturbations during passing stations and block sections as well as shunting operations result in some delays for trains and in the case that the delays are not absorbed by the assigned buffer intervals, and supplementary times, the delays could be propagated in the system. In this paper the methods to compute the delays are reviewed and applied in urban railway systems, An algorithm to compute the required buffer intervals based on the headway, and the required supplementary times to reach a safe and reliable system is presented. Moreover, the relation between supplementary times, perturbations, and the number of required trains to reach the advised headway, are discussed. Finally, the Karaj Metro Line 2 is considered and analyzed as the case study.