Step semi-Markov models and application to manpower management

The purpose of this paper is to introduce a class of stochastic processes that we call step semi-Markov processes and to illustrate the modelling capacity of such processes in practical applications. The name of this process comes from the fact that we have a semi-Markov process and the transition between two states is done through several steps. We first introduce these models and the main quantities that characterize them. Then, we derive the recursive evolution equations for two-step semi-Markov processes. The interest of using this type of model is illustrated by means of an application in manpower planning.