Cyclic Strong Ergodicity in Nonhomogeneous Markov Systems

This paper investigates the ergodic behaviour of the vector of means and the covariance matrix of the grade sizes for a nonhomogeneous Markov system that undergoes a cyclic behaviour, both in discrete and continuous time. It is shown that the first and second central moments converge to a cyclic family of multinomial type with the same period, independently of the initial distribution. The regions of cyclically ergodic distributions are determined as convex hulls of certain points as the recruitment distribution varies. The rate of convergence to the cyclic distribution is also examined, together with some transient aspects of the system concerning stability and quasi stationarity. Two numerical examples from the literature on manpower planning illustrate the theory.