Asymptotic variability of nonhomogeneous Markov systems under cyclic behaviour (Q1081965)

A finite-state, time-discrete nonhomogeneous Markov system is considered. A special pattern of nonhomogeneity is assumed, namely cyclic behavior of the transition, recruiting, and leaving probability distributions. In manpower planning, one often has such a situation. The paper investigates the asymptotic behavior of expectations, variances, and covariances of the state sizes. It is found that the sequence of state sizes has d subsequences which converge where d is the period of the cycle. A numerical example finally illustrates the mathematics.