On the Distributions of the State Sizes of the Closed Discrete-Time Homogeneous Markov System with Finite State Capacities (HMS/c)

2011, v.17, №1, 91-118

ABSTRACT

The evolution of the discrete-time Homogeneous Markov System with finite state size capacities (HMS/c) is studied. In order to examine the variability of the state sizes, recursive formulae for their factorial and mixed factorial moments are derived in matrix form and then the moments are computed at every time point. Also a recursive formula is provided concerning the moments of the number of the members who overflow because of the finite state size capacities. The p.m.f.'s of the state and overflow sizes follow directly by means of the moments.

Keywords: discrete-time homogeneous Markov models,Markov systems,stochastic population systems