Affiliation:
1. Service Innovation Research Institute, Annankatu 8 A, 00120 Helsinki, Finland
Abstract
We consider an irreducible positive-recurrent discrete-time Markov process on the state space X=ℤ+M×J, where ℤ+ is the set of non-negative integers and J={1,2,…,n}. The number of states in J may be either finite or infinite. We assume that the process is a homogeneous quasi-birth-and-death process (QBD). It means that the one-step transition probability between non-boundary states (k,i) and (n,j) may depend on i,j, and n−k but not on the specific values of k and n. It is shown that the stationary probability vector of the process is expressed through square matrices of order n, which are the minimal non-negative solutions to nonlinear matrix equations.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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