Abstract
It is shown that a class of infinite, block-partitioned, stochastic matrices has a matrix-geometric invariant probability vector of the form (x
0, x
1,…), where xk
= x
0
Rk
, for k ≧ 0. The rate matrix R is an irreducible, non-negative matrix of spectral radius less than one. The matrix R is the minimal solution, in the set of non-negative matrices of spectral radius at most one, of a non-linear matrix equation.
Applications to queueing theory are discussed. Detailed explicit and computationally tractable solutions for the GI/PH/1 and the SM/M/1 queue are obtained.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
18 articles.
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