GI / G /1 type processes

Abstract

A new general solution method is derived for the general GI / G /1 type processes --- for the steady-state distribution of infinite block-structured Markov chains with repetitive structure. While matrix inversion is needed in each iterational step of other general (and of more special) matrix analytical procedures, the method presented here uses matrix addition and matrix multiplication only. In exchange, the computational complexity and the memory requirement is increasing in each iterational step of the proposed method. This paper, however, lays priority on the theoretical aspect of the general solution.