Combined M/G/1-G/M/1 Type Structured Chains: A Simple Algorithmic Solution and Applications

| In this paper, we consider combined M/G/1-G/M/1 type Markov chains with block-structured transition. It is assumed that all the blocks are generated with rational generating matrices. We provide an algorithmic approach to nd the stationary probability distribution based on well-known concepts in linear system theory. These chains arise in the (correlated) G/G/1 queueing systems and known structured Markov chains such as canonical and non-canonical M/G/1 and G/M/1 types which frequently arising in teletraac analysis of computer and communications networks are special cases. We provide a truncation-free algorithmic solution in simple geometric form of the the stationary probability vector of the chain taking full advantage of the rational generating matrices.