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A stable recursion for the steady state vector in Markov chains of M/G/1 type. (English) Zbl 0646.60098
An algorithm to compute the steady state probability vector for the matrix analogues of Markov chains of the M/G/1 type is presented. It is a stable recursive scheme involving only nonnegative quantities. An essential constituent of the computational scheme is the minimal nonnegative solution of a nonlinear matrix equation. For the computation of the starting vector of the recursive scheme a method originally developed in the context of Markov renewal branching processes is recommended.
Reviewer: H.Schellhaas

MSC:
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
60K15 Markov renewal processes, semi-Markov processes
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