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 |