The Power-Series Algorithm for a Wide Class of Markov Processes

W.B. van den Hout, J.P.C. Blanc

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Abstract

The Power-Series Algorithm has been used to calculate the steady-state distribution of various queueing models with a multi-dimensional birth-and-death structure. In this paper, the method is generalized to a much wider class of Markov processes, including for example very general networks of queues and all kinds of non-queueing models. Also, the theoretical justification of the method is improved by deriving sufficient conditions for the steady-state probabilities and moments to be analytic. To do this, a lemma is derived that ensures ergodicity of a Markov process with generator if the set of balance equations has a solution that satisfies Pii = 1 and Pi ji ii j <1 but that need not be non-negative.
Original languageEnglish
PublisherUnknown Publisher
Volume1994-87
Publication statusPublished - 1994

Publication series

NameCentER Discussion Paper
Volume1994-87

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van den Hout, W. B., & Blanc, J. P. C. (1994). The Power-Series Algorithm for a Wide Class of Markov Processes. (CentER Discussion Paper; Vol. 1994-87). Unknown Publisher.