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The Power-Series Algorithm for a Wide Class of Markov Processes
van den Hout,W.B. Blanc,J.P.C.
van den Hout,W.B.
Blanc,J.P.C.
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.
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1994
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Unknown Publisher
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87.pdf
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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.