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

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Author Info
Hout, W.B. van den
Blanc, J.P.C. (Tilburg University, Center for Economic Research)

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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.

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Publisher Info
Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 87.

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Date of creation: 1994
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Handle: RePEc:dgr:kubcen:199487

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References listed on IDEAS
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  1. van den Hout, W.B. & Blanc, J.P.C., 1993. "The Power-Series Algorithm Extended to the BMAP/PH/1 Queue," Papers 9360, Tilburg - Center for Economic Research.
  2. Blanc, J.P.C. & Van Der Mei, R.D., 1993. "The Power-Series Algorithm Applied to Polling Systems with a Dormant Server," Papers 9346, Tilburg - Center for Economic Research.
  3. Blanc, J.P.C., 1993. "Performance Analysis and Optimization with the Power- Series Algorithm," Papers 9347, Tilburg - Center for Economic Research.
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