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

Fingerprint

Power series
Markov Process
Steady-state Distribution
Queueing Model
Balance Equations
Ergodicity
Pi
Justification
Queue
Lemma
Non-negative
Generator
Moment
Calculate
Sufficient Conditions
Class
Model

Cite this

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

The Power-Series Algorithm for a Wide Class of Markov Processes. / van den Hout, W.B.; Blanc, J.P.C.

Unknown Publisher, 1994. (CentER Discussion Paper; Vol. 1994-87).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - The Power-Series Algorithm for a Wide Class of Markov Processes

AU - van den Hout, W.B.

AU - Blanc, J.P.C.

PY - 1994

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N2 - 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.

AB - 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.

M3 - Discussion paper

VL - 1994-87

T3 - CentER Discussion Paper

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

PB - Unknown Publisher

ER -

van den Hout WB, Blanc JPC. The Power-Series Algorithm for a Wide Class of Markov Processes. Unknown Publisher. 1994. (CentER Discussion Paper).