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Probability in the Engineering and Informational Sciences Probability in the Engineering and Informational Sciences

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THE M/G/1-TYPE MARKOV CHAIN WITH RESTRICTED TRANSITIONS AND ITS APPLICATION TO QUEUES WITH BATCH ARRIVALS

Published online by Cambridge University Press:  21 July 2011

Juan F. Pérez  and
Benny Van Houdt
Juan F. Pérez
Affiliation:
Performance Analysis of Telecommunication Systems (PATS), Department of Mathematics and Computer Science, University of Antwerp – IBBT, Middelheimlaan 1, B-2020 Antwerp, Belgium E-mail: juanfernando.perez@ua.ac.be; benny.vanhoudt@ua.ac.be
Benny Van Houdt
Affiliation:
Performance Analysis of Telecommunication Systems (PATS), Department of Mathematics and Computer Science, University of Antwerp – IBBT, Middelheimlaan 1, B-2020 Antwerp, Belgium E-mail: juanfernando.perez@ua.ac.be; benny.vanhoudt@ua.ac.be
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Abstract

We consider M/G/1-type Markov chains where a transition that decreases the value of the level triggers the phase to a small subset of the phase space. We show how this structure—referred to as restricted downward transitions—can be exploited to speed up the computation of the stationary probability vector of the chain. To this end we define a new M/G/1-type Markov chain with a smaller block size, the G matrix of which is used to find the original chain's G matrix. This approach is then used to analyze the BMAP/PH/1 queue and the BMAP[2]/PH[2]/1 preemptive priority queue, yielding significant reductions in computation time.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 4 , October 2011 , pp. 487 - 517
Copyright
Copyright © Cambridge University Press 2011

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THE M/G/1-TYPE MARKOV CHAIN WITH RESTRICTED TRANSITIONS AND ITS APPLICATION TO QUEUES WITH BATCH ARRIVALS
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