Title
The M/G/1-type Markov chain with restricted transitions and its application to queues with batch arrivals The M/G/1-type Markov chain with restricted transitions and its application to queues with batch arrivals
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Cambridge, Mass. ,
Subject
Mathematics
Engineering sciences. Technology
Source (journal)
Probability in the engineering and informational sciences. - Cambridge, Mass.
Volume/pages
25(2011) :4 , p. 487-517
ISSN
0269-9648
ISI
000295964300005
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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 structurereferred to as restricted downward transitionscan 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.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/2fa8e8/1136.pdf
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