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Steady-state analysis of a multiclass MAP/PH/c queue with acyclic PH retrials

Part of: Markov processes Computer system organization

Published online by Cambridge University Press:  09 December 2016

Tuǧrul Dayar  and
M. Can Orhan
Tuǧrul Dayar*
Affiliation:
Bilkent University
M. Can Orhan*
Affiliation:
Bilkent University
*
* Postal address: Department of Computer Engineering, Bilkent University, TR‒06800 Bilkent, Ankara, Turkey.
* Postal address: Department of Computer Engineering, Bilkent University, TR‒06800 Bilkent, Ankara, Turkey.
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Abstract

A multiclass c-server retrial queueing system in which customers arrive according to a class-dependent Markovian arrival process (MAP) is considered. Service and retrial times follow class-dependent phase-type (PH) distributions with the further assumption that PH distributions of retrial times are acyclic. A necessary and sufficient condition for ergodicity is obtained from criteria based on drifts. The infinite state space of the model is truncated with an appropriately chosen Lyapunov function. The truncated model is described as a multidimensional Markov chain, and a Kronecker representation of its generator matrix is numerically analyzed.

Keywords

Markovian arrival processphase-type service time distributionacyclic phase-type retrial time distributionKronecker productMarkov chain

MSC classification

Primary: 60J22: Computational methods in Markov chains
Secondary: 60J28: Applications of continuous-time Markov processes on discrete state spaces 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 4 , December 2016 , pp. 1098 - 1110
Copyright
Copyright © Applied Probability Trust 2016 

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