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December 2016 Steady-state analysis of a multiclass MAP/PH/c queue with acyclic PH retrials
Tuǧrul Dayar, M. Can Orhan
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J. Appl. Probab. 53(4): 1098-1110 (December 2016).

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.

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Tuǧrul Dayar. M. Can Orhan. "Steady-state analysis of a multiclass MAP/PH/c queue with acyclic PH retrials." J. Appl. Probab. 53 (4) 1098 - 1110, December 2016.

Information

Published: December 2016
First available in Project Euclid: 7 December 2016

zbMATH: 1356.60144
MathSciNet: MR3581244

Subjects:
Primary: 60J22
Secondary: 60J28 , 68M20

Keywords: acyclic phase-type retrial time distribution , Kronecker product , Markov chain , Markovian arrival process , phase-type service time distribution

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 4 • December 2016
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