Gómez-Corral, Antonio and Ramalhoto, M.F.
(1999)
*The stationary distribution of a Markovian process arising in the theory of multiserver retrial queueing systems.*
Mathematical and Computer Modelling, 30
.
pp. 141-158.
ISSN 0895-7177

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Official URL: http://www.sciencedirect.com/science/article/pii/S0895717799001387

## Abstract

In this paper, we introduce a bivariate Markov process {X(t), t greater than or equal to 0} = {(C(t), Q(t)), t greater than or equal to 0} whose state space is a lattice semistrip E = {0, 1, 2, 3} x Z(+). The process {X(t), t greater than or equal to 0} can be seen as the joint process of the number of servers and waiting positions occupied, and the number of customers in orbit of a generalized Markovian multiserver queue with repeated attempts and state dependent intensities. Using a simple approach, we derive closed form expressions for the stationary distribution of {X(t), t greater than or equal to 0} when a sufficient condition is satisfied. The stationary analysis of the M/M/2/2 + 1 and M/M/3/3 queues with linear retrial rates is studied as a particular case in this process.

Item Type: | Article |
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Uncontrolled Keywords: | multiserver queue; repeated attempt; stationary distribution; closed form formulae |

Subjects: | Sciences > Mathematics > Stochastic processes |

ID Code: | 15876 |

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Last Modified: | 08 Mar 2016 16:09 |

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