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The stationary distribution of a Markovian process arising in the theory of multiserver retrial queueing systems

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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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
Uncontrolled Keywords:multiserver queue; repeated attempt; stationary distribution; closed form formulae
Subjects:Sciences > Mathematics > Stochastic processes
ID Code:15876
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