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

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Abstract

In this paper, we introduce a bivariate Markov process {X(t), t ≥ 0} = {(C(t), Q(t)), t ≥ 0} whose state space is a lattice semistrip E = {0, 1,2,3} x Z+. The process {X(t), t ≥ 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 ≥ 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.

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Gómez-Corral, A., & 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(3–4), 141–158. https://doi.org/10.1016/S0895-7177(99)00138-7

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