Bounds of the stationary distribution in M/G/1 retrial queue with two way communication and n types of outgoing calls ation and n type of outgoing call
In this article we analyze the M/G/1 retrial queue with two way communication and n type of outgoing calls from a stochastic comparison viewpoint. The main idea is that given a complex Markov chain which cannot be analyzed numerically, we propose to bound it by a new Markov chain which is easier to solve by using a stochastic comparison approach. Particularly, we analyze the notion of monotonicity of the transition operator of the embedded Markov chain relative to the stochastic and convex orderings. Bounds are also obtained for the stationary distribution of the embedded Markov chain at departures epochs. Additionally, the performance measures of the system considered can be estimated by those of the M/M/1 retrial queue with two way communication when the service time distribution is NBUE (respectively, NWUE). Finally, we test numerically the accuracy of the proposed bounds.
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