Geodesic
Bounds of the Stationary Distribution in M/G/1 Retrial Queue With Two-Way Communication and $n$ Types of Outgoing Calls
Yugoslav journal of operations research, Tome 29 (2019) no. 3, p. 375 .

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In this article we analyze the M/G/1 retrial queue with two-way communication and n types of outgoing calls from a stochastic comparison viewpoint. The main idea is that given a complex Markov chain that 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 study the 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 departure epochs. Additionally, the performance measures of the considered system can be estimated by those of an M/M/1 retrial queue with two-way communication and $n$ types of outgoing calls when the service time distribution is NBUE (respectively, NWUE). Finally, we test numerically the accuracy of the proposed bounds.
Classification : 60K25, 60E15, 60K10
Keywords: Retrial Queues, Outgoing Calls, Markov Chain, Stochastic Comparison, Simulation. 
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     author = {Lala Maghnia Alem and Mohamed Boualem and Djamil Aissani},
     title = {Bounds of the {Stationary} {Distribution} in {M/G/1} {Retrial} {Queue} {With} {Two-Way} {Communication} and $n$ {Types} of {Outgoing} {Calls}},
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Lala Maghnia Alem; Mohamed Boualem; Djamil Aissani. Bounds of the Stationary Distribution in M/G/1 Retrial Queue With Two-Way Communication and $n$ Types of Outgoing Calls. Yugoslav journal of operations research, Tome 29 (2019) no. 3, p. 375 . http://geodesic.mathdoc.fr/item/YJOR_2019_29_3_a5/