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

  • Lala Maghnia Alem University of Bejaia
  • Mohamed Boualem University of Bejaia
  • Djamil Aissani University of Bejaia

Abstract

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.

Published
May 13, 2019
How to Cite
ALEM, Lala Maghnia; BOUALEM, Mohamed; AISSANI, Djamil. 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. Yugoslav Journal of Operations Research, [S.l.], v. 29, n. 3, p. 375-391, may 2019. ISSN 2334-6043. Available at: <http://yujor.fon.bg.ac.rs/index.php/yujor/article/view/651>. Date accessed: 26 feb. 2021.
Section
Articles