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.

Author Biographies

Mohamed Boualem, University of Bejaia

Mohamed BOUALEM: Professor of Mathematics at the Department of Technology at the University of Bejaïa, Algeria. He received his Master’s degree in Stochastic Methods of Operational Research from the University of Sciences and Technology Houari Boumediene, USTHB in 2003. He received a Doctorate in Applied Mathematics from University of Béjaia in 2009 and from the same university in 2012 his University Habilitation (HDR) in Mathematics. He is a permanent researcher at the LAMOS Laboratory (Modeling and Optimization of Systems). His main current research interests include queueing theory, retrial queues, performance evaluation, reliability theory, stochastic orders, monotonicity, ageing distributions and Statistics. He has already published several scientific papers on these research topics.

Djamil Aissani, University of Bejaia

I am a Professor of Mathematics at the Department of Operations Research at the University of Bejaia, Algeria. I started my career at the University of Constantine in 1978. I received my Ph.D. in 1983 from Kiev State University (Soviet Union). I am at the University of Bejaia since its opening in 1983/1984. Director of Research, Head of the Faculty of Sciences and Engineering Sciences (1999 - 2000), Director of the LAMOS Laboratory (Laboratory of Modelling and Optimization of Systems), Scientific Head of the Computer Science Doctorate School. I have taught in many universities (USTHB Algiers, Annaba, Rouen, Dijon, ENITA). I have published many papers on Markov chains, queueing systems, reliability theory, performance evaluation and their applications in electrical and telecommunication networks and computer systems.

Published
2019-05-13
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: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/651>. Date accessed: 26 dec. 2024.
Citation Formats
Issue
Vol 29 No 3 (2019)
Section
Articles
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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