Open AccessBounds of the stationary distribution in M/G/1 retrial queue with two-way communication and n types of outgoing calls
Author(s) -
Lala Alem Maghnia,
Mohamed Boualem,
Djamil Aı̈ssani
Publication year - 2019
Publication title -
yugoslav journal of operations research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.221
H-Index - 21
eISSN - 1820-743X
pISSN - 0354-0243
DOI - 10.2298/yjor180715012a
Subject(s) - retrial queue , markov chain , queue , stationary distribution , computer science , mathematics , distribution (mathematics) , regular polygon , operator (biology) , mathematical optimization , monotonic function , discrete mathematics , queueing system , statistics , mathematical analysis , computer network , biochemistry , chemistry , geometry , repressor , transcription factor , gene
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.