Open AccessThe convergense rate of stationary distribution of retrial queueing system with queue
Author(s) -
I. Ya.,
I. A. Makushenko,
Iu. O. Protopop
Publication year - 2019
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2019/3.7
Subject(s) - mathematics , stationary distribution , markov chain , state space , queue , markov process , queueing theory , computer science , mathematical optimization , statistics , programming language
This paper describes a steady state behavior of the retrial system in the case of one server, one place in the queue and an infinity orbit. We research Markov`s models of retrial systems and variable rate of input flow controlled by threshold strategy. We defined stationary regime existence conditions and investigated probability characteristics of process for two-dimension Markov process with continuous time which we took as a main model of the specified system. In stationary regime for probability characteristics of the service process were found explicit formulas. Research methods which we used are based on the initial process approximation by the process with bounded state space. Results of the research allow us to evaluate convergence rates of stationary distribution of finite systems with repeated calls to stationary distribution of infinite systems. Method of probability flow equating is used for obtain explicit expressions for stationary system probabilities through the closed path which are defined in a special way. We considered model for one service devices and one place in the queue, which are controlled by threshold strategies.