Abstract
In this investigation, we consider an M/G/1 queue with general retrial times allowing balking and server subject to breakdowns and repairs. In addition, the customer whose service is interrupted can stay at the server waiting for repair or leave and return while the server is being repaired. The server is not allowed to begin service on other customers until the current customer has completed service, even if current customer is temporarily absent. This model has a potential application in various fields, such as in the cognitive radio network and the manufacturing systems, etc. The methodology is strongly based on the general theory of stochastic orders. Particularly, we derive insensitive bounds for the stationary distribution of the embedded Markov chain of the considered system.
Highlights
The study on queueing models have become an indispensable area due to its wide applicability in real life situations
(a) F is New Better than Used in Expectation (NBUE) iff F ⩽v F ∗, (b) F is New Worse than Used in Expectation (NWUE) iff F ∗ ⩽v F, (c) F is of class L iff F ⩾L F ∗, where F ∗ is the exponential distribution function with the same mean as F
The service time distribution B(x) and the repair time distribution C(x) are NBUE and the retrial time distribution is of class L, {πn} ⩽v {πn∗ }, where {πn∗ } is the stationary distribution in the Markovian retrial queue with the same parameters
Summary
The study on queueing models have become an indispensable area due to its wide applicability in real life situations. Even the Laplace transform or probability generating functions are not available in explicit forms To overcome these difficulties, approximation methods are often used to obtain quantitative and/or qualitative estimates for certain performance measures. The general idea of this method is to bound a complex system with a new system that is simpler to solve providing qualitative bounds for these performance measures These methods represent one of the main research activities in various scientific fields, such as economy, biology, operation research, reliability theory, decision theory, retrial queues and queueing networks [4]–[15]. Stochastic comparison analysis of an M /G/1 queue with server subject to breakdowns, general service times and non-exponential retrial time distributions by considering the both balking and reneging behavior of the customer is presented.
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