Abstract
This paper deals with the steady-state behavior of a discrete-time unreliableGeo/G/1retrial queueing system with balking customers and second optional service. The server may break down randomly while serving the customers. If the server breaks down, the server is sent to be repaired immediately. We analyze the Markov chain underlying the considered system and its ergodicity condition. Then, we obtain some performance measures based on the generating functions. Moreover, a stochastic decomposition result of the system size is investigated. Finally, some numerical examples are provided to illustrate the effect of some parameters on main performance measures of the system.
Highlights
During the past few decades, there has been increasing interest in studying retrial queueing systems because they are widely used in performance analysis of many practical systems such as call center, computer systems, and telecommunication networks
The main objective in this paper is to extend the analysis of continuous-time M/G/1 retrial queueing system with second optional service [13], exponential server lifetime [17], and general retrial times to discrete-time case
It is assumed that the lifetimes of the server for the first-phase service (FPS) and secondphase service (SPS) are geometrically distributed with parameters θ1 = 1 − θ1 and θ2 = 1 − θ2, respectively, where θ1 and θ2 are the probability that the failures do not occur in a slot, respectively
Summary
During the past few decades, there has been increasing interest in studying retrial queueing systems because they are widely used in performance analysis of many practical systems such as call center, computer systems, and telecommunication networks. On the other hand, queueing models in which the server may provide a second phase service have been proved very useful to analyze many practical situations, arising in manufacturing systems, call center, and computer systems. The continuous-time retrial queueing systems which take into account servers breakdowns and repairs were discussed by Kulkarni and Choi [16], Wang et al [17, 18], and Li et al [19]. To the best of our knowledge, there is no published work on discrete-time Geo/G/1 retrial queueing system with balking customer, second optional service, and unreliable server. The main objective in this paper is to extend the analysis of continuous-time M/G/1 retrial queueing system with second optional service [13], exponential server lifetime [17], and general retrial times to discrete-time case.
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