Abstract
This article studies an M/G/1 retrial queue with two types of breakdowns. When the server is idle, it is subject to breakdowns according to a Poisson process with rate δ and it cannot be repaired immediately. While when the server is busy, it may break down according to a Poisson process with rate θ and can be immediately repaired. Firstly, based on embedded Markov chain technique and probability generating function (PGF) method, we present the necessary and sufficient condition for the system to be stable and the PGF of the orbit size at the departure epochs. Secondly, we give the steady-state joint queue length distribution by supplementary variable method, and present some important performance measures and reliability indices. Thirdly, we provide the analysis of sojourn time of an arbitrary customer in the system when the system is in stable state. Finally, some numerical examples are presented to illustrate the effect of the some system parameters on important performance measures and reliability indices.
Highlights
Retrial queues with unreliable servers have been investigated extensively, due to their applications in various fields, such as telephone switching systems, call centers, computer communication and telecommunication networks, manufacturing systems etc
Choudhury and Ke [7], [8], respectively, studied a batch arrival and a single arrival unreliable retrial queue with general retrial times under Bernoulli vacation schedule, in which the server is subject to active breakdown and delaying repair, i.e., when the server’s failure occurs, it can begin its repair after some delaying time
In this article, we have conducted an exhaustive study on an unreliable M/G/1 retrial queue with two-type breakdowns: one is passive failures with delayed repairs, the other is active breakdowns with immediately repair
Summary
Retrial queues with unreliable servers have been investigated extensively, due to their applications in various fields, such as telephone switching systems, call centers, computer communication and telecommunication networks, manufacturing systems etc. Choudhury and Ke [7], [8], respectively, studied a batch arrival and a single arrival unreliable retrial queue with general retrial times under Bernoulli vacation schedule, in which the server is subject to active breakdown and delaying repair, i.e., when the server’s failure occurs, it can begin its repair after some delaying time. For such retrial queues, the authors obtained some important performance measures and reliability indices.
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