Performance Analysis of a Discrete-Time Retrial Queue with Bernoulli Feedback, Starting Failure and Single Vacation Policy

Abstract

In this study, we consider an unreliable discrete-time Geo/G/1 retrial queue with Bernoulli feedback. During the idle time, server may leave for a vacation of random length according to which at any time instant, when the system becomes empty and no new customer arrives, the server may leave for a vacation of random length and will immediately return from the vacation if at least one customer arrives in the system. The arrival stream is composed of repeated customers, priority customers, and impatient customers. The service time, retrial time, and vacation time are defined by general distribution. The probability generating function (PGF) method and supplementary variable technique (SVT) are employed to derive expressions for system size, orbit size, and other performance measures. A numerical illustration is provided to validate our results with the real-life systems.