A single-server retrial queue with server vacations and a finite number of input sources

In this paper, we consider a single-server retrial queueing system with no waiting space and finite population of customers. When a customer arrives and the server is idle then, according to a probability distribution, the server either immediately serves the arriving customer or takes a vacation during which it serves no customers. This model is a generalization of a few well known systems including the classical M/G/1 retrial queue and the M/G/1 queue with setup times. Using the method of supplementary variables, we derive formulae for the limiting probability distribution of the system and some major performance measures including system throughput and mean delay. Through a numerical example, we discuss its application to the analysis of a communication protocol.