Performance analysis of a discrete-time Geo/G/1 retrial queue under <i>J</i>-vacation policy

Abstract

We have investigated a discrete-time Geo/G/1 retrial queue under J vacation policy and general retrial times, which can be applicable to many digital systems, viz. broadband integrated services digital network (B-ISDN), asynchronous transfer mode (ATM) and circuit-switched time-division multiple access (TDMA) systems. In discrete-time systems, we consider time to be a discrete random variable and measure it in fixed size data units, such as machine cycle time, bits, bytes, packets, etc. The server follows J vacation policy according to which as soon as the retrial orbit becomes empty and no new customer arrives then the server may take at most J number of repeated vacations. The server immediately returns from the vacation if at least one customer arrives in the system. The inter arrival time is assumed to be geometrically distributed whereas retrial time, service time and vacation time are assumed to be generally distributed in the discrete environment. The underlying Markov process is analysed by using generating function method whereby we obtain various performance measures of interest. We provide stochastic decomposition laws for the system size of the developed model.