GENERAL DECREMENTING SERVICE POLICY IN THE GEOM/G/1 QUEUEING MODEL WITH MULTIPLE ADAPTIVE VACATIONS AND SETUP TIME

This paper analyses a discrete-time Geom/G/1 queue in which the server follows a general decrementing (GD) service rule, takes multiple adaptive vacations (MAV) whenever a service period ends, and needs a setup time before service is resumed. By means of an embedded Markov chain observed at vacation completion instants, combined with a regenerative-cycle argument, the probability generating functions (PGFs) of the stationary number of customers and of the stationary waiting time are derived, and each of them is shown to decompose stochastically into independent components. By specialising the parameters H and K, several classical vacation schemes are recovered as particular cases of the present policy. Numerical experiments then compare the expected number of customers and the expected waiting time across these particular cases. Setup time is added in general decrementing service policy to find the various characteristics.