The discrete-time Geom/G/1 queue with multiple adaptive vacations and server Setup/Closedown times

In this paper, we discuss the discrete-time Geom/G/1 queue with multiple adaptive vacations and server setup/closedown times. We consider two types of closedown time policies which differ from each other in the completion instant of the closedown times and contrast the effects of them on the queueing system. We derive the probability generating functions (PGFs) and stochastic decomposition results of the steady-state queue length and waiting time distributions through the method of embedded Markov chain in both cases. Many discussed models related to Geom/G/1 queue are special cases of our model.