General decrementing service M/G/1 queue with multiple adaptive vacations

In this paper, we introduce the multiple adaptive vacation policy and the general decrementing service rule based on the classical M/G/1 queueing systems, and obtain the P.G.F. (Probability Generating Function) of stationary queue length by using the embedded Markov chain method and regeneration cycle approach. Then, the LST (Laplace Stieltjes Transform) of stationary waiting time is also derived according to the independence between the waiting time and arrival process. At last some special cases are given to show the general properties of the new model, and some numerical results are shown to compare the mean queue length and waiting time of special cases.