.m/g/1 Type Bernoulli Reduction With Multiple Adaptive Vacation Queuing

An M/G/1 type queue with Adaptive multi-level vacation and Bernoulli-decreased service is studied in this paper, which belongs to nonexhaustive service queue systems with vacation. To date, various nonexhaustive service queue systems with vacation have been widely concerned, but the M/G/1 type queue with Adaptive multi-level vacation and Bernoulli-decreased service system has not been seen in the open literatures.Firstly, the probability generating function Q_b (z) of the customers Q_b of the system on the steady state is obtained with embedded Markov chain method when the period of service begins. And then the structure-analysis method is offered to get the stochastic decomposition of the queue length with the probability generating function and the waiting time with Laplace-Stieltijes transforms, besides the formulas which the average queue length and the average waiting time satisfy are given. At the same time, the condition that the system is going to a steady state with its probability meaning is also acquired. The service cycle period is further analysed, and the probability of service time, vocation time and idle time of the system on the steady state in any time have been got. Finally, a few special cases of the model are confirmed.