With The Start Of The General Reduction Service M/g/1 Single Vacation Queuing System

The paper mainly discusses an M/G/1 type queueing system with set-up period, generally-decreased service and a single vacation. In this article, we put set-up period, vacation and decrement together. The system is alternating in the states of vacation, set-up period and working.An M/G/1 type queueing system with set-up period and a single vacation is briefly introduced. We get the steady queue length with generating function of probability and the waiting time with Laplace-stieitjes transforms. The generally structure of the stochastic decomposition of the M/G/1 type queueing system with set-up period, generally-decreased service and a single vacation is emphatically analyzed. Under the service rule that customers who first come would first get the service, we use the structure analysis method to get the stochastic decomposition of the queue length with the generating function of probability and the steady waiting time with Laplace-stieitjes transforms. Meanwhile, the condition that the system is going to be a steady state with its visual explanation of probabilistic implication. Each performance index of the states when the system is in busy period, vacation and circular server busy period and distributions of the system states are further discussed .