M/g/1 Vacation Queue With Feedback System Analysis

In this paper, we discuss the queue system M/G/1 with feedback: A M~X/G/1 queue system with multiple vacation and feedback, the queue system M/G/1 with feedback on the multiple adaptive vacation and set-up times. The queue systems of M/G/1 have been studied by many researchers and a lot of results have been obtained. These are two new vacations queue models and have a good value of practical application.In the first queue model, we study the queue system by the method of embedded Markov chain. The generating function of queue length in the steady state and Laplace-Stieltjes transform of busy period are obtained. We also get the mean of the busy circulation. At last, the probability which the server is in various states in the steady-state situation is given. In the second model, the generator matrix of Markov process is given. We get the generating function of steady state queue length and the Laplace-Stieltjes transform of busy period. Finally we consider the several special models.