The Single Queuing Systems With Negative Customer And Bernoulli Feedback

The paper researches three kinds of queue model.Firstly,an M/M/1 multiple vacations with Bernoulli feedback with vacation time is Phase Type is studied.Using Matrix-geometric solution method,we get the number of customers waiting in the queue and waiting time as well as their expectation in the stable state.Secondly,an M/G/1 feedback queuing systems with negative customers under multiple vacation policy is studied. Using supplemental variables method,state transfer analyses and Laplace method,we get the generating function of queue.Finally,an M/G/1 retrial queuing system with two phases of services feedback and starting failure is studied.Using supplemental variables method,Markov chain,the steady-state distributions of the number of customers in the system and the orbit are obtained along with other performance measures.