M/G/1 Vacation Queueing System with Negative Customers and Bernoulli Feedback

An M/G/1 queueing system with negative customers and Bernoulli feedback was studied.Just after completion of his service,a positive customer may leave the system with probability θ(0θ≤1),or feedback with probability 1-θ.Negative customers remove positive customers at the head of the queue who is being serviced.By using supplemental variable method and state transfer analysis,the main queueing indexes,the steady-state probability generating function and the result of stochastic decomposition in the system are obtained.