M/G/1 Queueing Systems With Negative Customers And Feedback

The paper mainly researches queues with negative customers. The M/G/1 queueing system with negative customers and vacation has been studied by many researchers and many results have been obtained. On the other hand, the queueing system with repairable service station and retrial queues has also been studied by some researchers. But the queueing system combining negative, feedback, repairable service station, retrial queues, vacation and additional service has not been studied. Under this circumstance, we study queuing systems with negative, feedback, repairable service station, retrial queues, vacations and addition service.Firstly, we study a type of M/G/1 queueing system with negative customers and feedback. The necessary and sufficient conditions are given for their stability respectively. 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.Secondly, studies M/G/1 retrial queuing with negative customers feedback,and repairs, The steady state distributions of the number of customers in the system and the orbit, some queueing quantities of the system and the reliability quantities of the server are obtained.Finally, the M/G/1 queueing system with negative customers and additional service, by using supplemental variable method and state transfer analysis, the main queueing indexes and the steady-stateprobability generating function in the system are obtained.