Queuing Systems With Negative Customers And Bernoulli Feedback And Working Vacations

Queuing system with working vacations is an emerging research hotspot in queuing system in recent years.At the same time,literatures regarding queuing models incorporating negative customers are extensively discussed by researchers worldwide.In addition,feedback is another feature which has been widely studied in queuing system.In this paper,we study queuing systems taking together the above mentioned features.The organization of the paper is as follows:Firstly,an M/M/1 queuing system with RCE strategy of negative customers and working vacations and is studied.Using QBD and Matrix-geometric solution,we gain the steady-state distributions for the number of customers in the system,point out the result of stochastic decomposition of the queue length and obtain mean of the system size of positive customers and waiting time.Secondly,an M/M/1 Bernoulli feedback queue with negative customers and working vacations is studied.Using QBD(quasi birth and death) process and Matrix-geometric solution,we derive the steady-state distributions for the number of customers in the system and prove the result of stochastic decomposition of the queue length and gain mean of the system size of positive customers.Finally,a GI/M/1 queuing system with RCE strategy of negative customers and working vacations is studied.By adding supplementary variable,a new vector Markov process is obtained.Using Matrix-Geometric solution,we obtain the steady-state distributions for the number of customers in the system both at arrival and arbitrary epochs,and a generalization is made in the end.