Single Server Retrial Queuing System with Reneging, Feedback and Balking Customers

In this paper, we examine the single server retrial queuing system with reneging, feedback and balking customers. Arrival follows Poisson Processes and services are exponentially distributed. The customer enters the service channel while the server is idle. The customer leaves when the server is busy and returns to orbit to attempt their request again. Reneging occurs when customers abandon a queue due to prolonged wait or dissatisfaction. Customer who does not enter the queue because of queue length is balking. The dissatisfied customer again enters into the queue to a successful service until they get satisfied is feedback. When the server is idle, the server begins its vacation. Consider the Stochastic Processes {(S(t),N(t)): t ≥ 0} and derived the Probability vectors using Matrix Geometric Method. Performance measures such as Probability that the server is idle, Probability that the arriving customer enter into the retrial orbit, Probability that the customer arriving the system during busy period, Probability that the server is in vacation after serving all the customer and Probability that the total number of customers present in the system are derived by varying values for particular parameter. Some numerical tables and graphical representations are also obtained.