Analysis of Preemptive Priority Retrial Queueing System with Starting Failure, Modified Bernoulli Vacation with Vacation Interruption, Repair, Immediate Feedback and Impatient Customers

Abstract

This paper considers $M^{[X_{1} ]} ,M^{[X_{2} ]} /G_{1} ,G_{2} /1$ general retrial queueing system with priority services. The server serves two types of customers and follows the pre-emptive priority rule subject to starting failure, repair, immediate feedback, orbital search and modified Bernoulli vacation with vacation interruption. High priority customes are considered as a feedback customer. After vacation completion, service completion and repair completion if there is no high priority customers present in the system the server may go for orbital search or remains idle. The high priority customer may renege the queue and the low priority customers may balk the orbit. Retrial time, service times, repair time and vacation time are assumed to be arbitrarily distributed. Various performance measures are derived and numerical results are presented. Using the supplementary variable technique, the steady-state distributions of the server state and the number of customers in the orbit are obtained. Further, some particular cases of interest are discussed. Finally, numerical illustrations are provided.