An M=G=1 retrial G-queue with preemptive resume and feedback under N-policy subject to the server breakdowns and repairs

An M=G=1 retrial G-queue with preemptive resume and feedback under N-policy vacation subject to the server breakdowns and repairs, is investigated in this paper. Arrivals of both positive customers and negative customers are two independent Poisson processes, and positive customers receive service immediately if the server is free upon their arrivals. Otherwise, they may enter a retrial orbit and try their luck after a random time interval. All positive customers must receive preliminary first phase of service and primary second phase of service. While at the preliminary service, the server may push out the customer undergoing such service to the orbit, to commence preliminary service of an arriving positive customer. Negative customers not only remove the customer being in service, but also make the server under repair. The server leaves for an N-policy vacation as soon as the system empties. By applying the supplementary variables method, we obtain the steady- state solutions for both queueing measures and reliability quantities. The effects of various parameters on the system performance are analyzed numerically.