An M/G/1 retrial G-queue with preemptive resume priority and collisions subject to the server breakdowns and delayed repairs

Abstract

We consider an M/G/1 retrial G-queue with preemptive resume priority and collisions under linear retrial policy subject to the server breakdowns and delayed repairs. A breakdown at the busy server is represented by the arrival of a negative customer which causes the customer being in service to be lost. The stability condition of the system is derived. Using generating function technique, the steady-state distributions of the server state and the number of customers in the orbit are obtained along with some interesting and important performance measures. The stochastic decomposition property is investigated. Further, some special cases of interest are discussed. Finally, numerical illustrations are provided.