An M/G/1 retrial G-queue with optional re-service, impatient customers, multiple working vacations and vacation interruption

In this work, we consider a single server retrial queueing system with multiple working vacations and vacation interruption, where the regular busy server is subjected to breakdown due to the arrival of negative customers. After the completion of regular service the positive customers may demand re‐service of the previous service without joining the orbit or may leave the system. When the orbit becomes empty at service completion instant for a positive customer; the server goes for multiple working vacations. The steady state probability generating function for the system size and orbit size are obtained by using the method of supplementary variable technique. Some important system performance measures and the mean busy period are obtained. The conditional stochastic decomposition law is shown for good for this model. Finally, the effects of various parameters on the system performance are analysed numerically.