Analysis of an M/G/1 feedback retrial queue with unreliable server, non-persistent customers, single working vacation and vacation interruption

TLDR: A single server feedback retrial queueing system with single working vacation and vacation interruption, using the method of supplementary variable technique, the steady state probability generating function for the system/orbit size is obtained.

Abstract: In this paper, we consider a single server feedback retrial queueing system with single working vacation and vacation interruption. An arriving customer may balk (or renege) the system at some particular times. The single server provides two essential phases of regular service to each customer. When the orbit becomes empty at service completion instant; the server goes for a single working vacation. In working vacation period, the server works in lower service rate. The regular busy server may breakdown at any instance and the service channel will fail for a short interval of time. Using the method of supplementary variable technique, the steady state probability generating function for the system/orbit size is obtained. Some important system performance measures and the mean busy period are obtained. The conditional decomposition law is shown for this retrial queueing system. Finally, the effects of various parameters on the system performance are analysed numerically.