Analysis of multistage M[X]/GK/1 queue with different server's interruptions and its application in energy consumption

In this paper, we consider multistage batch arrival, batch service (fixed batch size) queue having multiple vacation policy subject to server breakdown with the delayed repair. In addition, the server may extend the vacation at each vacation completion points and the server may renege during vacation and breakdown periods. Using the supplementary variable technique, transient and its corresponding steady-state solutions are derived. The results obtained are comprehended by using a numerical example.