study priority queueing system consisting of working breakdown, repair, single vacation and vacation interruption. At a breakdown instant during the busy period, without stop the servie, the server provides service at slower rate for the current customer. After completion of priority service, depending on the environment, the server can choose type I or type II vacation. Both types of vacation are considered as a single vacation. On completion of type I vacation if the server finds thepriority queue is empty, he has the option to take type II vacation. During the type II vacation, when priority customers arrive the server has the option to interrupt the vacation. We use the established norm which is the corresponding steady state results for time dependent probability generating functions are obtained. Along with that, the expected waiting time for theexpected number of customers for both high and low priority queues are computed. Numerical results along with the graphical representations are shown elaborately
