ANALYSIS OF PRIORITY QUEUEING SYSTEM WITH WORKING BREAKDOWN, REPAIR, IMMEDIATE FEEDBACK, BALKING, VACATION AND VACATION INTERRUPTION UNDER RANDOM ENVIRONMENT
We examine priority queueing system consisting of working breakdown, repair, immediate feedback, single vacation and vacation interruption. At a breakdown instant during the busy period, the server provides slow rate service for the current customer. After completion of high 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 the high priority queue is empty, it has the option to take type II vacation. During the type II vacation, when high priority customers arrive the server has the option to interrupt the vacation. Whenever the low priority customer arrives, either they join the queue or leave the system forever with some probabilities. However, after completion of each high priority service, if the customer is dissatisfied with the given service, immediately he can get the service again. The stabilized norm for respective steady-state outcomes for time-dependent probability generating functions is used. Also, the average number of customers in the respective queues, as well as the average waiting times, are computed. Numerical results along with the graphical representations are shown elaborately.
batch arrival, priority queue, working breakdown, immediate feedback, random environment, vacation interruption.