A Markovian Queue With Feedback and Second Optional Working Vacation

A Markovian queue with feedback and second optional working vacation is analysed in this study. Rather of fully suspending service during a vacation, the server operates with varying service times. After the completion of the regular working vacation, the server may opt for second optional working vacation. After getting the service the customer who is unsatisfied with incomplete, partial or unsatisfactory service may opt the feedback with probability r<overline> or leave the system with the probability r. We use the matrix-geometric approach to find the essential and acceptable conditions for the system to be secure. After deriving the stationary probability distribution, various performance indicators are calculated. Some numerical examples are illustrated to show the model's stability.