Discrete time multi-class feedback queue with vacations and close-time under random order of service discipline

We study a discrete-time single server priority queueing model with vacations under random order of service discipline within each class. This model captures the behavior of the head-of-line request queues in large input-buffered ATM switches. The server takes vacations when the queue has been empty for a random number of slots. We presume a message consists of a geometrically distributed number of cells. To represent this aspect, we assume that once a message is in turn for service, it is served for a constant time which corresponds to one-cell-time and it rejoins the queue after service with a given probability. We derive the joint probability distribution of the queue length and waiting time through probability generating function approach. Mean waiting times are obtained and their numerical results are shown.