Analysis of two-class discrete packet queues with homogenous arrivals and prioritized service

In this article we analyze the system occupancy of a discrete time queue of packets, where each packet is either of class-1 or of class-2, with class-1 receiving higher service priority than class-2. Such a queue is naturally formed in many computer and digital communications systems, e.g. multiuser computers, multiprocessing computers, file servers, ATM multiplexers, and ATM switches, when the packet sources are multimedia applications. The analysis considers both priority disci- plines, nonpreemptive and preemptive, and identifies the relation between them. It demonstrates mathematically the intuitive fact that when service time is deterministically 1 slot, both priority disciplines result in the same system occupancy. The analysis is carried out under the assumption that the service time is geometric, and that the packets arrive in batches of general size, at the rate of one batch per slot. These batches are homogeneous in the sense that each batch is either totally of class-1 packets or totally of class-2 packets. Two special cases are given at the end where the batch size is assumed once binomial and once Poisson. Given their timely nature, class-1 packets need to be served more rapidly than class-2. This can be done by implementing a priority scheme for the queue, where class-1 packets are given higher priority over class-2. Two disciplines may be used if such a scheme is implemented, based on what is supposed to happen to a class-2 packet being served when a class-1 packet arrives. In the nonpreemptive discipline, the arriving class-1 packet will have to wait until the class-2 packet is served. In the preemptive discipline, on the other hand, the class-1 packet will enter service in the next slot, ejecting the class-2 packet back to the buer. When there are no more class-1 packets in the queue, the ejected class-2 packet will reenter service. It can be