Single Node Queueing Models with Priorities

Abstract

Most of the queue disciplines presented so far are the first-come-first-served systems. As pointed out earlier in the introductory part of single node systems other types of queue disciplines include the priority types, last-come-first-served, service in a random order, and several variants of these. In this chapter we present two types of priority service disciplines – the preemptive and non-preemptive types. We focus mainly on cases with just two classes of packets. The results for such a system can be used to approximate multiple classes systems, if needed. For the two classes presented in this chapter we assume there are two sources sending packets; one source sending one class type and the other sending another class type. The result is that we may have, in one time slot, no packet arrivals, just one packet arrival of either class, or two packet arrivals with one of each class. The other type of situation with no more than one packet arrival during a time slot is a special case of the model presented here. We study the priority queues with geometric arrivals and geometric services in detail.