Bounds for Queue Lengths in a Contention Packet Broadcast System

A finite number of users communicating through a broadcast channel is considered. Each user has a buffer of infinile capacity, and a user randomly accesses the channel ( ALOHA-type protocol). Moreover, only one packet per user might be sent in an access time. Both symmetric and asymmetric models are considered, that is, we assume either indistinguishable or distinguishable users. An exact analysis is now not available, therefore, based on some algebraic studies we shall present some lower and some upper bounds for the average queue lengths. These bounds are quite tight for a wide range of input parameters in the symmelric case. In the asymmetric case the bounds are "good" for light and heavy input traffic. In addition, sla. bility conditions for lhe system will be presented.