A Queuing System with a Branching Process Arrival Stream, the Case of Short-Range Dependence

Abstract

In a previous paper, we defined and studied a branching process input stream that can be used to model the organization of packets (in packetized communication) in messages. In this paper we derive a central result on the effect that such streams have on a packet switch (or queue) and further study one particular model (the case of so-called short-range dependence), where the distribution of the number of packets in a buffer can explicitly be found (albeit in the form of a transform). The solution to this particular model suggests an approximation for the average buffer content in the general case.