Inequality Comparisons and Traffic Smoothing in Multi-Stage ATM Multiplexers

In this paper we examine the queuing behavior of a multi-stage multiplexer with fixed length packets flowing through the stages. The system consists of two components: a front end multi-input, multi-output device as a preliminary stage, and a single-server, deterministic service time queue system (multiplexer) as a final stage. We treat arbitrary exogenous arrival patterns and examine sample path characteristics of packet occupancy in the system. Under identical inputs, we compare the multi-stage system to the corresponding single-stage system without the front end. Treating both the infinite buffer (unlimited capacity) and finite buffer (fixed capacity) cases, we prove a two-part MultiStage Multiplexing Theorem. From the first part, we conclude that any type of multi-staging is “sub-optimal.” However, from the second part we find that deterministic service time queues--if they need to be installed as front ends for a larger network--actually improve upon or smooth the data traffic for downstream nodes.