Sticky States in Banyan Network Queues and Their Application to Analysis

Abstract

A finite-buffered banyan network analysis technique designed to model networks at high traffic loads is presented. The technique specially models two states of the network queues: queue empty and queue congested (roughly, zero or one slots free). A congested queue tends to stay congested because packets bound for the queue accumulate in the previous stage. The expected duration of this state is computed using a probabilistic model of a switching module feeding the congested queue. A technique for finding a lower arrival rate to an empty queue is also described. The queues themselves are modeled using independent Markov chains with an additional congested state added. The new analysis technique is novel in its modeling the higher arrival rate to a congested queue and a lower arrival rate to an empty queue. Comparison of queue state distributions obtained with the analysis and simulation show that an important feature of congestion is modeled.

Congested Banyan network analysis using congested-queue states and neighboring-queue effects

“…An advantage of the model is that a queue's stationary distribution can be found in closed form [8]. (Iteration is still required to compute expected congestion duration and to solve the entire network.)…”