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

Abstract

A Banyan network analysis technique is presented which more accurately models a congested network than other reported techniques. The analysis is based on the observation that a full queue (within the switching modules making up the network) causes traffic to back up. For a short time after becoming full, the free space in the queue is limited to no more than one slot. A queue in such a condition is called congested. Because of blocking the arrival rate to a congested queue is higher; this tends to maintain congestion. The arrival rate to a congested queue's dual is lower, as is the service rate for queues feeding the congested queue. These effects are captured in the analysis by using a state model that codes the condition of a queue and its neighbors. From a queue's state it can be determined if the queue, its dual, or a next-stage queue to which it connects is congested, as well as the number of items in the queue. Network throughput computed with the model is closer to that obtained from simulations than other Banyan analyses appearing in literature, including those designed to model congestion. Further, the queue-occupancy distributions are much closer than other analyses, suggesting that the analysis better models conditions in congested Banyan networks.