TECHNICAL REPORT LSU-ECE-95-163* Congested Banyan Network Analysis Using Congested-Queue States and Neighboring-Queue Effects

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. The state model used for a queue encodes congested as well as normal operation. Further, the model codes whether the connected next-stage and dual queues are congested. Network throughput computed with the model is closer to that obtained from simulations than other banyan analyses appearing in the 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. * A shorter version of this report is to appear in IEEE/ACM Transactions on Networking circa February 1996. ** This work is supported in part by the Louisiana Board of Regents through the Louisiana Education Quality Support Fund, contract number LEQSF (1993-95)-RD-A-07 and by the National Science Foundation under Grant No. MIP-9410435.