Modeling virtual channel flow control in hypercubes

Abstract

An analytical model for virtual channel flow control in n-dimensional hypercubes using the e-cube routing algorithm is developed. The model is based on determining the values of the different components that make up the average message latency. These components include the message transfer time, the blocking delay at each dimension, the multiplexing delay at each dimension, and the waiting delay at the source node. The first two components are determined using a probabilistic analysis. The average degree of multiplexing is determined using a Markov model, and the waiting delay at the source node is determined using an M/M/m queueing system. The model is fairly accurate in predicting the average message latency for different message sizes and a varying number of virtual channels per physical channel. It is demonstrated that wormhole switching along with virtual channel flow control make the average message latency insensitive to the network size when the network is relatively lightly loaded (message arrival rate is equal to 40% of channel capacity), and that the average message latency increases linearly with the average message size. The simplicity and accuracy of the analytical model make it an attractive and effective tool for predicting the behavior of n-dimensional hypercubes.<>