k -ary n -trees: High Performance Networks for Massively Parallel Architectures

The past few years have seen a rise in popularity of massively parallel architectures that use fat-trees as their interconnection networks. In this paper we study the communication performance of a parametric family of fat-trees, the k-ary n-trees, built with constant arity switches interconnected in a regular topology. Through simulation on a 4-ary 4-tree with 256 nodes, we analyze some variants of an adaptive algorithm that utilize wormhole routing with one, two and four virtual channels. The experimental results show that the uniform, bit reversal and transpose traffic patterns are very sensitive to the flow control strategy. In all these cases, the saturation points are between 35 40% of the network capacity with one virtual channel, 55 60% with two virtual channels and around 75% with four virtual channels. The complement traffic, a representative of the class of the congestion-free communication patterns, reaches an optimal performance, with a saturation point at 97% of the capacity for all flow control strategies.