Performance analysis of deterministically-routed bi-directional torus with non-uniform traffic distribution

Existing research has most often relied on simulation and considered the uniform traffic distribution when investigating the performance properties of multicomputer networks (e.g. the torus). However, there are numerous parallel applications that generate non-uniform traffic patterns, such as hot-spot. Furthermore, much more attention has been paid to capturing the impact of non-uniform traffic on network performance, resulting in the development of a number of analytical models for predicting message latency in the presence of hot-spots in the network. For instance, analytical models have been reported for the adaptively-routed torus with uni-directional as well as bi-directional channels. However, models for the deterministically-routed torus have considered uni-directional channels only. In an effort to fill in this gap, this paper describes an analytical model for the deterministically-routed torus with bi-directional channels when subjected to hot-spot traffic. The modelling approach adopted for deterministic routing is totally different from that for adaptive routing due to the inherently different nature of the two types of routing. The validity of the model is demonstrated by comparing analytical results against those obtained through extensive simulation experiments.