Combinatorial performance modelling of toroidal cubes

Although several analytical models have been proposed in the literature for deterministic routing in different interconnection networks, very few of them have considered the effects of virtual channel multiplexing on network performance. This paper proposes a new analytical model to compute message latency in a general n-dimensional torus network with an arbitrary number of virtual channels per physical channel. Unlike the previous models proposed for toroidal-based networks, this model uses a combinatorial approach to consider all different possible cases for the source-destination pairs, thus resulting in an accurate prediction. The results obtained from simulation experiments confirm that the proposed model exhibits a high degree of accuracy for various network sizes, under different operating conditions, compared to a similar model proposed very recently, which considers virtual channel utilization in the k-ary n-cube network.