Analytical modelling of wormhole-routed k-ary n-cubes in the presence of matrix-transpose traffic

Several analytical models of fully adaptive routing in wormhole-routed k-ary n-cubes under the uniform traffic pattern have recently been proposed in the literature. Although the uniform reference model has been widely used in the past, it is not always true in practice as there are many applications that exhibit non-uniform traffic patterns. There has not been so far any study that describes an analytical model of fully adaptive routing under non-uniform traffic conditions. This paper describes a new analytical model of fully adaptive routing in k-ary n-cubes in the presence of non-uniform traffic generated by matrix-transpose permutations, which is an important communication operation found in many matrix computation problems. Results obtained through simulation experiments confirm that the model predicts message latency with a high degree of accuracy under different working conditions.