A Performance Model of Adaptive Wormhole Routing in k-Ary n-Cubes in the Presence of Digit-Reversal 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 by researchers, it is not always true in practice as there are many applications that exhibit traffic nonuniformity. There has hardly been any study that describes an analytical model of fully adaptive routing under nonuniform traffic conditions. This paper describes the first analytical model of fully adaptive routing in k-ary n-cubes in the presence of nonuniform traffic generated by the digit-reversal permutation, 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 good degree of accuracy under different working conditions.