Mathematical Modelling of Wormhole-Routed x-Folded TM Topology in the Presence of Uniform Traffic

Abstract

Recently, x-Folded TM topology was introduced as a desirable design in k-ary n-cube networks due to the low diameter and short average distance. In this article, we propose a mathematical model to predict the average network delay for (k X k) x-Folded TM in the presence of uniform traffic pattern. Our model accurately formulates the applied traffic pattern over network virtual channels based on the average distance and number of nodes. The mathematical results indicate that the average network delay for x-Folded TM topology is reduced when compared with other topologies in the presence of uniform traffic pattern. Finally, the results obtained from simulation experiments confirm that the mathematical model exhibits a significant degree of accuracy for x-Folded TM topology under the traffic pattern even in varied virtual channels.