Optimal Clustering of Hierarchical Hyper-Ring Multicomputers

The Hyper-Ring (HR) is presented as a hierarchical and scalable ring-based topology for small-scale to massively parallel systems which eliminates the major disadvantages of large-scale rings. With a fixed node degree, a low cost, symmetric properties, and a simple routing scheme, the HR topology is very suitable for small-scale to large-scale multicomputer systems. Assuming pipelined communication, the performance of 4- and 5-dimensional HR multicomputers is modeled, the performance model is evaluated, and the results of the performance model evaluation are analyzed. Moreover, the impact of the traffic load and message length on the system performance is analyzed. The major objective of this work is to shed light on how to cluster HRs in order to optimize the system efficiency. Assuming a uniform message arrival rate into the nodes of the HR, the results show that the efficiency of HR topologies with an equal number of nodes is best when the topologies are perfectly balanced. The next best-performing HRs are those with larger rings at the lower (outer) levels and smaller rings at the higher levels (near the root ring). The results confirm that the HR topology is suitable for massively parallel and scalable multicomputer systems as well as for networks of workstations.