An Asymptotically Minimal Node-Degree Topology for Load-Balanced Architectures

Load-balanced architectures appear to be a promising way to scale Internet to extra high capacity. However, architectures based on mesh topology have a node-degree of N, which prevents these architectures from large node numbers. This consideration motivates us to study the properties of node degree and its impact on the corresponding load-balanced architectures. In this paper we first show the asymptotically minimal node degree for any topology to achieve a constant ideal throughput under uniform traffic pattern when the channel bandwidth is fixed. We further introduce a unidirectional direct interconnection topology, named Plus 2^i (P2i), with this minimal node degree and prove that it has an ideal throughput of no less than twice the channel bandwidth under uniform traffic pattern. Based on the property, we provide the P2i load-balanced (PLB) architecture. Using this architecture, we show that scalability, 100% throughput and packet ordering can be all achieved and the scheduling algorithm is easy to implement. To the best of our knowledge, this is the first load-balanced architecture constructed on multi-hop direct interconnection topologies without packet reordering problem.