Optimal loop topologies for distributed systems

Double loop network architectures offer higher performance and reliability than single loop networks. In this paper, a double loop network which is optimal among all double loops is described. This network topology consists of a loop in the forward direction connecting all the neighboring nodes, and a backward loop connecting nodes that are separated by a distance @@@@@@@@N@@@@, where N is the number of nodes in the network. We show that this network is optimal in terms of hop distance between nodes, delay, throughput, and terminal reliability. The paper includes derivation of closed form expressions for the maximum and average hop distance between nodes, number of distinct routes between two farthest nodes, and throughput. The effect of node and link failures on network performance is also considered.