Cost-bandwidth tradeoffs for communication networks

A major component of a large-scale parallel computer is the interconnection network that connects processors to memories in a shared-memory machine, or processors to processors in a multicomputer. Such a network often consists of switches interconnected by links. Both the cost and performance of a network are affected by its topology. A huge variety of network topologies have been proposed in the literature, and studied in an ad hoc manner. A systematic, comparative study of these proposals is hampered by the lack of good performance criteria. Various topological parameters, such as diameter or cut-width, have been used as "measures of goodhess" for network topologies. However, it is clear that network performance depends on the type of traffic it supports; for example, a star topology that performs well for centralized traffic will have poor performance for uniformly distributed traffic. We propose in this paper a formal approach to the study of the relationship between network topology and network performance. We characterize the traffic pattern in terms of the relative frequency of communications between each pair of nodes. We assume that networks are "pin-limited"; there is a fixed upper bound on the number of links incident to any one node or switch. Network bandwidth is taken to be the main figure of merit. We further assume that the cost of a network is essentially proportional to its number of links. Formal definitions are given in the next section. Bandwidth is defined to depend only on the network