A theory of wormhole routing in parallel computers

Virtually all theoretical work on message routing in parallel computers has dwelt on packet routing: messages are conveyed as packets, an entire packet can reside at a node of the network, and a packet is sent from the queue of one node to the queue of another node until its reaches its destination. A trend in multicomputer architecture, however, is to use wormhole routing. In wormhole routing a message is transmitted as a contiguous stream of bits, physically occupying a sequence of nodes/edges in the network. Thus, a message resembles a worm burrowing through the network. In this paper we give theoretical analyses of simple wormhole routing algorithms, showing them to be nearly optimal for butterfly and mesh connected networks. Our analysis requires initial random delays in injecting messages to the network. We report simulation results suggesting that the idea of random initial delays may have an impact beyond theoretical analysis.