Increasing the Size of a Network by a Constant Factor can Increase Performance by more than a Constant Factor

The performance of unbuffered routing algorithms for parallel computer architectures is analyzed. Unbuffered algorithms are an alternative to the use of queues. When the capacity of a switch or communications link is exceeded, the extra messages are discarded, and another attempt to transmit the message will be made at a later time. The analysis presented here is relevant for routing on the BBN Butterfly and Agarwal and Knight’s Alewife architecture, both of which have interconnection networks based on the butterfly graph.Suppose that each of the N inputs of the butterfly independently decides to send a message with probability p, and that the message is sent to a random output, with each output having an equal probability of being chosen. If more than q messages attempt to traverse an edge, the extra messages over q are discarded. q is called the dilation of the network. The bandwidth is the number of messages that reach their destinations. It is shown that if $p = \Omega ((\log N)^{ - 1/q} )$, the expec...