Communication delay in hypercubes in the presence of bit-reversal traffic

A number of studies have recently proposed analytical models of adaptive routing in wormhole-switched hypercubes under the uniform traffic pattern. However, there has been hardly any work reported yet that deals with other important non-uniform traffic patterns found in many parallel applications. This paper describes a new analytical model of adaptive routing in wormhole-switched hypercubes in the presence of highly non-uniform traffic generated by bit-reversal permutations, which is an important communication operation in parallel applications such as FFT computations. The analysis focuses Duato's fully adaptive routing algorithm [J. Duato, IEEE Trans. Parallel Distrib. Syst. 4(12) (1993) 320], which is widely accepted as the most general algorithm for achieving adaptivity in wormhole-routed networks while allowing for an efficient router implementation. Results obtained through simulation experiments confirm that the proposed model exhibits a good degree of accuracy in predicting message latency under different traffic conditions.