Asymptotic performance of a buffered shufflenet with deflection routing

Abstract

Throughput of a shufflenet with deflection routing under high load and low load is obtained as a function of the network and buffer sizes. The authors give general routing conditions which achieve high performance in a shufflenet. Using a routing algorithm similar to the algorithm considered, the throughput of a shufflenet with only one buffer can be increased by more than 45% compared with the shufflenet without any buffer, the so-called hot-potato case. The increase is general for a shufflenet of size ranging from as few as 24 nodes to more than 10,000 nodes. The increase is more significant when the network becomes larger. The authors note that a large number of routing algorithms proposed to be used in the shufflenet satisfy the general routing conditions mentioned. Using the routing algorithm the authors mention, a shufflenet with only two buffers can achieve performance comparable to the store-and-forward case. In previous studies of the shufflenet, the derivation of the important parameter-the probability of deflection of a packet in the network-is usually complicated. The authors have obtained a simple approximation of this parameter, which greatly simplifies the analysis of a shufflenet of any size and with any number of buffers. This enables to conclude that the performance of a shufflenet scales well with different network and buffer sizes if the routing algorithm is chosen properly. They finally verify the results with the simulations that have been done.