Load-balanced Birkhoff-von Neumann switches and fat-tree networks

Fat-tree networks have been widely used in the field of Network-on-Chip. One of the key issues in a fat-tree network is that the degree of a node has to be increased rapidly from the bottom of the tree to the root. As such, the complexity of implementing the switches near the root could be extremely high, and this poses a serious scalability issue. To cope with the scalability issue in fat-tree networks, many previous works require changing the tree topology and adding buffers in nodes. Unlike the existing arts, we adopt a different approach that can still maintain the original tree topology without adding any buffers in internal nodes. Our key idea is to explore various nice features of the load-balanced Birkhoff-von Neumann switches. Such switches have been shown to achieve 100% throughput for all admissible traffic and have comparable delay performance to the ideal output-buffered switch when traffic is heavy and bursty. We show that the implementation complexity can be greatly reduced if a fat-tree network is only required to realize a set of N permutations needed for the N × N load-balanced Birkhoff-von Neumann switches. For this, we first derive a lower bound on the required degree for each node in a fat-tree network. By using the uniform mapping property of the bit-reverse permutation, we show that there exists a set of N permutations that achieve the lower bound.