Analytical performance modelling of adaptive wormhole routing in the star interconnection network

The star graph was introduced as an attractive alternative to the well-known hypercube and its properties have been well studied in the past. Most of these studies have focused on topological properties and algorithmic aspects of this network. Although several analytical models have been proposed in the literature for different interconnection networks, none of them have dealt with star graphs. This paper proposes the first analytical model to predict message latency in wormhole-switched star interconnection networks with fully adaptive routing. The analysis focuses on a fully adaptive routing algorithm which has shown to be the most effective for star graphs. The results obtained from simulation experiments confirm that the proposed model exhibits a good accuracy under different operating conditions

An Optimal Single-Path Routing Algorithm in the Datacenter Network DPillar

DPillar has recently been proposed as a server-centric datacenter network and is combinatorially related to (but distinct from) the well-known wrapped butterfly network. We explain the relationship between DPillar and the wrapped butterfly network before proving that the underlying graph of DPillar is a Cayley graph; hence, the datacenter network DPillar is node-symmetric. We use this symmetry property to establish a single-path routing algorithm for DPillar that computes a shortest path and has time complexity O(k), where k parameterizes the dimension of DPillar (we refer to the number of ports in its switches as n). Our analysis also enables us to calculate the diameter of DPillar exactly. Moreover, our algorithm is trivial to implement, being essentially a conditional clause of numeric tests, and improves significantly upon a routing algorithm earlier employed for DPillar. Furthermore, we provide empirical data in order to demonstrate this improvement. In particular, we empirically show that our routing algorithm improves the average length of paths found, the aggregate bottleneck throughput, and the communication latency. A secondary, yet important, effect of our work is that it emphasises that datacenter networks are amenable to a closer combinatorial scrutiny that can significantly improve their computational efficiency and performance

An efficient shortest path routing algorithm in the data centre network DPillar

DPillar has recently been proposed as a server-centric data centre network and is combinatorially related to the well-known wrapped butterfly network. We explain the relationship between DPillar and the wrapped butterfly network before proving a symmetry property of DPillar. We use this symmetry property to establish a single-path routing algorithm for DPillar that computes a shortest path and has time complexity O(klog(n))O(klog⁡(n)), where k parameterizes the dimension of DPillar and n the number of ports in its switches. Moreover, our algorithm is trivial to implement, being essentially a conditional clause of numeric tests, and improves significantly upon a routing algorithm earlier employed for DPillar. A secondary and important effect of our work is that it emphasises that data centre networks are amenable to a closer combinatorial scrutiny that can significantly improve their computational efficiency and performance

The stellar transformation: from interconnection networks to datacenter networks

The first dual-port server-centric datacenter network, FiConn, was introduced in 2009 and there are several others now in existence; however, the pool of topologies to choose from remains small. We propose a new generic construction, the stellar transformation, that dramatically increases the size of this pool by facilitating the transformation of well-studied topologies from interconnection networks, along with their networking properties and routing algorithms, into viable dual-port server-centric datacenter network topologies. We demonstrate that under our transformation, numerous interconnection networks yield datacenter network topologies with potentially good, and easily computable, baseline properties. We instantiate our construction so as to apply it to generalized hypercubes and obtain the datacenter networks GQ⋆. Our construction automatically yields routing algorithms for GQ⋆ and we empirically compare GQ⋆ (and its routing algorithms) with the established datacenter networks FiConn and DPillar (and their routing algorithms); this comparison is with respect to network throughput, latency, load balancing, fault-tolerance, and cost to build, and is with regard to all-to-all, many all-to-all, butterfly, random, hot-region, and hot-spot traffic patterns. We find that GQ⋆ outperforms both FiConn and DPillar (sometimes significantly so) and that there is substantial scope for our stellar transformation to yield new dual-port server-centric datacenter networks that are a considerable improvement on existing ones