Towards a more realistic comparative analysis of multicomputer networks

Abstract

SUMMARYSeveral studies have examined the relative performance merits of the torus and hypercube taking into account the channel bandwidth constraints imposed by implementation technology. While the torus has been shown to outperform the hypercube under the constant wiring density constraint, the opposite conclusion has been reached when the constant pin-out constraint is considered. However, these studies have assumed a pure uniform traffic pattern and deterministic routing. The 'uniform traffic' assumption is not always justifiable in practice as there are many real-world parallel applications that exhibit nonuniform traffic patterns, which can create unbalanced traffic such as hotspots in the network. This paper re-examines the performance merits of the torus and hypercube in the presence of hotspot traffic. The comparative analysis is based on fully adaptive routing as this has been gaining popularity in recent practical multicomputers. Moreover, it uses a new cost model that takes into account the implementation cost of the network and its routers. The results reveal that for moderate and large system sizes, lower dimensional k-ary n-cubes (e.g. 2D torus) always outperform their higher dimensional counterparts even under the pin-out constraint.

Hypercube versus Torus under Pin-Out Constraint and Finite Buffers

“…In this study we would rather focus on the unidirectional versions of these networks in order to contrast our results with those reached in previous similar studies [1,3,7,11,12,13].…”

“…2D torus outperforms the hypercube). On the other hand, when the pin-out constraint is imposed, the study in [12] has concluded that for small, moderate, and large networks, the topology exhibiting the best relative performance is, respectively, the hypercube, the 2D torus, and the 3D torus.…”

“…Sarbazi-Azad et al [12], however, have compared the performance of adaptive routing in different topologies under both constant bisection width and constant pin-out constraints. They have arrived at the same conclusion as Dally [7] when constant bisection width constraint is imposed (i.e.…”

“…Comparative performance studies of k-ary n-cubes under different design constraints and operating conditions have been widely reported in the literature [1, 3,7,11,12,13]. It has been shown that when systems are implemented in a single VLSI chip the wiring density of the network determines the overall system cost and performance [14].…”

“…These studies [1,3,7,11,12,13] have assumed single-flit buffers per virtual channels. Deploying finite size buffers, however, may add extra complexity to the router design and hence will influence the cost and the performance of the network.…”