A framework for designing deadlock-free wormhole routing algorithms

Abstract

Abstract-This paper presents a framework to design fully-adaptive, deadlock-free wormhole algorithms for a variety of network topologies. The main theoretical contributions are (a) design of new wormhole algorithms using store-and-forward algorithms, (b) a sufficient condition for deadlock free routing by the wormhole algorithms so designed, and (c) a sufficient condition for deadlock free routing by these wormhole algorithms with centralized flit buffers shared among multiple channels. To illustrate the theory, several wormhole algorithms based on store-and-forward hop schemes are designed. The hop-based wormhole algorithms can be applied to a variety of networks including torus, mesh, de Brujin, and a class of Cayley networks, with the best known bounds on virtual channels for minimal routing on the last two classes of networks. An analysis of the resource requirements and performances of a proposed algorithm, called negative-hop algorithm, with some of the previously proposed algorithms for torus and mesh networks is presented.

Performance Evaluation of Fully Adaptive Routing for the Torus Interconnect Networks

“…These virtual channels are used according to the Duato-Nbc routing scheme, which are divided into V 1 and V 2 classes (V = V 1 + V 2 ). This number of virtual channels yields the optimal performance compared to the other schemes proposed in [4].…”

“…In [5], the Nbc routing scheme has been used in the context of Duato's methodology [6] and a routing algorithm, named Duato-Nbc with high performance and minimum virtual channel requirements was resulted. Investigations showed that Duato-Nbc has a better performance compared to other algorithms reported in the literature and the other algorithms proposed in [4].…”

“…This paper proposes an analytical approach to investigate the performance behavior of a fully adaptive routing algorithm in wormhole-switched 2-D torus fortified with a routing scheme suggested in [4], as an instance of routing methodology widely used in the literature to achieve high adaptivity.…”

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

“…The structure of S n is a bipartite graph, and its nodes can be partitioned into two subsets; therefore, it can be coloured using only two colours [5]. Because adjacent nodes are in distinct partitions, the maximum number of negative hops a message may take is at most half the diameter of S n , which equals…”

“…In the negative-hop algorithm [5], the network is partitioned into several subsets, such that no subset contains adjacent nodes (this is equivalent to the wellknown graph colouring problem). If C is the number of subsets, then the subsets are labelled as 0, 1, …, C-1, and nodes in subset i are labelled (or coloured) as i.…”