Cycle Breaking in Wormhole Routed Computer Communication Networks

Because of its simplicity, low channel setup times, and high performance in delivering messages, wormhole routing has been adopted in second generation multicomputing environments [13]. Furthermore, irregular topologies formed by ad-hoc interconnection of low cost workstations provide cost effective alternative to massively parallel computing platforms. Switches used in these networks of workstations, NOWs, implement wormhole routing [1, 12]. However, due to a number of channels being held up while requesting others, wormhole routing is susceptible to deadlocks. In this paper we investigated deadlock-free routing algorithms in wormhole routed irregular network topologies. We used a modified version of the Turn Prohibition algorithm [4] to break cycles and prevent channel deadlocks. We then used shortest path algorithm to determine the routing tables for each computational node in the topology, avoiding prohibited turns along the paths from source to destination. We used EMA to import topologies into Opnet and simulated for message delivery using both our approaches and for the competing Up/Down [1] approach. We then repeated this sequence for hundreds of different topologies and determine the average latencies for all algorithms. Our results show that the modified turn prohibition based routing has outperformed both, the original Turn Prohibition and the Up/Down algorithms. Introduction Because of its simplicity, low channel setup times, high performance in delivering messages, wormhole routing has been adopted in second generation multicomputing environments [3]. Because of their incremental scalability, workstation clusters, also known as Network of Workstations, or NOWs, have enjoyed considerable popularity [3, 5, 6]. However providing, deadlock-free routing in irregular networks has proven to be a difficult problem. Many routing algorithms for regular topologies, such as meshes, hypercubes, tori etc, have been developed providing deadlock free, low latency message delivery [6-11]. Providing deadlock freedom in irregular topologies with low latencies for delivering messages, in a cost effective manner is not trivial [5]. Authors in [5] assumed virtual cut-through switching in the routers which had no routing tables. All worms or messages use wormhole routing until it is blocked at a router. Upon blockage, the message is absorbed in its entirety at the router and forwarded later when the requested outbound channel gets freed up. In their approach, authors used a spanning tree for delivering messages, hereby avoiding deadlocks. However, any spanning tree based approach is not very efficient in terms of link utilization. In a network of N nodes only 1 N − links are used with root node links being most heavily loaded. The Up/Down routing approach, first reported in [12], is also a spanning tree based approach. However, in Up/Down routing, nodes are labeled in a partial order with the root having the smallest label and the leaves having the largest labels. Authors prescribe direction to both tree links and non-tree links, latter referred to as cross-links. Routing is then permitted to follow a path formed by zero or more up-links followed by zero or more downlinks. One disadvantage of this approach is that the construction of the best spanning tree is a hard problem. As in any spanning-tree based approach, links of the root node usually are most heavily used. In addition, given a topology and a spanning tree, selection of the root node would result in unpredictable routing performance [14, 19]. Turn prohibition was first reported in [10, 13], where turn model was thoroughly investigated for multi-dimensional meshes, and some turns were prohibited to prevent all possible deadlocks. Authors considered only 90 degree turns which are sufficient for meshes to prevent deadlock formation. In [4, 14-18] authors generalized the notion of turn, and developed an algorithm to construct minimal sets of prohibited turns, to break all cycles and prevent deadlock formation. Authors also established that the fraction of prohibited turns could be used as one of the criteria of efficiency of a routing strategy. In [19] authors extended the use of turn prohibition as described in [4] to general topologies and applied the Network Calculus techniques, which, until then, used to be strictly for feed-forward routing networks. In this paper, we modified the selection rule in the original Turn Prohibition algorithm, to investigate if the fraction of prohibited turns could be further improved. Motivation for this investigation is shown in Figure 1, adopted from [20] in which, we show the percentage gain in maximum sustained throughput versus the percentage improvement, i.e. reduction, in the fraction of prohibited turns. This plot, which is approximately linear, predicts an improvement of 7.7% in the saturation point per 1% reduction in the fraction of prohibited turns. In order to provide an unbiased comparison of competing routing algorithms, we developed a wormhole node model in Opnet, where flit level simulation has been used to determine the message latencies, and the saturation points for each topology and each algorithm. In our implementation of the model, we assume only one flit storage at the router per input port. We use routing tables constructed for each routing algorithm to determine which output port to use to forward the flits. Since our interest is to compare only the impact of fraction of prohibited turns on