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

The impacts of timing constraints on virtual channels multiplexing in interconnect networks

Interconnect networks employing wormhole-switching play a critical role in shared memory multiprocessor systems-on-chip (MPSoC) designs, multicomputer systems and system area networks. Virtual channels greatly improve the performance of wormhole-switched networks because they reduce blocking by acting as "bypass" lanes for non-blocked messages. Capturing the effects of virtual channel multiplexing has always been a crucial issue for any analytical model proposed for wormhole-switched networks. Dally has developed a model to investigate the behaviour of this multiplexing which have been widely employed in the subsequent analytical models of most routing algorithms suggested in the literature. It is indispensable to modify Dally's model in order to evaluate the performance of channel multiplexing in more general networks where restrictions such as timing constraints of input arrivals and finite buffer size of queues are common. In this paper we consider timing constraints of input arrivals to investigate the virtual channel multiplexing problem inherent in most current networks. The analysis that we propose is completely general and therefore can be used with any interconnect networks employing virtual channels. The validity of the proposed equations has been verified through simulation experiments under different working conditions

Are feedback loops destructive to synchronization?

We study the effects of directionality on synchronization of dynamical networks. Performing the linear stability analysis and the numerical simulation of the Kuramoto model in directed networks, we show that balancing in- and out-degrees of all nodes enhances the synchronization of sparse networks, especially in networks with high clustering coefficient and homogeneous degree distribution. Furthermore, by omitting all the feedback loops, we show that while hierarchical directed acyclic graphs are structurally highly synchronizable, their global synchronization is too sensitive to the choice of natural frequencies and is strongly affected by noise

A simple mathematical model of adaptive routing in wormhole k-ary n-cubes

Many fully-adaptive algorithms have been proposed for k-ary n-cubes over the past decade. The performance characteristics of most of these algorithms have been analysed by means of software simulation only. This paper proposes a simple yet reasonably accurate analytical model to predict message latency in wormhole-routed k-ary n-cubes with fully adaptive routing. This model requires a running time of O(I) which is the fastest model yet reported in the literature while maintaining reasonable accuracy. 1

Parallel hermite interpolation on the pyramid

The pyramid network is one of the most important interconnection topologies used as hardware architecture or software data structure. It has a combined tree-mesh structure making it suitable for solving many parallel problems and applications. This paper proposes a parallel algorithm for Hermite Interpolation on the Pyramid network which has at least N nodes. The proposed algorithm has 3 phases: initialization, main, and final. The algorithm is optimal with a time complexity of O(N) for an appoint interpolation

The effect of adaptivity on the performance of the OTIS-hypercube under different traffic patterns

Abstract. The OTIS-hypercube is an optoelectronic architecture for interconnecting the processing nodes of a multiprocessor system. In this paper, an empirical performance evaluation of the OTIS-hypercube is conducted for different traffic patterns and routing algorithms. It is shown that, depending on the traffic pattern, minimal path routing may not have the best performance and that adaptivity may be of no improvement. All judgments made are based on observations from the results of extensive simulation experiments of the interconnection network. In addition, logical explanations are suggested for the cause of certain noticeable performance characteristics. 1