On the performance of routing algorithms in wormhole-switched multicomputer networks

This paper presents a comparative performance study of adaptive and deterministic routing algorithms in wormhole-switched hypercubes and investigates the performance vicissitudes of these routing schemes under a variety of network operating conditions. Despite the previously reported results, our results show that the adaptive routing does not consistently outperform the deterministic routing even for high dimensional networks. In fact, it appears that the superiority of adaptive routing is highly dependent to the broadcast traffic rate generated at each node and it begins to deteriorate by growing the broadcast rate of generated message

A performance model of multicast communication in wormhole-routed networks on-chip

Collective communication operations form a part of overall traffic in most applications running on platforms employing direct interconnection networks. This paper presents a novel analytical model to compute communication latency of multicast as a widely used collective communication operation. The novelty of the model lies in its ability to predict the latency of the multicast communication in wormhole-routed architectures employing asynchronous multi-port routers scheme. The model is applied to the Quarc NoC and its validity is verified by comparing the model predictions against the results obtained from a discrete-event simulator developed using OMNET++

A communication model of broadcast in wormhole-routed networks on-chip

This paper presents a novel analytical model to compute communication latency of broadcast as the most fundamental collective communication operation. The novelty of the model lies in its ability to predict the broadcast communication latency in wormhole-routed architectures employing asynchronous multi-port routers scheme. The model is applied to the Quarc NoC and its validity is verified by comparing the model predictions against the results obtained from a discrete-event simulator developed using OMNET++

Quarc: a novel network-on-chip architecture

This paper introduces the Quarc NoC, a novel NoC architecture inspired by the Spidergon NoC. The Quarc scheme significantly outperforms the Spidergon NoC through balancing the traffic which is the result of the modifications applied to the topology and the routing elements.The proposed architecture is highly efficient in performing collective communication operations including broadcast and multicast. We present the topology, routing discipline and switch architecture for the Quarc NoC and demonstrate the performance with the results obtained from discrete event simulations

Performance evaluation of distributed crossbar switch hypermesh

The interconnection network is one of the most crucial components in any multicomputer as it greatly influences the overall system performance. Several recent studies have suggested that hypergraph networks, such as the Distributed Crossbar Switch Hypermesh (DCSH), exhibit superior topological and performance characteristics over many traditional graph networks, e.g. k-ary n-cubes. Previous work on the DCSH has focused on issues related to implementation and performance comparisons with existing networks. These comparisons have so far been confined to deterministic routing and unicast (one-to-one) communication. Using analytical models validated through simulation experiments, this thesis extends that analysis to include adaptive routing and broadcast communication. The study concentrates on wormhole switching, which has been widely adopted in practical multicomputers, thanks to its low buffering requirement and the reduced dependence of latency on distance under low traffic. Adaptive routing has recently been proposed as a means of improving network performance, but while the comparative evaluation of adaptive and deterministic routing has been widely reported in the literature, the focus has been on graph networks. The first part of this thesis deals with adaptive routing, developing an analytical model to measure latency in the DCSH, and which is used throughout the rest of the work for performance comparisons. Also, an investigation of different routing algorithms in this network is presented. Conventional k-ary n-cubes have been the underlying topology of contemporary multicomputers, but it is only recently that adaptive routing has been incorporated into such systems. The thesis studies the relative performance merits of the DCSH and k-ary n-cubes under adaptive routing strategy. The analysis takes into consideration real-world factors, such as router complexity and bandwidth constraints imposed by implementation technology. However, in any network, the routing of unicast messages is not the only factor in traffic control. In many situations (for example, parallel iterative algorithms, memory update and invalidation procedures in shared memory systems, global notification of network errors), there is a significant requirement for broadcast traffic. The DCSH, by virtue of its use of hypergraph links, can implement broadcast operations particularly efficiently. The second part of the thesis examines how the DCSH and k-ary n-cube performance is affected by the presence of a broadcast traffic component. In general, these studies demonstrate that because of their relatively high diameter, k-ary n-cubes perform poorly when message lengths are short. This is consistent with earlier more simplistic analyses which led to the proposal for the express-cube, an enhancement of the basic k-ary n-cube structure, which provides additional express channels, allowing messages to bypass groups of nodes along their paths. The final part of the thesis investigates whether this "partial bypassing" can compete with the "total bypassing" capability provided inherently by the DCSH topology

Performance analysis of wormhole routing in multicomputer interconnection networks

Perhaps the most critical component in determining the ultimate performance potential of a multicomputer is its interconnection network, the hardware fabric supporting communication among individual processors. The message latency and throughput of such a network are affected by many factors of which topology, switching method, routing algorithm and traffic load are the most significant. In this context, the present study focuses on a performance analysis of k-ary n-cube networks employing wormhole switching, virtual channels and adaptive routing, a scenario of especial interest to current research. This project aims to build upon earlier work in two main ways: constructing new analytical models for k-ary n-cubes, and comparing the performance merits of cubes of different dimensionality. To this end, some important topological properties of k-ary n-cubes are explored initially; in particular, expressions are derived to calculate the number of nodes at/within a given distance from a chosen centre. These results are important in their own right but their primary significance here is to assist in the construction of new and more realistic analytical models of wormhole-routed k-ary n-cubes. An accurate analytical model for wormhole-routed k-ary n-cubes with adaptive routing and uniform traffic is then developed, incorporating the use of virtual channels and the effect of locality in the traffic pattern. New models are constructed for wormhole k-ary n-cubes, with the ability to simulate behaviour under adaptive routing and non-uniform communication workloads, such as hotspot traffic, matrix-transpose and digit-reversal permutation patterns. The models are equally applicable to unidirectional and bidirectional k-ary n-cubes and are significantly more realistic than any in use up to now. With this level of accuracy, the effect of each important network parameter on the overall network performance can be investigated in a more comprehensive manner than before. Finally, k-ary n-cubes of different dimensionality are compared using the new models. The comparison takes account of various traffic patterns and implementation costs, using both pin-out and bisection bandwidth as metrics. Networks with both normal and pipelined channels are considered. While previous similar studies have only taken account of network channel costs, our model incorporates router costs as well thus generating more realistic results. In fact the results of this work differ markedly from those yielded by earlier studies which assumed deterministic routing and uniform traffic, illustrating the importance of using accurate models to conduct such analyses

Analysis of wormhole routings in cayley graphs of permutation groups.

Over a decade, a new class of switching technology, called wormhole routing, has been investigated in the multicomputer interconnection network field. Several classes of wormhole routing algorithms have been proposed. Most of the algorithms have been centered on the traditional binary hypercube, k-ary n-cube mesh, and torus networks. In the design of a wormhole routing algorithm, deadlock avoidance scheme is the main concern. Recently, new classes of networks called Cayley graphs of permutation groups are considered very promising alternatives. Although proposed Cayley networks have superior topological properties over the traditional network topologies, the design of the deadlock-free wormhole routing algorithm in these networks is not simple. In this dissertation, we investigate deadlock free wormhole routing algorithms in the several classes of Cayley networks, such as complete-transposition and star networks. We evaluate several classes of routing algorithms on these networks, and compare the performance of each algorithm to the simulation study. Also, the performances of these networks are compared to the traditional networks. Through extensive simulation we found that adaptive algorithm outperformed deterministic algorithm in general with more virtual channels. On the network performance comparison, the complete transposition network showed the best performance among the similar sized networks, and the binary hypercube performed better compared to the star graph

Hypergraph-Based Interconnection Networks for Large Multicomputers

This thesis deals with issues pertaining to multicomputer interconnection networks namely topology, technology, switching method, and routing algorithm. It argues that a new class of regular low-dimensional hypergraph networks, the distributed crossbar switch hypermesh (DCSH), represents a promising alternative high-performance interconnection network for future large multicomputers to graph networks such as meshes, tori, and binary n-cubes, which have been widely used in current multicomputers. Channels in existing hypergraph and graph structures suffer from bandwidth limitations imposed by implementation technology. The first part of the thesis shows how the low-dimensional DCSH can use an innovative implementation scheme to alleviate this problem. It relies on the separation of processing and communication functions by physical layering in order to accommodate high wiring density and necessary message buffering, improving performance considerably. Various mathematical models of the DCSH, validated through discrete-event simulation, are then introduced. Effects of different switching methods (e.g., wormhole routing, virtual cut-through, and message switching), routing algorithms (e.g., restricted and random), and different switching element designs are investigated. Further, the impact on performance of different communication patterns, such as those including locality and hot-spots, are assessed. The remainder of the thesis compares the DCSH to other common hypergraph and graph networks assuming different implementation technologies, such as VLSI, multiple-chip technology, and the new layered implementation scheme. More realistic assumptions are introduced such as pipeline-bit transmission and non-zero delays through switching elements. The results show that the proposed structure has superior characteristics assuming equal implementation cost in both VLSI and multiple-chip technology. Furthermore, optimal performance is offered by the new layered implementation

Performance analysis of wormhole switched interconnection networks with virtual channels and finite buffers

An efficient interconnection network that provides high bandwidth and low latency interprocessor communication is critical to harness fully the computational power of large scale multicomputer. K-ary n-cube networks have been widely adopted in contemporary multicomputers due to their desirable properties. As such, the present study focuses on a performance analysis of K-ary n-cubes employing wormhole switching, virtual channels, and adaptive routing. The objective of this dissertation is twofold: to examine the performance of these networks, and to compare the performance merits of various topologies under different working conditions, by means of analytical modelling. Most existing analytical models reported in the literature have used a method originally proposed by Dally to capture the effects of virtual channels on network performance. This method is based on a Markov chain and it has been shown that its prediction accuracy degrades as traffic increases. Moreover, these studies have also constrained the buffer capacity to a single flit per channel, a simplifying assumption that has often been invoked to ease the derivation of the analytical models. Motivated by these observations, the first part of this research proposes a new method for modelling virtual channels, based on an M/G/1 queue. Owing to the generality of this method. Daily's method is shown to be a special case when the message service time is exponentially distributed. The second part of this research uses theoretical results of queuing systems to relax the single-flit buffer assumption. New analytical models are then proposed to capture the effects of deploying arbitrary size buffers on the performance of deterministic and adaptive routing algorithms. Simulation experiments reveal that results from the proposed analytical models are in close agreement with those obtained through simulation. Building on these new analytical models, the third part of this research compares the relative performance merits of K-ary n-cubes under different operating conditions, in the presence of finite size buffers and multiple virtual channels. Namely, the analysis first revisits the relative performance merits of the well-known 2D torus, 3D torus and hypercube under different implementation constraints. The analysis has then been extended to investigate the performance impact of arranging the total buffer space, allocated to a physical channel, into multiple virtual channels. Finally, the performance of adaptive routing has been compared to that of deterministic routing. While previous similar studies have only taken account of channel and router costs, the present analysis incorporates different intra-router delays, as well, and thus generates more realistic results. In fact, the results of this research differ notably from those reported in previous studies, illustrating the sensitivity of such studies to the level of detail, degree of accuracy and the realism of the assumptions adopted