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

Analytical modelling of hot-spot traffic in deterministically-routed k-ary n-cubes

Many research studies have proposed analytical models to evaluate the performance of k-ary n-cubes with deterministic wormhole routing. Such models however have so far been confined to uniform traffic distributions. There has been hardly any model proposed that deal with non-uniform traffic distributions that could arise due to, for instance, the presence of hot-spots in the network. This paper proposes the first analytical model to predict message latency in k-ary n-cubes with deterministic routing in the presence of hot-spots. The validity of the model is demonstrated by comparing analytical results with those obtained through extensive simulation experiments

Fault tolerant adaptive routing in multicomputer networks

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (p. 149-152).by Thucydides Xanthopoulos.M.S

Analysis of interconnection networks in heterogeneous multi-cluster systems

The study of interconnection networks is important because the overall performance of a distributed system is often critically hinged on the effectiveness of its interconnection network. In the mean time, the heterogeneity is one of the most important factors of such systems. This paper addresses the problem of interconnection networks performance modeling of large-scale distributed systems with emphases on heterogeneous multi-cluster computing systems. So, we present an analytical model to predict message latency in multi-cluster systems in the presence of cluster size heterogeneity. The model is validated through comprehensive simulation, which demonstrates that the proposed model exhibits a good degree of accuracy for various system organizations and under different working conditions.<br /

Performance modelling and high performance buffer design for the system with network on chip

High performance novel dynamically allocated multi-queue (DAMQ) buffer schemes forsystems with network on chip (NoC) have been proposed and evaluated in this dissertation. Ananalytical model to predict performance of a NoC where wormhole switching technique andfully adaptive routing protocols has been developed and compared with simulations.In this dissertation, a novel analytical model for NoC which makes use of simple closeform calculations is presented. This model provides accurate network performance prediction inthe network stable region. The validity of this model is demonstrated by comparing analyticalprediction with simulation results obtained on high-radix k-ary 2-cube networks.Three novel switch buffer schemes, DAMQall, DAMQmin and DAMQshared, for system onchip with an interconnection network are also reported. The proposed schemes are based on aDAMQ self-compacting buffer hardware design. These schemes outperform existing approaches.DAMQall have similar performance using only half of the buffer size used in traditional SAMQimplementations. DAMQmin provides an excellent approach to optimize buffer managementproviding a good throughput when the network has a larger load. DAMQshared scheme lets virtualchannels from different physical channel share free buffer space. While providing similarperformance, DAMQshared scheme uses only around sixty percent of the buffer size that is used intraditional implementation for NoCs. In addition, using same size buffers, DAMQsharedoutperforms existing approaches such as SAMQ and DAMQall by 1% to 2% in throughput. Theproposed schemes also make a better utilization of the available buffer space

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

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

Off-chip Communications Architectures For High Throughput Network Processors

In this work, we present off-chip communications architectures for line cards to increase the throughput of the currently used memory system. In recent years there is a significant increase in memory bandwidth demand on line cards as a result of higher line rates, an increase in deep packet inspection operations and an unstoppable expansion in lookup tables. As line-rate data and NPU processing power increase, memory access time becomes the main system bottleneck during data store/retrieve operations. The growing demand for memory bandwidth contrasts the notion of indirect interconnect methodologies. Moreover, solutions to the memory bandwidth bottleneck are limited by physical constraints such as area and NPU I/O pins. Therefore, indirect interconnects are replaced with direct, packet-based networks such as mesh, torus or k-ary n-cubes. We investigate multiple k-ary n-cube based interconnects and propose two variations of 2-ary 3-cube interconnect called the 3D-bus and 3D-mesh. All of the k-ary n-cube interconnects include multiple, highly efficient techniques to route, switch, and control packet flows in order to minimize congestion spots and packet loss. We explore the tradeoffs between implementation constraints and performance. We also developed an event-driven, interconnect simulation framework to evaluate the performance of packet-based off-chip k-ary n-cube interconnect architectures for line cards. The simulator uses the state-of-the-art software design techniques to provide the user with a flexible yet robust tool, that can emulate multiple interconnect architectures under non-uniform traffic patterns. Moreover, the simulator offers the user with full control over network parameters, performance enhancing features and simulation time frames that make the platform as identical as possible to the real line card physical and functional properties. By using our network simulator, we reveal the best processor-memory configuration, out of multiple configurations, that achieves optimal performance. Moreover, we explore how network enhancement techniques such as virtual channels and sub-channeling improve network latency and throughput. Our performance results show that k-ary n-cube topologies, and especially our modified version of 2-ary 3-cube interconnect - the 3D-mesh, significantly outperform existing line card interconnects and are able to sustain higher traffic loads. The flow control mechanism proved to extensively reduce hot-spots, load-balance areas of high traffic rate and achieve low transmission failure rate. Moreover, it can scale to adopt more memories and/or processors and as a result to increase the line card\u27s processing power