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

System level modelling and design of hypergraph based wireless system area networks for multi-computer systems

This thesis deals with issues pertaining the wireless multicomputer interconnection networks namely topology and Medium Access Control (MAC). It argues that new channel assignment technique based on regular low-dimensional hypergraph networks, the dual radio wireless hypermesh, represents a promising alternative high-performance wireless interconnection network for the future multicomputers to shared communication medium networks and/or ordinary wireless mesh networks, which have been widely used in current wireless networks. The focus of this work is on improving the network throughput while maintaining a relatively low latency of a wireless network system. By means of a Carrier Sense Multiple Access (CSMA) based design of the MAC protocol and based on the desirable features of hypermesh network topology a relatively high performance network has been introduced. Compared to the CSMA shared communication channel model, which is currently the de facto MAC protocol for most of wireless networks, our design is shown to achieve a significant increase in network throughput with less average network latency for large number of communication nodes. SystemC model of the proposed wireless hypermesh, validated through mathematical models, are then introduced. The analysis has been incorporated in the proper SystemC design methodology which facilitates the integration of communication modelling into the design modelling at the early stages of the system development. Another important application of SystemC modelling techniques is to perform meaningful comparative studies of different protocols, or new implementations to determine which communication scenario performs better and the ability to modify models to test system sensitivity and tune performance. Effects of different design parameters (e.g., packet sizes, number of nodes) has been carried out throughout this work. The results shows that the proposed structure has out perform the existing shared medium network structure and it can support relatively high number of wireless connected computers than conventional networks

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

Small-world interconnection networks for large parallel computer systems

The use of small-world graphs as interconnection networks of multicomputers is proposed and analysed in this work. Small-world interconnection networks are constructed by adding (or modifying) edges to an underlying local graph. Graphs with a rich local structure but with a large diameter are shown to be the most suitable candidates for the underlying graph. Generation models based on random and deterministic wiring processes are proposed and analysed. For the random case basic properties such as degree, diameter, average length and bisection width are analysed, and the results show that a fast transition from a large diameter to a small diameter is experienced when the number of new edges introduced is increased. Random traffic analysis on these networks is undertaken, and it is shown that although the average latency experiences a similar reduction, networks with a small number of shortcuts have a tendency to saturate as most of the traffic flows through a small number of links. An analysis of the congestion of the networks corroborates this result and provides away of estimating the minimum number of shortcuts required to avoid saturation. To overcome these problems deterministic wiring is proposed and analysed. A Linear Feedback Shift Register is used to introduce shortcuts in the LFSR graphs. A simple routing algorithm has been constructed for the LFSR and extended with a greedy local optimisation technique. It has been shown that a small search depth gives good results and is less costly to implement than a full shortest path algorithm. The Hilbert graph on the other hand provides some additional characteristics, such as support for incremental expansion, efficient layout in two dimensional space (using two layers), and a small fixed degree of four. Small-world hypergraphs have also been studied. In particular incomplete hypermeshes have been introduced and analysed and it has been shown that they outperform the complete traditional implementations under a constant pinout argument. Since it has been shown that complete hypermeshes outperform the mesh, the torus, low dimensional m-ary d-cubes (with and without bypass channels), and multi-stage interconnection networks (when realistic decision times are accounted for and with a constant pinout), it follows that incomplete hypermeshes outperform them as well

Predictive and distributed routing balancing (PR-DRB) : high speed interconnection networks

Current parallel applications running on clusters require the use of an interconnection network to perform communications among all computing nodes available. Imbalance of communications can produce network congestion, reducing throughput and increasing latency, degrading the overall system performance. On the other hand, parallel applications running on these networks posses representative stages which allow their characterization, as well as repetitive behavior that can be identified on the basis of this characterization. This work presents the Predictive and Distributed Routing Balancing (PR-DRB), a new method developed to gradually control network congestion, based on paths expansion, traffic distribution and effective traffic load, in order to maintain low latency values. PR-DRB monitors messages latencies on intermediate routers, makes decisions about alternative paths and record communication pattern information encountered during congestion situation. Based on the concept of applications repetitiveness, best solution recorded are reapplied when saved communication pattern re-appears. Traffic congestion experiments were conducted in order to evaluate the performance of the method, and improvements were observed.Les aplicacions paral·leles actuals en els Clústers requereixen l'ús d'una xarxa d'interconnexió per comunicar a tots els nodes de còmput disponibles. El desequilibri en la càrrega de comunicacions pot congestionar la xarxa, incrementant la latència i disminuint el throughput, degradant el rendiment total del sistema. D'altra banda, les aplicacions paral·leles que s'executen sobre aquestes xarxes contenen etapes representatives durant la seva execució les quals permeten caracteritzar-les, a més d'extraure un comportament repetitiu que pot ser identificat en base a aquesta caracterització. Aquest treball presenta el Balanceig Predictiu de Encaminament Distribuït (PR-DRB), un nou mètode desenvolupat per controlar la congestió a la xarxa en forma gradual, basat en l'expansió de camins, la distribució de trànsit i càrrega efectiva actual per tal de mantenir una latència baixa. PR-DRB monitoritza la latència dels missatges en els encaminadors, pren decisions sobre els camins alternatius a utilitzar i registra la informació de la congestió sobre la base del patró de comunicacions detectat, utilitzant com a concepte base la repetitivitat de les aplicacions per després tornar a aplicar la millor solució quan aquest patró es repeteixi. Experiments de trànsit amb congestió van ser portats a terme per avaluar el rendiment del mètode, els quals van mostrar la bondat del mateix.Las aplicaciones paralelas actuales en los Clústeres requieren el uso de una red de interconexión para comunicar a todos los nodos de cómputo disponibles. El desbalance en la carga de comunicaciones puede congestionar la red, incrementando la latencia y disminuyendo el throughput, degradando el rendimiento total del sistema. Por otro lado, las aplicaciones paralelas que corren sobre estas redes contienen etapas representativas durante su ejecución las cuales permiten caracterizarlas, además de un comportamiento repetitivo que puede ser identificado en base a dicha caracterización. Este trabajo presenta el Balanceo Predictivo de Encaminamiento Distribuido (PR-DRB), un nuevo método desarrollado para controlar la congestión en la red en forma gradual; basado en la expansión de caminos, la distribución de tráfico y carga efectiva actual, a fin de mantener una latencia baja. PR-DRB monitorea la latencia de los mensajes en los encaminadores, toma decisiones sobre los caminos alternativos a utilizar y registra la información de la congestión en base al patrón de comunicaciones detectado, usando como concepto base la repetitividad de las aplicaciones para luego volver a aplicar la mejor solución cuando dicho patrón se repita. Experimentos de tráfico con congestión fueron llevados a cabo para evaluar el rendimiento del método, los cuales mostraron la bondad del mismo

Evaluating the communications capabilities of the generalized hypercube interconnection network

This thesis presents results of evaluating the communications capabilities of the generalized hypercube interconnection network. The generalized hypercube has outstanding topological properties, but it has not been implemented in a large scale because of its very high wiring complexity. For this reason, this network has not been studied extensively in the past. However, recent and expected technological advancements will soon render this network viable for massively parallel systems. We first present implementations of randomized many-to-all broadcasting and multicasting on generalized hypercubes, using as the basis the one-to-all broadcast algorithm presented in [3]. We test the proposed implementations under realistic communication traffic patterns and message generations, for the all-port model of communication. Our results show that the size of the intermediate message buffers has a significant effect on the total communication time, and this effect becomes very dramatic for large systems with large numbers of dimensions. We also propose a modification of this multicast algorithm that applies congestion control to improve its performance. The results illustrate a significant improvement in the total execution time and a reduction in the number of message contentions, and also prove that the generalized hypercube is a very versatile interconnection network

New fault-tolerant routing algorithms for k-ary n-cube networks

The interconnection network is one of the most crucial components in a multicomputer as it greatly influences the overall system performance. Networks belonging to the family of k-ary n-cubes (e.g., tori and hypercubes) have been widely adopted in practical machines due to their desirable properties, including a low diameter, symmetry, regularity, and ability to exploit communication locality found in many real-world parallel applications. A routing algorithm specifies how a message selects a path to cross from source to destination, and has great impact on network performance. Routing in fault-free networks has been extensively studied in the past. As the network size scales up the probability of processor and link failure also increases. It is therefore essential to design fault-tolerant routing algorithms that allow messages to reach their destinations even in the presence of faulty components (links and nodes). Although many fault-tolerant routing algorithms have been proposed for common multicomputer networks, e.g. hypercubes and meshes, little research has been devoted to developing fault-tolerant routing for well-known versions of k-ary n-cubes, such as 2 and 3- dimensional tori. Previous work on fault-tolerant routing has focused on designing algorithms with strict conditions imposed on the number of faulty components (nodes and links) or their locations in the network. Most existing fault-tolerant routing algorithms have assumed that a node knows either only the status of its neighbours (such a model is called local-information-based) or the status of all nodes (global-information-based). The main challenge is to devise a simple and efficient way of representing limited global fault information that allows optimal or near-optimal fault-tolerant routing. This thesis proposes two new limited-global-information-based fault-tolerant routing algorithms for k-ary n-cubes, namely the unsafety vectors and probability vectors algorithms. While the first algorithm uses a deterministic approach, which has been widely employed by other existing algorithms, the second algorithm is the first that uses probability-based fault- tolerant routing. These two algorithms have two important advantages over those already existing in the relevant literature. Both algorithms ensure fault-tolerance under relaxed assumptions, regarding the number of faulty components and their locations in the network. Furthermore, the new algorithms are more general in that they can easily be adapted to different topologies, including those that belong to the family of k-ary n-cubes (e.g. tori and hypercubes) and those that do not (e.g., generalised hypercubes and meshes). Since very little work has considered fault-tolerant routing in k-ary n-cubes, this study compares the relative performance merits of the two proposed algorithms, the unsafety and probability vectors, on these networks. The results reveal that for practical number of faulty nodes, both algorithms achieve good performance levels. However, the probability vectors algorithm has the advantage of being simpler to implement. Since previous research has focused mostly on the hypercube, this study adapts the new algorithms to the hypercube in order to conduct a comparative study against the recently proposed safety vectors algorithm. Results from extensive simulation experiments demonstrate that our algorithms exhibit superior performance in terms of reachability (chances of a message reaching its destination), deviation from optimality (average difference between minimum distance and actual routing distance), and looping (chances of a message continuously looping in the network without reaching destination) to the safety vectors

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