Assessing the Suitability of King Topologies for Interconnection Networks

In the late years many different interconnection networks have been used with two main tendencies. One is characterized by the use of high-degree routers with long wires while the other uses routers of much smaller degree. The latter rely on two-dimensional mesh and torus topologies with shorter local links. This paper focuses on doubling the degree of common 2D meshes and tori while still preserving an attractive layout for VLSI design. By adding a set of diagonal links in one direction, diagonal networks are obtained. By adding a second set of links, networks of degree eight are built, named king networks. This research presents a comprehensive study of these networks which includes a topological analysis, the proposal of appropriate routing procedures and an empirical evaluation. King networks exhibit a number of attractive characteristics which translate to reduced execution times of parallel applications. For example, the execution times NPB suite are reduced up to a 30 percent. In addition, this work reveals other properties of king networks such as perfect partitioning that deserves further attention for its convenient exploitation in forthcoming high-performance parallel systems

Interconnection Networks Based on Gaussian and Eisenstein-Jacobi Integers

Quotient rings of Gaussian and Eisenstein-Jacobi(EJ) integers can be deployed to construct interconnection networks with good topological properties. In this thesis, we propose deadlock-free deterministic and partially adaptive routing algo­rithms for hexagonal networks, one special class of EJ networks. Then we discuss higher dimensional Gaussian networks as an alternative to classical multidimen­sional toroidal networks. For this topology, we explore many properties including distance distribution and the decomposition of higher dimensional Gaussian net­ works into Hamiltonian cycles. In addition, we propose some efficient communi­cation algorithms for higher dimensional Gaussian networks including one-to-all broadcasting and shortest path routing. Simulation results show that the rout­ing algorithm proposed for higher dimensional Gaussian networks outperforms the routing algorithm of the corresponding torus networks with approximately the same number of nodes. These simulation results are expected since higher dimen­sional Gaussian networks have a smaller diameter and a smaller average message latency as compared with toroidal networks. Finally, we introduce a degree-three interconnection network obtained from pruning a Gaussian network. This network shows possible performance improve­ment over other degree-three networks since it has a smaller diameter compared to other degree-three networks. Many topological properties of degree-three pruned Gaussian network are explored. In addition, an optimal shortest path routing algorithm and a one-to-all broadcasting algorithm are given

SpiNNaker: Fault tolerance in a power- and area- constrained large-scale neuromimetic architecture

AbstractSpiNNaker is a biologically-inspired massively-parallel computer designed to model up to a billion spiking neurons in real-time. A full-fledged implementation of a SpiNNaker system will comprise more than 105 integrated circuits (half of which are SDRAMs and half multi-core systems-on-chip). Given this scale, it is unavoidable that some components fail and, in consequence, fault-tolerance is a foundation of the system design. Although the target application can tolerate a certain, low level of failures, important efforts have been devoted to incorporate different techniques for fault tolerance. This paper is devoted to discussing how hardware and software mechanisms collaborate to make SpiNNaker operate properly even in the very likely scenario of component failures and how it can tolerate system-degradation levels well above those expected

On Fault Resilient Network-on-Chip for Many Core Systems

Rapid scaling of transistor gate sizes has increased the density of on-chip integration and paved the way for heterogeneous many-core systems-on-chip, significantly improving the speed of on-chip processing. The design of the interconnection network of these complex systems is a challenging one and the network-on-chip (NoC) is now the accepted scalable and bandwidth efficient interconnect for multi-processor systems on-chip (MPSoCs). However, the performance enhancements of technology scaling come at the cost of reliability as on-chip components particularly the network-on-chip become increasingly prone to faults. In this thesis, we focus on approaches to deal with the errors caused by such faults. The results of these approaches are obtained not only via time-consuming cycle-accurate simulations but also by analytical approaches, allowing for faster and accurate evaluations, especially for larger networks. Redundancy is the general approach to deal with faults, the mode of which varies according to the type of fault. For the NoC, there exists a classification of faults into transient, intermittent and permanent faults. Transient faults appear randomly for a few cycles and may be caused by the radiation of particles. Intermittent faults are similar to transient faults, however, differing in the fact that they occur repeatedly at the same location, eventually leading to a permanent fault. Permanent faults by definition are caused by wires and transistors being permanently short or open. Generally, spatial redundancy or the use of redundant components is used for dealing with permanent faults. Temporal redundancy deals with failures by re-execution or by retransmission of data while information redundancy adds redundant information to the data packets allowing for error detection and correction. Temporal and information redundancy methods are useful when dealing with transient and intermittent faults. In this dissertation, we begin with permanent faults in NoC in the form of faulty links and routers. Our approach for spatial redundancy adds redundant links in the diagonal direction to the standard rectangular mesh topology resulting in the hexagonal and octagonal NoCs. In addition to redundant links, adaptive routing must be used to bypass faulty components. We develop novel fault-tolerant deadlock-free adaptive routing algorithms for these topologies based on the turn model without the use of virtual channels. Our results show that the hexagonal and octagonal NoCs can tolerate all 2-router and 3-router faults, respectively, while the mesh has been shown to tolerate all 1-router faults. To simplify the restricted-turn selection process for achieving deadlock freedom, we devised an approach based on the channel dependency matrix instead of the state-of-the-art Duato's method of observing the channel dependency graph for cycles. The approach is general and can be used for the turn selection process for any regular topology. We further use algebraic manipulations of the channel dependency matrix to analytically assess the fault resilience of the adaptive routing algorithms when affected by permanent faults. We present and validate this method for the 2D mesh and hexagonal NoC topologies achieving very high accuracy with a maximum error of 1%. The approach is very general and allows for faster evaluations as compared to the generally used cycle-accurate simulations. In comparison, existing works usually assume a limited number of faults to be able to analytically assess the network reliability. We apply the approach to evaluate the fault resilience of larger NoCs demonstrating the usefulness of the approach especially compared to cycle-accurate simulations. Finally, we concentrate on temporal and information redundancy techniques to deal with transient and intermittent faults in the router resulting in the dropping and hence loss of packets. Temporal redundancy is applied in the form of ARQ and retransmission of lost packets. Information redundancy is applied by the generation and transmission of redundant linear combinations of packets known as random linear network coding. We develop an analytic model for flexible evaluation of these approaches to determine the network performance parameters such as residual error rates and increased network load. The analytic model allows to evaluate larger NoCs and different topologies and to investigate the advantage of network coding compared to uncoded transmissions. We further extend the work with a small insight to the problem of secure communication over the NoC. Assuming large heterogeneous MPSoCs with components from third parties, the communication is subject to active attacks in the form of packet modification and drops in the NoC routers. Devising approaches to resolve these issues, we again formulate analytic models for their flexible and accurate evaluations, with a maximum estimation error of 7%

Efficient Connection Allocator in Network-on-Chip

As semiconductor technologies develop, a System-on-Chip (SoC) that integrates all semiconductor intellectual property (IP) cores is suggested and widely used for various applications. A traditional bus interconnection does not support transmitting data between IP cores for high performance. Because of this reason, a Network-on-Chip (NoC) has been suggested to provide an efficient and scalable solution to interconnect among all IP cores. High throughput and low latency have recently become the main important factors of NoC for achieving hard guaranteed real-time systems. In order to guarantee these factors and provide real-time service (i.e., Guaranteed Service, GS), the circuit switching (CS) approach has been widely utilized. The CS approach allocates mutually exclusive paths to transmitting data between different sources and destinations using dedicated NoC resources. However, the exclusive occupancy of the allocated path reduces the efficiency of the overall use of NoC resources. In order to solve this problem, Space-Division-Multiplexing (SDM) and Time-Division-Multiplexing (TDM) techniques have been suggested. SDM implements a circuit switching technique by assigning physically different NoC-links between different connections. Path connections of the SDM technique based on spatial resources assignment do not provide high scalability. In contrast to this, using virtual time slots for a path connection, the TDM technique can share physical links between exclusively established connections, thereby improving NoC path diversity. For all of these mentioned techniques, the factor that significantly impacts the system efficiency or performance scaling is how the path is allocated. In recent years, a dynamic connection allocation approach that can cope with highly dynamic workloads has been gaining attention due to the sudden and diverse demands of applications in real-time systems. There are two groups in the dynamic connection allocation approach. One is a distributed allocation technique, and the other is a centralized allocation technique. While distributed allocation exploits additional logic integrated into the NoC-routers for path search and allocation, the centralized approach makes use of a central unit to manage the path allocation problem. There are several algorithms for the centralized allocation technique. Trellis search-based allocation approach shows the best performance among them. Many algorithms related to centralized connection allocators have been studied extensively during the past decade. However, relatively little attention was paid to methodology in analyzing and evaluating the centralized connection allocation algorithms. In order to further develop the algorithms, it is necessary to understand and evaluate the centralized connection allocator by establishing a new analysis methodology. Thus, this thesis presents a performance analysis methodology for the trellis search-based allocation approach. Firstly, this thesis proposes a system model for analysis. Secondly, performance metrics are defined. Finally, the analysis results of each performance metric related to the trellis search-based allocation approach are presented. Through this analysis, the performance of the trellis search-based allocation approach can be accurately analyzed. Although a simulation is not performed, the upper limit of performance of the trellis search-based allocation approach can also be predicted through the analysis metrics. Additionally, we introduce the general formulation of the trellis search-based path allocation algorithm. The weight values among available paths through the branch metric and path metric are proposed to enable higher performance path connection. Furthermore, according to network size, topology, TDM, interface load delivery, and router internal storage, the performance of trellis search-based path allocation algorithms is also described. In the end, the Application Specific Instruction Processor (ASIP) hardware platform customized for the trellis search-based path allocation algorithm is presented. The shortest available and lowest-cost (SALC) path search algorithm is proposed to improve the success rate of path connection in the ASIP hardware platform. We evaluate the algorithm performance and implementation synthesis results. In order to realize the dynamic connection approach, a short execution cycle of ASIP time is essential. We develop several algorithms to achieve this short execution cycle. The first one is a rectangular region of search algorithm that allows adapting the size and form of path search region according to the particular source-destination positions and considers actual operational constraints. The average execution cycles for searching an optimum path are decreased because the unnecessary region for path-search is excluded. The second one is a path-spreading search algorithm that separates between involved routers and uninvolved routers in path search. The involved routers are selected and spread out from source to destination at each intermediate trellis-search process. The path-search overhead is considerably reduced due to the router involvements. The third one is a three-directional path-spreading search algorithm that eliminates one direction movement among four spreading movements. Because of this reason, the trellis search-based path connection algorithm, which omits the back-tracing process, can be implemented in the ASIP platform. Thus, the whole algorithm execution time can be halved. The last one is a moving regional path search algorithm that significantly reduces computation complexity by selecting a constant dimensional path-search region that affects performance and moving the region from source to destination. The moving regional path search algorithm achieves a considerable decrement of computational complexity.:1 Introduction 1 1.1 NoC-interconnect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Connection allocation in a Network-on-Chip 7 2.1 Circuit Switching NoCs . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Guaranteed Service in NoCs . . . . . . . . . . . . . . . . . . . 7 2.1.2 Spatial-Division-Multiplexing technique . . . . . . . . . . . . 8 2.1.3 Time-Division-Multiplexing technique . . . . . . . . . . . . . 10 2.2 System architectures employing circuit switching NoCs . . . . . . . . 11 2.2.1 Static and dynamic connection allocation . . . . . . . . . . . 12 2.2.2 Distributed connection allocation technique . . . . . . . . . . 14 2.2.3 Centralized connection allocation technique . . . . . . . . . . 16 2.2.4 Algorithms for centralized connection allocation . . . . . . . . 17 2.2.4.1 Software based run-time path allocation approach . 18 2.2.4.2 Trellis search-based allocation approach . . . . . . . 19 3 Performance analysis methodology for a centralized connection allocator 23 3.1 System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Performance metrics and analysis methodology . . . . . . . . . . . . 25 3.3 System simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 Trellis search-based path allocation algorithm 45 4.1 General formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.1.1 Trellis graph structure . . . . . . . . . . . . . . . . . . . . . . 45 4.1.2 Survivor path selection criterion . . . . . . . . . . . . . . . . . 52 ix 4.1.2.1 Branch metric and path metric . . . . . . . . . . . . 52 4.1.2.2 The shortest-available and lowest-cost path selection criterion . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2 Algorithm Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.2.1 Network topology . . . . . . . . . . . . . . . . . . . . . . . . 55 4.2.2 Network size . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.2.3 Time-Division-Multiplexing . . . . . . . . . . . . . . . . . . . 61 4.2.4 NoC interface load diversity . . . . . . . . . . . . . . . . . . . 63 4.2.5 The internal storage of the router . . . . . . . . . . . . . . . . 66 5 ASIP approach for Trellis search-based connection allocation 73 5.1 System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.1.1 Trellis search-based ASIP platform architecture . . . . . . . . 74 5.2 Algorithm for improving success rates of path connection . . . . . . . 81 5.2.1 SALC algorithm for Trellis search-based ASIP platform . . . . 81 5.2.2 Performance evaluation of the SALC algorithm . . . . . . . . 88 5.2.2.1 Simulation results . . . . . . . . . . . . . . . . . . . 88 5.2.2.2 Synthesis results . . . . . . . . . . . . . . . . . . . . 91 5.3 Algorithm for reducing path-search time . . . . . . . . . . . . . . . . 93 5.3.1 Rectangular regional path search algorithm . . . . . . . . . . 93 5.3.2 Path-spreading search algorithm . . . . . . . . . . . . . . . . 99 5.3.3 Three directional path-spreading search algorithm . . . . . . 108 5.3.4 Moving regional path search algorithm . . . . . . . . . . . . . 114 5.3.5 Performance evaluation . . . . . . . . . . . . . . . . . . . . . 123 5.3.5.1 Simulation results . . . . . . . . . . . . . . . . . . . 123 5.3.5.2 Synthesis results . . . . . . . . . . . . . . . . . . . . 126 6 Conclusion and Future work 131 6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Bibliography 13

From MARTE to Reconfigurable NoCs: A model driven design methodology

Due to the continuous exponential rise in SoC's design complexity, there is a critical need to find new seamless methodologies and tools to handle the SoC co-design aspects. We address this issue and propose a novel SoC co-design methodology based on Model Driven Engineering and the MARTE (Modeling and Analysis of Real-Time and Embedded Systems) standard proposed by Object Management Group, to raise the design abstraction levels. Extensions of this standard have enabled us to move from high level specifications to execution platforms such as reconfigurable FPGAs. In this paper, we present a high level modeling approach that targets modern Network on Chips systems. The overall objective: to perform system modeling at a high abstraction level expressed in Unified Modeling Language (UML); and afterwards, transform these high level models into detailed enriched lower level models in order to automatically generate the necessary code for final FPGA synthesis

A computation of the shortest paths in optimal two-dimensional circulant networks

Для семейства оптимальных двумерных циркулянтных сетей с аналитическим описанием получены две новые улучшенные версии алгоритма поиска кратчайших путей с константной оценкой сложности. Дано простое, основанное на геометрической модели циркулянтных графов, доказательство формул, используемых для алгоритма поиска кратчайших путей. Представлены алгоритмы парных обменов и даны их оценки для сетей на кристалле с топологией в виде рассмотренных графов. Новые версии алгоритма улучшают также предложенный ранее автором алгоритм поиска кратчайших путей для оптимальных обобщённых графов Петерсена с аналитическим описанием

Multi-Objective Routing for Distributed Controllers

A long-term goal of future naval shipboard power systems is the ability to manage energy flow with sufficient flexibility to accommodate future platform requirements such as better survivability, continuity, and support of pulsed and other demanding loads. To facilitate scalable, low-latency global distributed system control, each control module can include an integrated network interface connected through multiple channels onto a direct, multi-hop network topology. In this work, we focus on a 2D Torus, in which control nodes are arranged in a regular 2D grid, with each node connected through point-to-point connections to its four immediate neighbors. An important advantage of 2D Tori is their redundant topology where there is more than one minimal path between any source and destination as long as they do not share the same row or column in the grid. For the static, all-to-one traffic pattern used by a central controller, the number of minimal routing tables grows as O(N!N2). This dissertation presents a novel approach to generating routing tables that achieve two performance objectives: (1) minimal control period latency, the lower bound of which is the round trip latency of the messages exchanged between the controller and the node having the longest route, and (2) minimal latency jitter. Our approach relies on creating a large system of integer linear algebra equations describing (i) functionality of a network and (ii) constraints needed for perfect load balance and low jitter. We use Gurobi ILA solver to find a satisfying assignment of all boolean variables representing where packets are scheduled to be in a certain timeframe. Experimental results show that our software pipeline generates routing tables that (i) are guaranteed to have perfect load balance regardless of shape and size of the network and (ii) lower jitter than any of randomly generated routing tables which we simulated. Our software also has an option of generating routing tables that allow packets to follow non minimum hop count paths as well as being held in the source nodes for some time instead of immediately rushing to the master node. That helps packets avoid congested areas, and, as the results show, achieves up to 2x improvement in jitter

General broadcasting algorithms in one-port wormhole routed hypercubes

Wormhole routing has been accepted as an efficient switching mechanism in point-to-point interconnection networks. Here the network resource, i.e. node buffers and communication channels, are effectively utilized to deliver message across the network; We consider the problem of broadcasting a message in the hypercue equipped with the wormhole switching mechanism. The model is a generalization of an earlier work and considers a broadcast path-length of {dollar}m\ (1\leq m\leq n{dollar}) in the n-cube with a single-port communication capability. In this thesis, the scheme of e-cube and a Gray code path routing and intermediate reception capability have been adopted in order to solve the problem of broadcasting in one-port wormhole routed hypercubes. Two methods have been suggested; one is based on utilizing the Gray codes (Gray code path-based routing), while the other is based on the recursive partitioning of the cube (cube-based routing). The number of routing steps in both methods are compared to those in the previous results, as well as to the lower bounds derived based on the path-length m assumption. A cube-based and a path-based algorithm give {dollar}T(R)+(k\sb{c}+1)T(m){dollar} and {dollar}k\sb{G} +T(m){dollar} routing steps, respectively. By comparison with routing steps of both algorithms, the performance of the path-based algorithm shows better than that of the cube-based; The results of this work are significant and can be used for immediate implementation in contemporary machines most of which are equipped with wormhole routing and serial communication capability