Asynchronous neighborhood task synchronization

Faults are likely to occur in distributed systems. The motivation for designing self-stabilizing system is to be able to automatically recover from a faulty state. As per Dijkstra\u27s definition, a system is self-stabilizing if it converges to a desired state from an arbitrary state in a finite number of steps. The paradigm of self-stabilization is considered to be the most unified approach to designing fault-tolerant systems. Any type of faults, e.g., transient, process crashes and restart, link failures and recoveries, and byzantine faults, can be handled by a self-stabilizing system; Many applications in distributed systems involve multiple phases. Solving these applications require some degree of synchronization of phases. In this thesis research, we introduce a new problem, called asynchronous neighborhood task synchronization ( NTS ). In this problem, processes execute infinite instances of tasks, where a task consists of a set of steps. There are several requirements for this problem. Simultaneous execution of steps by the neighbors is allowed only if the steps are different. Every neighborhood is synchronized in the sense that all neighboring processes execute the same instance of a task. Although the NTS problem is applicable in nonfaulty environments, it is more challenging to solve this problem considering various types of faults. In this research, we will present a self-stabilizing solution to the NTS problem. The proposed solution is space optimal, fault containing, fully localized, and fully distributed. One of the most desirable properties of our algorithm is that it works under any (including unfair) daemon. We will discuss various applications of the NTS problem

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

Optimal torus exploration by oblivious robots

International audienceWe deal with a team of autonomous robots that are endowed with motion actuators and visibility sensors. Those robots are weak and evolve in a discrete environment. By weak, we mean that they are anonymous, uniform, unable to explicitly communicate, and oblivious. We first show that it is impossible to solve the terminating exploration of a simple torus of arbitrary size with less than 4 or 5 such robots, respectively depending on whether the algorithm is probabilistic or deterministic. Next, we propose in the SSYNC model a probabilistic solution for the terminating exploration of torus-shaped networks of size ℓ×L, where 7≤ℓ≤L, by a team of 4 such weak robots. So, this algorithm is optimal w.r.t. the number of robots

Design of robust asynchronous reconfigurable controllers for parallel synchronization using embedded graphs

PhD Thesis: This is a revised version received 24/5/16. The definitive version is the print copy in the Research Reserve Collection of the University LibrarySynchronization is a key System-on-Chip (SoC) design issue in modern technologies. As the number of operating points under consideration increases, specifications which are capable of altering key parameters such as the time available for synchronization and Mean Time Between Failures (MTBF) in response to input from the user/system become desirable. This thesis explores how a combination of parallelism and scheduling, referred to as wagging, can be utilized to construct schedulers for synchronizer designs which are capable of pooling the gain-bandwidth products of their composite devices, in order to satisfy this requirement. In this work, we explore the ways in which the areas of graph theory and reconfigurable hardware design can be applied to generate both combinational and sequential scheduler designs, which satisfy the behavior requirement above. Further to this point, this work illustrates that such a scheduler is primarily comprised of an interrupt subsystem, and a reconfigurable token ring. This thesis explores how both of these components can be controlled in absence of a clock signal, as well as the design challenges inherent to each part. The final noteworthy issue in this study is with regard to the flow control of data in a parallel synchronizer that incorporates a First-In First-Out (FIFO) buffer to decouple the reading and writing operations from each other. Such a structure incurs penalties if the data rates on both sides are not well matched. This work presents a method by which combinations of serial and parallel reading operations are used to minimize this mismatch

Decoupled synchronized states in networks of linearly coupled limit cycle oscillators

Networks of limit cycle oscillators can show intricate patterns of synchronization such as splay states and cluster synchronization. Here we analyze dynamical states that display a continuum of seemingly independent splay clusters. Each splay cluster is a block splay state consisting of sub-clusters of fully synchronized nodes with uniform amplitudes. Phases of nodes within a splay cluster are equally spaced, but nodes in different splay clusters have an arbitrary phase difference that can be fixed or evolve linearly in time. Such coexisting splay clusters form a decoupled state in that the dynamical equations become effectively decoupled between oscillators that can be physically coupled. We provide the conditions that allow the existence of particular decoupled states by using the eigendecomposition of the coupling matrix. Additionally, we provide an algorithm to search for admissible decoupled states using the external equitable partition and orbital partition considerations combined with symmetry groupoid formalism. Unlike previous studies, our approach is applicable when existence does not follow from symmetries alone and also illustrates the differences between adjacency and Laplacian coupling. We show that the decoupled state can be linearly stable for a substantial range of parameters using a simple eight-node cube network and its modifications as an example. We also demonstrate how the linear stability analysis of decoupled states can be simplified by taking into account the symmetries of the Jacobian matrix. Some network structures can support multiple decoupled patterns. To illustrate that, we show the variety of qualitatively different decoupled states that can arise on two-dimensional square and hexagonal lattices.Comment: 19 pages, 11 figure

Synchronization of coupled oscillators

Tese de mestrado em Física (Física Estatística e Não Linear), apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2010In this work we begin by introducing the Kuramoto model, constructing its solutions in the thermodynamic limit and showing the close connection between statistical physics and dynamical systems that lead to the main theoretical insights. The systematic study of a finite population of self sustained oscillators began in the first decade of this century. Unlike most of the papers we have found, we are not interested in the synchronization transition in itself but rather in phase locked patterns and their relation with frequency distribution among oscillators. The problem of stability, as we have already mentioned, experienced great advances in recent years. In a brief discussion we only address the problem of stability of the simplest solution allowed by the Kuramoto model: the incoherent solution. After that we introduce chimera states, first noticed by Kuramoto and his colleagues ([17] and references therein), in which the introduction of a non local coupling gives origin to a split in a region with synchronised oscillators and other with asynchronous one. Then we proceed by exploring the literature and the results with a finite number of oscillators, field explored with persistence only since mainly 2004 [29]. But here we are yet in Kuramoto framework which is abandoned, in a rigorous terminology, when we pursuit structured and not all-to-all coupling. Although we could introduce the same mean fields quantities if well defined in each situation, this did not help us in making sense of the results and is not an help in any analytical work. In our analysis of a ring of coupled oscillators we construct a space that allows us to relate the stable solutions with the eigenvectors of the laplacian of the graph in which we work.Neste trabalho começamos por introduzir o modelo de Kuramoto e realizar a construção das suas soluções no limite termodinâmico, mostrando a relação estreita entre física estatística e sistemas dinâmicos que levaram aos desenvolvimentos mais significativos. O estudo sistemático das populações de osciladores com um número finito de elementos começaram na primeira década deste século. Ao contrário de muitos trabalhos nesta área, não estamos interessados no processo de sincronização em si mas antes em padrões de fases que surgem em sincronia e sua relação com a distribuição das frequências próprias entre osciladores. O problema da estabilidade das soluções teve grandes desenvolvimento nos últimos anos. Numa breve análise apenas atendemos ao problema da estabilidade da mais simples solução do modelo de kuramoto: a solução incoerente. Depois introduzimos as quimeras, estados de sincronização descobertos por Kuramoto e que resultam da introdução de acoplamento não local, resultando numa separação entre uma zona de sincronia e uma zona assíncrona num mesmo sistema. Prosseguimos analisando a literatura e os resultados conhecidos com um número finito de osciladores, um campo explorado de forma sistemática apenas após, grosso modo, 2004. Abandonamos o modelo de Kuramoto quando passamos ao estudo de um número finito de osciladores e introduzimos acoplamentos estruturados saindo do acoplamento de todos com todos. Nesta situação as quantidades de campo médio, na origem do êxito do modelo de Kuramoto, ficam sem utilidade evidente, ainda que caso a caso se possam ainda definir e trabalhar. A nossa análise num círculo onde os osciladores acoplam entre primeiros vizinhos e construímos um espaço onde podemos visualizar a relação entre as soluções estáveis e os vectores próprios do operador Laplaciano do grafo associado

New Fault Tolerant Multicast Routing Techniques to Enhance Distributed-Memory Systems Performance

Distributed-memory systems are a key to achieve high performance computing and the most favorable architectures used in advanced research problems. Mesh connected multicomputer are one of the most popular architectures that have been implemented in many distributed-memory systems. These systems must support communication operations efficiently to achieve good performance. The wormhole switching technique has been widely used in design of distributed-memory systems in which the packet is divided into small flits. Also, the multicast communication has been widely used in distributed-memory systems which is one source node sends the same message to several destination nodes. Fault tolerance refers to the ability of the system to operate correctly in the presence of faults. Development of fault tolerant multicast routing algorithms in 2D mesh networks is an important issue. This dissertation presents, new fault tolerant multicast routing algorithms for distributed-memory systems performance using wormhole routed 2D mesh. These algorithms are described for fault tolerant routing in 2D mesh networks, but it can also be extended to other topologies. These algorithms are a combination of a unicast-based multicast algorithm and tree-based multicast algorithms. These algorithms works effectively for the most commonly encountered faults in mesh networks, f-rings, f-chains and concave fault regions. It is shown that the proposed routing algorithms are effective even in the presence of a large number of fault regions and large size of fault region. These algorithms are proved to be deadlock-free. Also, the problem of fault regions overlap is solved. Four essential performance metrics in mesh networks will be considered and calculated; also these algorithms are a limited-global-information-based multicasting which is a compromise of local-information-based approach and global-information-based approach. Data mining is used to validate the results and to enlarge the sample. The proposed new multicast routing techniques are used to enhance the performance of distributed-memory systems. Simulation results are presented to demonstrate the efficiency of the proposed algorithms