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

Petrinetze zum Entwurf selbststabilisierender Algorithmen

Edsger W. Dijkstra prägte im Jahr 1974 den Begriff Selbststabilisierung (self-stabilization) in der Informatik. Ein System ist selbststabilisierend, wenn es von jedem denkbaren Zustand aus nach einer endlichen Anzahl von Aktionen ein stabiles Verhalten erreicht. Im Mittelpunkt dieser Arbeit steht der Entwurf selbststabilisierender Algorithmen. Wir stellen eine Petrinetz-basierte Methode zum Entwurf selbststabilisierender Algorithmen vor. Wir validieren unsere Methode an mehreren Fallstudien: Ausgehend von algorithmischen Ideen existierender Algorithmen beschreiben wir jeweils die die schrittweise Entwicklung eines neuen Algorithmus. Dazu gehört ein neuer randomisierter selbststabilisierender Algorithmus zur Leader Election in einem Ring von Prozessoren. Dieser Algorithmus ist abgeleitet aus einem publizierten Algorithmus, von dem wir hier erstmals zeigen, daß er fehlerhaft arbeitet. Wir weisen die Speicherminimalität unseres Algorithmus nach. Ein weiteres Ergebnis ist der erste Algorithmus, der ohne Time-Out-Aktionen selbststabilisierenden Tokenaustausch in asynchronen Systemen realisiert. Petrinetze bilden einen einheitlichen formalen Rahmen für die Modellierung und Verifikation dieser Algorithmen.In 1974, Edsger W. Dijkstra suggested the notion of self-stabilization. A system is self-stabilizing if regardless of the initial state it eventually reaches a stable behaviour. This thesis focuses on the design of self-stabilizing algorithms. We introduce a new Petri net based method for the design of self-stabilizing algorithms. We validate our method on several case studies. In each of the case studies, our stepwise design starts from an algorithmic idea and leads to a new self-stabilizing algorithm. One of these algorithms is a new randomized self-stabilizing algorithm for leader election in a ring of processors. This algorithm is derived from a published algorithm which we show to be incorrect. We prove that our algorithm is space-minimal. A further result is the first algorithm for token-passing in a asynchronous environment which works without time-out actions. Petri nets form a unique framework for modelling and verification of these algorithms