Self-stabilizing protocol for anonymous oriented bi-directional rings under unfair distributed schedulers with a leader

We propose a self-stabilizing protocol for anonymous oriented bi-directional rings of any size under unfair distributed schedulers with a leader. The protocol is a randomized self-stabilizing, meaning that starting from an arbitrary configuration it converges (with probability 1) in finite time to a legitimate configuration (i.e. global system state) without the need for explicit exception handler of backward recovery. A fault may throw the system into an illegitimate configuration, but the system will autonomously resume a legitimate configuration, by regarding the current illegitimate configuration as an initial configuration, if the fault is transient. A self-stabilizing system thus tolerates any kind and any finite number of transient faults. The protocol can be used to implement an unfair distributed mutual exclusion in any ring topology network; Keywords: self-stabilizing protocol, anonymous oriented bi-directional ring, unfair distributed schedulers. Ring topology network, non-uniform and anonymous network, self-stabilization, fault tolerance, legitimate configuration

Weak vs. Self vs. Probabilistic Stabilization

Self-stabilization is a strong property that guarantees that a network always resume correct behavior starting from an arbitrary initial state. Weaker guarantees have later been introduced to cope with impossibility results: probabilistic stabilization only gives probabilistic convergence to a correct behavior. Also, weak stabilization only gives the possibility of convergence. In this paper, we investigate the relative power of weak, self, and probabilistic stabilization, with respect to the set of problems that can be solved. We formally prove that in that sense, weak stabilization is strictly stronger that self-stabilization. Also, we refine previous results on weak stabilization to prove that, for practical schedule instances, a deterministic weak-stabilizing protocol can be turned into a probabilistic self-stabilizing one. This latter result hints at more practical use of weak-stabilization, as such algorthms are easier to design and prove than their (probabilistic) self-stabilizing counterparts

Preserving Stabilization while Practically Bounding State Space

Stabilization is a key dependability property for dealing with unanticipated transient faults, as it guarantees that even in the presence of such faults, the system will recover to states where it satisfies its specification. One of the desirable attributes of stabilization is the use of bounded space for each variable. In this paper, we present an algorithm that transforms a stabilizing program that uses variables with unbounded domain into a stabilizing program that uses bounded variables and (practically bounded) physical time. While non-stabilizing programs (that do not handle transient faults) can deal with unbounded variables by assigning large enough but bounded space, stabilizing programs that need to deal with arbitrary transient faults cannot do the same since a transient fault may corrupt the variable to its maximum value. We show that our transformation algorithm is applicable to several problems including logical clocks, vector clocks, mutual exclusion, leader election, diffusing computations, Paxos based consensus, and so on. Moreover, our approach can also be used to bound counters used in an earlier work by Katz and Perry for adding stabilization to a non-stabilizing program. By combining our algorithm with that earlier work by Katz and Perry, it would be possible to provide stabilization for a rich class of problems, by assigning large enough but bounded space for variables.Comment: Moved some content from the Appendix to the main paper, added some details to the transformation algorithm and to its descriptio

Self-Stabilizing Message Routing in Mobile ad hoc Networks

We present a self-stabilizing algorithm for routing messages between arbitrary pairs of nodes in a mobile ad hoc network. Our algorithm assumes the availability of a reliable GPS service, which supplies mobile nodes with accurate information about real time and about their own geographical locations. The GPS service provides an external, shared source of consistency for mobile nodes, allowing them to label and timestamp messages, and thereby aiding in recovery from failures. Our algorithm utilizes a Virtual Infrastructure programming abstraction layer, consisting of mobile client nodes, virtual stationary timed machines called Virtual Stationary Automata (VSAs), and a local broadcast service connecting VSAs and mobile clients. VSAs are associated with predetermined regions in the plane, and are emulated in a self-stabilizing manner by the mobile nodes. VSAs are relatively stable in the face of node mobility and failure, and can be used to simplify algorithm development for mobile networks. Our routing algorithm consists of three subalgorithms: [(1)] a VSA-to-VSA geographical routing algorithm, [2] a mobile client location management algorithm, and [3] the main algorithm, which utilizes both location management and geographical routing. All three subalgorithms are self-stabilizing, and consequently, the entire algorithm is also self-stabilizing

Contributions à la réplication de données dans les systèmes distribués à grande échelle

Data replication is a key mechanism for building a reliable and efficient data management system. Indeed, by keeping several replicas for each piece of data, it is possible to improve durability. Furthermore, well-placed copies reduce data accesstime. However, having multiple copies for a single piece of data creates consistency problems when the data is updated. Over the last years, I made contributions related to these three aspects: data durability, data access performance and data consistency. RelaxDHT and SPLAD enhance data durability by placing data copies smartly. Caju, AREN and POPS reduce access time by improving data locality and by taking popularity into account. To enhance data lookup performance, DONUT creates efficient shortcuts taking data distribution into account. Finally, in the replicated database context, Gargamel parallelizes independent transactions only, improving database performance and avoiding aborting transactions. My research has been carried out in collaboration with height PhD students, four of which have defended. In my future work, I plan to extend these contributions by (i) designing a storage system tailored for MMOGs, which are very demanding, and (ii) designing a data management system that is able to re-distribute data automatically in order to scale the number of servers up and down according to the changing workload, leading to a greener data management.La réplication de données est une technique clé pour permettre aux systèmes de gestion de données distribués à grande échelle d'offrir un stockage fiable et performant. Comme il gère un nombre suffisant de copies de chaque donnée, le système peut améliorer la pérennité. De plus, la présence de copies bien placées réduit les temps d'accès. Cependant, cette même existence de plusieurs copies pose des problèmes de cohérence en cas de modification. Ces dernières années, mes contributions ont porté sur ces trois aspects liés à la réplication de données: la pérennité des données, la performance desaccès et la gestion de la cohérence. RelaxDHT et SPLAD permettent d'améliorer la pérennité des données en jouant sur le placement des copies. Caju, AREN et POPS permettent de réduire les temps d'accès aux données en améliorant la localité et en prenant en compte la popularité. Pour accélérer la localisation des copies, DONUT crée des raccourcis efficaces prenant en compte la distribution des données. Enfin, dans le contexte des bases de données répliquées,Gargamel permet de ne paralléliser que les transactions qui sont indépendantes, améliorant ainsi les performances et évitant tout abandon de transaction pour cause de conflit. Ces travaux ont été réalisés avec huit étudiants en thèse dont quatre ont soutenu. Pour l'avenir, je me propose d'étendre ces travaux, d'une part en concevant un système de gestion de données pour les MMOGs, une classe d'application particulièrement exigeante; et, d'autre part, en concevant des mécanismes de gestion de données permettant de n'utiliser que la quantité strictement nécessaire de ressources, en redistribuant dynamiquement les données en fonction des besoins, un pas vers une gestion plus écologique des données

Stabilization, Safety, and Security of Distributed Systems, 9th International Symposium, SSS 2007, Paris, France, November 14-16, 2007, Proceedings

International audienc

Pulse propagation, graph cover, and packet forwarding

We study distributed systems, with a particular focus on graph problems and fault tolerance. Fault-tolerance in a microprocessor or even System-on-Chip can be improved by using a fault-tolerant pulse propagation design. The existing design TRIX achieves this goal by being a distributed system consisting of very simple nodes. We show that even in the typical mode of operation without faults, TRIX performs significantly better than a regular wire or clock tree: Statistical evaluation of our simulated experiments show that we achieve a skew with standard deviation of O(log log H), where H is the height of the TRIX grid. The distance-r generalization of classic graph problems can give us insights on how distance affects hardness of a problem. For the distance-r dominating set problem, we present both an algorithmic upper and unconditional lower bound for any graph class with certain high-girth and sparseness criteria. In particular, our algorithm achieves a O(r·f(r))-approximation in time O(r), where f is the expansion function, which correlates with density. For constant r, this implies a constant approximation factor, in constant time. We also show that no algorithm can achieve a (2r + 1 − δ)-approximation for any δ > 0 in time O(r), not even on the class of cycles of girth at least 5r. Furthermore, we extend the algorithm to related graph cover problems and even to a different execution model. Furthermore, we investigate the problem of packet forwarding, which addresses the question of how and when best to forward packets in a distributed system. These packets are injected by an adversary. We build on the existing algorithm OED to handle more than a single destination. In particular, we show that buffers of size O(log n) are sufficient for this algorithm, in contrast to O(n) for the naive approach.Wir untersuchen verteilte Systeme, mit besonderem Augenmerk auf Graphenprobleme und Fehlertoleranz. Fehlertoleranz auf einem System-on-Chip (SoC) kann durch eine fehlertolerante Puls- Weiterleitung verbessert werden. Das bestehende Puls-Weiterleitungs-System TRIX toleriert Fehler indem es ein verteiltes System ist das nur aus sehr einfachen Knoten besteht. Wir zeigen dass selbst im typischen, fehlerfreien Fall TRIX sich weitaus besser verhält als man naiverweise erwarten würde: Statistische Analysen unserer simulierten Experimente zeigen, dass der Verzögerungs-Unterschied eine Standardabweichung von lediglich O(log logH) erreicht, wobei H die Höhe des TRIX-Netzes ist. Das Generalisieren einiger klassischer Graphen-Probleme auf Distanz r kann uns neue Erkenntnisse bescheren über den Zusammenhang zwischen Distanz und Komplexität eines Problems. Für das Problem der dominierenden Mengen auf Distanz r zeigen wir sowohl eine algorithmische obere Schranke als auch eine bedingungsfreie untere Schranke für jede Klasse von Graphen, die bestimmte Eigenschaften an Umfang und Dichte erfüllt. Konkret erreicht unser Algorithmus in Zeit O(r) eine Annäherungsgüte von O(r · f(r)). Für konstante r bedeutet das, dass der Algorithmus in konstanter Zeit eine Annäherung konstanter Güte erreicht. Weiterhin zeigen wir, dass kein Algorithmus in Zeit O(r) eine Annäherungsgüte besser als 2r + 1 erreichen kann, nicht einmal in der Klasse der Kreis-Graphen von Umfang mindestens 5r. Weiterhin haben wir das Paketweiterleitungs-Problem untersucht, welches sich mit der Frage beschäftigt, wann genau Pakete in einem verteilten System idealerweise weitergeleitetwerden sollten. Die Paketewerden dabei von einem Gegenspieler eingefügt. Wir bauen auf dem existierenden Algorithmus OED auf, um mehr als ein Paket-Ziel beliefern zu können. Dadurch zeigen wir, dass Paket-Speicher der Größe O(log n) für dieses Problem ausreichen, im Gegensatz zu den Paket-Speichern der Größe O(n) die für einen naiven Ansatz nötig wären