Self-stabilizing distributed algorithms for acyclic graphs

A self-stabilizing distributed system is a network of processors, which when started from an arbitrary and possibly illegal state, always returns to a legal state in a finite number of steps. Two self-stabilizing protocols for distributed systems are presented in this thesis. The first protocol topologically sorts the processors in a distributed system of directed acyclic graph (DAG) topology and uses this information to build a shortest path routing table in each node in the system to all accessible nodes from that node. The second protocol determines the rank of the individual processors in a distributed tree network based on the values possessed by them. Due to the self-stabilizing nature of these protocols the system can withstand transient errors and recover automatically from them

Optimal Collision/Conflict-free Distance-2 Coloring in Synchronous Broadcast/Receive Tree Networks

This article is on message-passing systems where communication is (a) synchronous and (b) based on the "broadcast/receive" pair of communication operations. "Synchronous" means that time is discrete and appears as a sequence of time slots (or rounds) such that each message is received in the very same round in which it is sent. "Broadcast/receive" means that during a round a process can either broadcast a message to its neighbors or receive a message from one of them. In such a communication model, no two neighbors of the same process, nor a process and any of its neighbors, must be allowed to broadcast during the same time slot (thereby preventing message collisions in the first case, and message conflicts in the second case). From a graph theory point of view, the allocation of slots to processes is know as the distance-2 coloring problem: a color must be associated with each process (defining the time slots in which it will be allowed to broadcast) in such a way that any two processes at distance at most 2 obtain different colors, while the total number of colors is "as small as possible". The paper presents a parallel message-passing distance-2 coloring algorithm suited to trees, whose roots are dynamically defined. This algorithm, which is itself collision-free and conflict-free, uses $\Delta + 1$ colors where $\Delta$ is the maximal degree of the graph (hence the algorithm is color-optimal). It does not require all processes to have different initial identities, and its time complexity is $O(d \Delta)$, where d is the depth of the tree. As far as we know, this is the first distributed distance-2 coloring algorithm designed for the broadcast/receive round-based communication model, which owns all the previous properties.Comment: 19 pages including one appendix. One Figur

Liveness of Randomised Parameterised Systems under Arbitrary Schedulers (Technical Report)

We consider the problem of verifying liveness for systems with a finite, but unbounded, number of processes, commonly known as parameterised systems. Typical examples of such systems include distributed protocols (e.g. for the dining philosopher problem). Unlike the case of verifying safety, proving liveness is still considered extremely challenging, especially in the presence of randomness in the system. In this paper we consider liveness under arbitrary (including unfair) schedulers, which is often considered a desirable property in the literature of self-stabilising systems. We introduce an automatic method of proving liveness for randomised parameterised systems under arbitrary schedulers. Viewing liveness as a two-player reachability game (between Scheduler and Process), our method is a CEGAR approach that synthesises a progress relation for Process that can be symbolically represented as a finite-state automaton. The method is incremental and exploits both Angluin-style L*-learning and SAT-solvers. Our experiments show that our algorithm is able to prove liveness automatically for well-known randomised distributed protocols, including Lehmann-Rabin Randomised Dining Philosopher Protocol and randomised self-stabilising protocols (such as the Israeli-Jalfon Protocol). To the best of our knowledge, this is the first fully-automatic method that can prove liveness for randomised protocols.Comment: Full version of CAV'16 pape

Découverte et allocation des ressources pour le traitement de requêtes dans les systèmes grilles

De nos jours, les systèmes Grille, grâce à leur importante capacité de calcul et de stockage ainsi que leur disponibilité, constituent l'un des plus intéressants environnements informatiques. Dans beaucoup de différents domaines, on constate l'utilisation fréquente des facilités que les environnements Grille procurent. Le traitement des requêtes distribuées est l'un de ces domaines où il existe de grandes activités de recherche en cours, pour transférer l'environnement sous-jacent des systèmes distribués et parallèles à l'environnement Grille. Dans le cadre de cette thèse, nous nous concentrons sur la découverte des ressources et des algorithmes d'allocation de ressources pour le traitement des requêtes dans les environnements Grille. Pour ce faire, nous proposons un algorithme de découverte des ressources pour le traitement des requêtes dans les systèmes Grille en introduisant le contrôle de topologie auto-stabilisant et l'algorithme de découverte des ressources dirigé par l'élection convergente. Ensuite, nous présentons un algorithme d'allocation des ressources, qui réalise l'allocation des ressources pour les requêtes d'opérateur de jointure simple par la génération d'un espace de recherche réduit pour les nœuds candidats et en tenant compte des proximités des candidats aux sources de données. Nous présentons également un autre algorithme d'allocation des ressources pour les requêtes d'opérateurs de jointure multiple. Enfin, on propose un algorithme d'allocation de ressources, qui apporte une tolérance aux pannes lors de l'exécution de la requête par l'utilisation de la réplication passive d'opérateurs à état. La contribution générale de cette thèse est double. Premièrement, nous proposons un nouvel algorithme de découverte de ressource en tenant compte des caractéristiques des environnements Grille. Nous nous adressons également aux problèmes d'extensibilité et de dynamicité en construisant une topologie efficace sur l'environnement Grille et en utilisant le concept d'auto-stabilisation, et par la suite nous adressons le problème de l'hétérogénéité en proposant l'algorithme de découverte de ressources dirigé par l'élection convergente. La deuxième contribution de cette thèse est la proposition d'un nouvel algorithme d'allocation des ressources en tenant compte des caractéristiques de l'environnement Grille. Nous abordons les problèmes causés par la grande échelle caractéristique en réduisant l'espace de recherche pour les ressources candidats. De ce fait nous réduisons les coûts de communication au cours de l'exécution de la requête en allouant des nœuds au plus près des sources de données. Et enfin nous traitons la dynamicité des nœuds, du point de vue de leur existence dans le système, en proposant un algorithme d'affectation des ressources avec une tolérance aux pannes.Grid systems are today's one of the most interesting computing environments because of their large computing and storage capabilities and their availability. Many different domains profit the facilities of grid environments. Distributed query processing is one of these domains in which there exists large amounts of ongoing research to port the underlying environment from distributed and parallel systems to the grid environment. In this thesis, we focus on resource discovery and resource allocation algorithms for query processing in grid environments. For this, we propose resource discovery algorithm for query processing in grid systems by introducing self-stabilizing topology control and converge-cast based resource discovery algorithms. Then, we propose a resource allocation algorithm, which realizes allocation of resources for single join operator queries by generating a reduced search space for the candidate nodes and by considering proximities of candidates to the data sources. We also propose another resource allocation algorithm for queries with multiple join operators. Lastly, we propose a fault-tolerant resource allocation algorithm, which provides fault-tolerance during the execution of the query by the use of passive replication of stateful operators. The general contribution of this thesis is twofold. First, we propose a new resource discovery algorithm by considering the characteristics of the grid environments. We address scalability and dynamicity problems by constructing an efficient topology over the grid environment using the self-stabilization concept; and we deal with the heterogeneity problem by proposing the converge-cast based resource discovery algorithm. The second main contribution of this thesis is the proposition of a new resource allocation algorithm considering the characteristics of the grid environment. We tackle the scalability problem by reducing the search space for candidate resources. We decrease the communication costs during the query execution by allocating nodes closer to the data sources. And finally we deal with the dynamicity of nodes, in terms of their existence in the system, by proposing the fault-tolerant resource allocation algorithm

An Adaptive Policy Management Approach to BGP Convergence

The Border Gateway Protocol (BGP) is the current inter-domain routing protocol used to exchange reachability information between Autonomous Systems (ASes) in the Internet. BGP supports policy-based routing which allows each AS to independently adopt a set of local policies that specify which routes it accepts and advertises from/to other networks, as well as which route it prefers when more than one route becomes available. However, independently chosen local policies may cause global conflicts, which result in protocol divergence. In this paper, we propose a new algorithm, called Adaptive Policy Management Scheme (APMS), to resolve policy conflicts in a distributed manner. Akin to distributed feedback control systems, each AS independently classifies the state of the network as either conflict-free or potentially-conflicting by observing its local history only (namely, route flaps). Based on the degree of measured conflicts (policy conflict-avoidance vs. -control mode), each AS dynamically adjusts its own path preferences—increasing its preference for observably stable paths over flapping paths. APMS also includes a mechanism to distinguish route flaps due to topology changes, so as not to confuse them with those due to policy conflicts. A correctness and convergence analysis of APMS based on the substability property of chosen paths is presented. Implementation in the SSF network simulator is performed, and simulation results for different performance metrics are presented. The metrics capture the dynamic performance (in terms of instantaneous throughput, delay, routing load, etc.) of APMS and other competing solutions, thus exposing the often neglected aspects of performance.National Science Foundation (ANI-0095988, EIA-0202067, ITR ANI-0205294