A contribution to the evaluation and optimization of networks reliability

L’évaluation de la fiabilité des réseaux est un problème combinatoire très complexe qui nécessite des moyens de calcul très puissants. Plusieurs méthodes ont été proposées dans la littérature pour apporter des solutions. Certaines ont été programmées dont notamment les méthodes d’énumération des ensembles minimaux et la factorisation, et d’autres sont restées à l’état de simples théories. Cette thèse traite le cas de l’évaluation et l’optimisation de la fiabilité des réseaux. Plusieurs problèmes ont été abordés dont notamment la mise au point d’une méthodologie pour la modélisation des réseaux en vue de l’évaluation de leur fiabilités. Cette méthodologie a été validée dans le cadre d’un réseau de radio communication étendu implanté récemment pour couvrir les besoins de toute la province québécoise. Plusieurs algorithmes ont aussi été établis pour générer les chemins et les coupes minimales pour un réseau donné. La génération des chemins et des coupes constitue une contribution importante dans le processus d’évaluation et d’optimisation de la fiabilité. Ces algorithmes ont permis de traiter de manière rapide et efficace plusieurs réseaux tests ainsi que le réseau de radio communication provincial. Ils ont été par la suite exploités pour évaluer la fiabilité grâce à une méthode basée sur les diagrammes de décision binaire. Plusieurs contributions théoriques ont aussi permis de mettre en place une solution exacte de la fiabilité des réseaux stochastiques imparfaits dans le cadre des méthodes de factorisation. A partir de cette recherche plusieurs outils ont été programmés pour évaluer et optimiser la fiabilité des réseaux. Les résultats obtenus montrent clairement un gain significatif en temps d’exécution et en espace de mémoire utilisé par rapport à beaucoup d’autres implémentations. Mots-clés: Fiabilité, réseaux, optimisation, diagrammes de décision binaire, ensembles des chemins et coupes minimales, algorithmes, indicateur de Birnbaum, systèmes de radio télécommunication, programmes.Efficient computation of systems reliability is required in many sensitive networks. Despite the increased efficiency of computers and the proliferation of algorithms, the problem of finding good and quickly solutions in the case of large systems remains open. Recently, efficient computation techniques have been recognized as significant advances to solve the problem during a reasonable period of time. However, they are applicable to a special category of networks and more efforts still necessary to generalize a unified method giving exact solution. Assessing the reliability of networks is a very complex combinatorial problem which requires powerful computing resources. Several methods have been proposed in the literature. Some have been implemented including minimal sets enumeration and factoring methods, and others remained as simple theories. This thesis treats the case of networks reliability evaluation and optimization. Several issues were discussed including the development of a methodology for modeling networks and evaluating their reliabilities. This methodology was validated as part of a radio communication network project. In this work, some algorithms have been developed to generate minimal paths and cuts for a given network. The generation of paths and cuts is an important contribution in the process of networks reliability and optimization. These algorithms have been subsequently used to assess reliability by a method based on binary decision diagrams. Several theoretical contributions have been proposed and helped to establish an exact solution of the stochastic networks reliability in which edges and nodes are subject to failure using factoring decomposition theorem. From this research activity, several tools have been implemented and results clearly show a significant gain in time execution and memory space used by comparison to many other implementations. Key-words: Reliability, Networks, optimization, binary decision diagrams, minimal paths set and cuts set, algorithms, Birnbaum performance index, Networks, radio-telecommunication systems, programs

A logic-based analysis of Dempster-Shafer theory

AbstractDempster-Shafer (DS) theory is formulated in terms of propositional logic, using the implicit notion of provability underlying DS theory. Dempster-Shafer theory can be modeled in terms of propositional logic by the tuple (Σ, ϱ), where Σ is a set of propositional clauses and ϱ is an assignment of mass to each clause Σi ϵ Σ. It is shown that the disjunction of minimal support clauses for a clause Σi with respect to a set Σ of propositional clauses, ξ(Σi, Σ), when represented in terms of symbols for the ϱi 's, corresponds to a symbolic representation of the Dempster-Shafer belief function for δi. The combination of Belief functions using Dempster's rule of combination corresponds to a combination of the corresponding support clauses. The disjointness of the Boolean formulas representing DS Belief functions is shown to be necessary. Methods of computing disjoint formulas using network reliability techniques are discussed.In addition, the computational complexity of deriving DS Belief functions, including that of the logic-based methods which are the focus of this paper, is explored. Because of intractability even for moderately sized problem instances, efficient approximation methods are proposed for such computations. Finally, implementations of DS theory based on domain restrictions of DS theory, hypertree embeddings, and the ATMS, are examined

Reliability Analysis of the Hypercube Architecture.

This dissertation presents improved techniques for analyzing network-connected (NCF), 2-connected (2CF), task-based (TBF), and subcube (SF) functionality measures in a hypercube multiprocessor with faulty processing elements (PE) and/or communication elements (CE). These measures help study system-level fault tolerance issues and relate to various application modes in the hypercube. Solutions discussed in the text fall into probabilistic and deterministic models. The probabilistic measure assumes a stochastic graph of the hypercube where PE\u27s and/or CE\u27s may fail with certain probabilities, while the deterministic model considers that some system components are already failed and aims to determine the system functionality. For probabilistic model, MIL-HDBK-217F is used to predict PE and CE failure rates for an Intel iPSC system. First, a technique called CAREL is presented. A proof of its correctness is included in an appendix. Using the shelling ordering concept, CAREL is shown to solve the exact probabilistic NCF measure for a hypercube in time polynomial in the number of spanning trees. However, this number increases exponentially in the hypercube dimension. This dissertation, then, aims to more efficiently obtain lower and upper bounds on the measures. Algorithms, presented in the text, generate tighter bounds than had been obtained previously and run in time polynomial in the cube dimension. The proposed algorithms for probabilistic 2CF measure consider PE and/or CE failures. In attempting to evaluate deterministic measures, a hybrid method for fault tolerant broadcasting in the hypercube is proposed. This method combines the favorable features of redundant and non-redundant techniques. A generalized result on the deterministic TBF measure for the hypercube is then described. Two distributed algorithms are proposed to identify the largest operational subcubes in a hypercube C\sb{n} with faulty PE\u27s. Method 1, called LOS1, requires a list of faulty components and utilizes the CMB operator of CAREL to solve the problem. In case the number of unavailable nodes (faulty or busy) increases, an alternative distributed approach, called LOS2, processes m available nodes in O(mn) time. The proposed techniques are simple and efficient

On the Implementation of the Probabilistic Logic Programming Language ProbLog

The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension of Prolog motivated by the mining of large biological networks. In ProbLog, facts can be labeled with probabilities. These facts are treated as mutually independent random variables that indicate whether these facts belong to a randomly sampled program. Different kinds of queries can be posed to ProbLog programs. We introduce algorithms that allow the efficient execution of these queries, discuss their implementation on top of the YAP-Prolog system, and evaluate their performance in the context of large networks of biological entities.Comment: 28 pages; To appear in Theory and Practice of Logic Programming (TPLP

Reliability and performance analysis of multi-state systems based on analytical load flow considerations

The last three decades have been marked by the advent of various analytical and simulation algorithms, enhanced for the reliability evaluation of multi-state systems. Though the latter are widely believed to be the most applicable to realistic systems, they impose a greater degree of computational burden. Consequently, they have been outshone, especially in structural optimization, redundancy allocation and maintenance optimization problems. On the flip side, analytical techniques are constrained by their various unique limitations. Prominent amongst these being, inapplicability to multiple output systems with competing demand and reliance on the enumeration of system path or cut sets prior to analysis. The development, therefore, of a single approach that addresses these limitations is desirable. In this paper, the fact that most engineering systems satisfy the flow conservation principle and can be regarded as multi-state flow networks is exploited. An analytical algorithm that efficiently derives all the possible system performance levels and uses basic probability algebra to estimate their probabilities of occurrence is developed. The algorithm is enhanced to support systems with flow losses, Common-Cause Failures (CCF), and minimal system reconfigurations. These attributes, as applied to two case studies, ensure the limitations of existing techniques are overcome

Simplification of inclusion-exclusion on intersections of unions with application to network systems reliability

Reliability of safety-critical systems is an important issue in system engineering and in most practical situations the reliability of a non series-parallel network system has to be calculated. Some methods for calculating reliability use the probability principle of inclusion-exclusion. When dealing with complex networks, this leads to very long mathematical expressions which are usually computationally very expensive to calculate. In this paper, we provide a new expression to simplify the probability principle of inclusion-exclusion's formula for intersections of unions, which appear when calculating reliability on non series parallel network systems. This new expression has much less terms, which reduces enormously the computational cost. We also show that the general form of the probability principle of inclusion-exclusion's formula has double exponential complexity whereas the simplified form has only exponential complexity with a linear exponent. Finally, we illustrate how to use this result when calculating the reliability of a door management system in aircraft engineering

Investigation of the robustness of star graph networks

The star interconnection network has been known as an attractive alternative to n-cube for interconnecting a large number of processors. It possesses many nice properties, such as vertex/edge symmetry, recursiveness, sublogarithmic degree and diameter, and maximal fault tolerance, which are all desirable when building an interconnection topology for a parallel and distributed system. Investigation of the robustness of the star network architecture is essential since the star network has the potential of use in critical applications. In this study, three different reliability measures are proposed to investigate the robustness of the star network. First, a constrained two-terminal reliability measure referred to as Distance Reliability (DR) between the source node u and the destination node I with the shortest distance, in an n-dimensional star network, Sn, is introduced to assess the robustness of the star network. A combinatorial analysis on DR especially for u having a single cycle is performed under different failure models (node, link, combined node/link failure). Lower bounds on the special case of the DR: antipode reliability, are derived, compared with n-cube, and shown to be more fault-tolerant than n-cube. The degradation of a container in a Sn having at least one operational optimal path between u and I is also examined to measure the system effectiveness in the presence of failures under different failure models. The values of MTTF to each transition state are calculated and compared with similar size containers in n-cube. Meanwhile, an upper bound under the probability fault model and an approximation under the fixed partitioning approach on the ( n-1)-star reliability are derived, and proved to be similarly accurate and close to the simulations results. Conservative comparisons between similar size star networks and n-cubes show that the star network is more robust than n-cube in terms of ( n-1)-network reliability