Discrete and hybrid methods for the diagnosis of distributed systems

Many important activities of modern society rely on the proper functioning of complex systems such as electricity networks, telecommunication networks, manufacturing plants and aircrafts. The supervision of such systems must include strong diagnosis capability to be able to effectively detect the occurrence of faults and ensure appropriate corrective measures can be taken in order to recover from the faults or prevent total failure. This thesis addresses issues in the diagnosis of large complex systems. Such systems are usually distributed in nature, i.e. they consist of many interconnected components each having their own local behaviour. These components interact together to produce an emergent global behaviour that is complex. As those systems increase in complexity and size, their diagnosis becomes increasingly challenging. In the first part of this thesis, a method is proposed for diagnosis on distributed systems that avoids a monolithic global computation. The method, based on converting the graph of the system into a junction tree, takes into account the topology of the system in choosing how to merge local diagnoses on the components while still obtaining a globally consistent result. The method is shown to work well for systems with tree or near-tree structures. This method is further extended to handle systems with high clustering by selectively ignoring some connections that would still allow an accurate diagnosis to be obtained. A hybrid system approach is explored in the second part of the thesis, where continuous dynamics information on the system is also retained to help better isolate or identify faults. A hybrid system framework is presented that models both continuous dynamics and discrete evolution in dynamical systems, based on detecting changes in the fundamental governing dynamics of the system rather than on residual estimation. This makes it possible to handle systems that might not be well characterised and where parameter drift is present. The discrete aspect of the hybrid system model is used to derive diagnosability conditions using indicator functions for the detection and isolation of multiple, arbitrary sequential or simultaneous events in hybrid dynamical networks. Issues with diagnosis in the presence of uncertainty in measurements due sensor or actuator noise are addressed. Faults may generate symptoms that are in the same order of magnitude as the latter. The use of statistical techniques,within a hybrid system framework, is proposed to detect these elusive fault symptoms and translate this information into probabilities for the actual operational mode and possibility of transition between modes which makes it possible to apply probabilistic analysis on the system to handle the underlying uncertainty present

A Local Diagnosis Algorithm for Hypercube-like Networks under the BGM Diagnosis Model

System diagnosis is process of identifying faulty nodes in a system. An efficient diagnosis is crucial for a multiprocessor system. The BGM diagnosis model is a modification of the PMC diagnosis model, which is a test-based diagnosis. In this paper, we present a specific structure and propose an algorithm for diagnosing a node in a system under the BGM model. We also give a polynomial-time algorithm that a node in a hypercube-like network can be diagnosed correctly in three test rounds under the BGM diagnosis model

Random induced subgraphs of Cayley graphs induced by transpositions

In this paper we study random induced subgraphs of Cayley graphs of the symmetric group induced by an arbitrary minimal generating set of transpositions. A random induced subgraph of this Cayley graph is obtained by selecting permutations with independent probability, $\lambda_n$. Our main result is that for any minimal generating set of transpositions, for probabilities $\lambda_n=\frac{1+\epsilon_n}{n-1}$ where $n^{-{1/3}+\delta}\le \epsilon_n0$, a random induced subgraph has a.s. a unique largest component of size $\wp(\epsilon_n)\frac{1+\epsilon_n}{n-1}n!$, where $\wp(\epsilon_n)$ is the survival probability of a specific branching process.Comment: 18 pages, 1 figur

Multilevel distributed diagnosis and the design of a distributed network fault detection system based on the SNMP protocol.

In this thesis, we propose a new distributed diagnosis algorithm using the multilevel paradigm. This algorithm is a generalization of both the ADSD and Hi-ADSD algorithms. We present all details of the design and implementation of this multilevel adaptive distributed diagnosis algorithm called the ML-ADSD algorithm. We also present extensive simulation results comparing the performance of these three algorithms.In 1967, Preparata, Metze and Chien proposed a model and a framework for diagnosing faulty processors in a multiprocessor system. To exploit the inherent parallelism available in a multiprocessor system and thereby improving fault tolerance, Kuhl and Reddy, in 1980, pioneered a new area of research known as distributed system level diagnosis. Following this pioneering work, in 1991, Bianchini and Buskens proposed an adaptive distributed algorithm to diagnose fully connected networks. This algorithm called the ADSD algorithm has a diagnosis latency of O(N) testing rounds for a network with N nodes. With a view to improving the diagnosis latency of the ADSD algorithm, in 1998 Duarte and Nanya proposed a hierarchical distributed diagnosis algorithm for fully connected networks. This algorithm called the Hi-ADSD algorithm has a diagnosis latency of O(log2N) testing rounds. The Hi-ADSD algorithm can be viewed as a generalization of the ADSD algorithm.In all cases, the time required by the ML-ADSD algorithm is better than or the same as for the Hi-ADSD algorithm. The performance of the ML-ADSD algorithm can be improved by an appropriate choice of the number of clusters and the number of levels. Also, the ML-ADSD algorithm is scalable in the sense that only some minor modifications will be required to adapt the algorithm to networks of varying sizes. This property is not shared by the Hi-ADSD algorithm. The primary application of our research is to develop and implement a prototype network fault detection/monitoring system by integrating the ML-ADSD algorithm into a SNMP-based (Simple Network Management Protocol) fault management system. We report the details of the design and implementation of such a distributed network fault detection system

Scalable fault management architecture for dynamic optical networks : an information-theoretic approach

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.MIT Barker Engineering Library copy: printed in pages.Also issued printed in pages.Includes bibliographical references (leaves 255-262).All-optical switching, in place of electronic switching, of high data-rate lightpaths at intermediate nodes is one of the key enabling technologies for economically scalable future data networks. This replacement of electronic switching with optical switching at intermediate nodes, however, presents new challenges for fault detection and localization in reconfigurable all-optical networks. Presently, fault detection and localization techniques, as implemented in SONET/G.709 networks, rely on electronic processing of parity checks at intermediate nodes. If similar techniques are adapted to all-optical reconfigurable networks, optical signals need to be tapped out at intermediate nodes for parity checks. This additional electronic processing would break the all-optical transparency paradigm and thus significantly diminish the cost advantages of all-optical networks. In this thesis, we propose new fault-diagnosis approaches specifically tailored to all-optical networks, with an objective of keeping the diagnostic capital expenditure and the diagnostic operation effort low. Instead of the aforementioned passive monitoring paradigm based on parity checks, we propose a proactive lightpath probing paradigm: optical probing signals are sent along a set of lightpaths in the network, and network state (i.e., failure pattern) is then inferred from testing results of this set of end-to-end lightpath measurements. Moreover, we assume that a subset of network nodes (up to all the nodes) is equipped with diagnostic agents - including both transmitters/receivers for probe transmission/detection and software processes for probe management to perform fault detection and localization. The design objectives of this proposed proactive probing paradigm are two folded: i) to minimize the number of lightpath probes to keep the diagnostic operational effort low, and ii) to minimize the number of diagnostic hardware to keep the diagnostic capital expenditure low.(cont.) The network fault-diagnosis problem can be mathematically modeled with a group testing-over-graphs framework. In particular, the network is abstracted as a graph in which the failure status of each node/link is modeled with a random variable (e.g. Bernoulli distribution). A probe over any path in the graph results in a value, defined as the probe syndrome, which is a function of all the random variables associated in that path. A network failure pattern is inferred through a set of probe syndromes resulting from a set of optimally chosen probes. This framework enriches the traditional group-testing problem by introducing a topological structure, and can be extended to model many other network-monitoring problems (e.g., packet delay, packet drop ratio, noise and etc) by choosing appropriate state variables. Under the group-testing-over-graphs framework with a probabilistic failure model, we initiate an information-theoretic approach to minimizing the average number of lightpath probes to identify all possible network failure patterns. Specifically, we have established an isomorphic mapping between the fault-diagnosis problem in network management and the source-coding problem in Information Theory. This mapping suggests that the minimum average number of lightpath probes required is lower bounded by the information entropy of the network state and efficient source-coding algorithms (e.g. the run-length code) can be translated into scalable fault-diagnosis schemes under some additional probe feasibility constraint. Our analytical and numerical investigations yield a guideline for designing scalable fault-diagnosis algorithms: each probe should provide approximately 1-bit of state information, and thus the total number of probes required is approximately equal to the entropy of the network state.(cont.) To address the hardware cost of diagnosis, we also developed a probabilistic analysis framework to characterize the trade-off between hardware cost (i.e., the number of nodes equipped with Tx/Rx pairs) and diagnosis capability (i.e., the probability of successful failure detection and localization). Our results suggest that, for practical situations, the hardware cost can be reduced significantly by accepting a small amount of uncertainty about the failure status.by Yonggang Wen.Ph.D