Publisher Summary Network reliability encompasses a range of issues related to the design and analysis of networks which are subject to the random failure of their components. Relatively simple, and yet quite general, network models can represent a variety of applied problem environments. Network classes for which the models are discussed are particularly appropriate include data communications networks, voice communications networks, transportation networks, computer architectures, electrical power networks and command and control systems. The ultimate objective of research in the area of network reliability is to give design engineers procedures to enhance their ability to design networks for which reliability is an important consideration. Ideally, one would like to generate network design models and algorithms which take as input the characteristics of network components as well as network design criteria, and produce as output an "optimal" network design.

Chapter 11 Network reliability

We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the multilayer setting. Using random sampling techniques, we develop polynomial-time approximation algorithms for the failure polynomial. Our approach gives an approximate expression for reliability as a function of the link failure probability, eliminating the need to resample for different values of the failure probability. Furthermore, it gives insight on how the routings of the logical topology on the physical topology impact network reliability. We show that maximizing the min cut of the (layered) network maximizes reliability in the low-failure-probability regime. Based on this observation, we develop algorithms for routing the logical topology to maximize reliability.

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Reliability in layered networks with random link failures

Disclaimer This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. ABSTRACT Planning the development, use and regulation of computer systems in nuclear reactor protection systems in such a way as to enhance reliability and safety is a complex issue. This report is one of a series of reports from the Computer Safety and Reliability Group, Lawrence Livermore National Laboratory, that investigates different aspects of computer software in reactor protection systems. There are two central themes in the report. First, software considerations cannot be fully understood in isolation from computer hardware and application considerations. Second, the process of engineering reliability and safety into a computer system requires activities to be carried out throughout the software life cycle. The report discusses the many activities that can be carried out during the software life cycle to improve the safety and reliability of the resulting product. The viewpoint is primarily that of the assessor, or auditor. iv v CONTENTS

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Software reliability and safety in nuclear reactor protection systems

Communications networks used for transmitting and receiving voice or digital data involve copper wire, fiber optics, radio, satellite, and microwave links. In general, these networks are large, diffuse, and complex. Even using modern high-speed computers, exact computations of the network reliability for use as a figure of merit in an interactive network design procedure can take an inordinate amount of time. This paper discusses various exact techniques whose complexity results in run-times short enough for practical network design. We model the network by an undirected probabilistic graph whose vertices represent the nodes and whose edges represent the links. A special feature of our model is that it allows nodes to be imperfect and associates a reliability measure with each node, assumed to succeed or fail independently. Therefore, the network reliability measure is based upon the reliability measures of the individual links and nodes. >

Algorithms for network reliability and connection availability analysis

Due to considerable use of electric drives in industrial applications, reliability assessment of drive-motor systems both in design and operating phases is of considerable importance. Reliability assessment of drive-motor systems is presented in this paper. Using the basic component of a drive-motor system, a suitable reliability block diagram is first developed. The system availability and reliability is then determined using developed block diagram. The impacts on system reliability of various parameters such as failure rate and repair rate of system components are investigated. The proposed technique is then applied to a practical drive-motor system and the results are presented.

Markov Model of Drive-Motor Systems for Reliability Calculation

The authors have designed and implemented a graph-reduction algorithm for computing the k-terminal reliability of an arbitrary network with possibly unreliable nodes. The two contributions of the present work are a version of the delta-y transformation for k-terminal reliability and an extension of Satyanarayana and Wood's polygon to chain transformations to handle graphs with imperfect vertices. The exact algorithm is faster than or equal to that of Satyanarayana and Wood and the simple algorithm without delta-y and polygon to chain transformations for every problem considered. The exact algorithm runs in linear time on series-parallel graphs and is faster than the above-stated algorithms for huge problems which run in exponential time. The approximate algorithms reduce the computation time for the network reliability problem by two to three orders of magnitude for large problems, while providing reasonably accurate answers (relative error less than 10/sup -3/) in most cases. >

A.M. Shooman

Papers

Methods for communication-network reliability analysis: probabilistic graph reduction