Exact Methods to Compute Network Reliability

Lucet, Corinne; Manouvrier, Jean-François

doi:10.1007/978-1-4612-1782-4_20

Cited by 27 publications

(20 citation statements)

References 34 publications

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“…SDP methods involve adding probabilities; however, the calculation of each constituent probability is generally involved [10]. It is also important to emphasize that the effectiveness of these methods can be highly dependent on the specific ordering given to the events A i .…”

Section: Sum Of Disjoint Products Methods (Sdp)mentioning

confidence: 99%

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Equivalent reliability polynomials modeling EAS and their geometries

Hassan

Udrişte

2015

Annals of West University of Timisoara - Mathematics and Computer Science

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Abstract. In this paper we shall introduce two equivalent techniques in order to evaluate reliability analysis of electrical aircrafts systems (EAS): (i) graph theory technique, and (ii) simplifying diffeomorphism technique. Geometric modeling of reliability models is based on algebraic hypersurfaces, whose intrinsic properties are able to select those models which are relevant for applications. The basic idea is to cover the reliability hypersurfaces by exponentially decay curves. Most of the calculations made in this paper have used Maple and Matlab software.

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Section: Sum Of Disjoint Products Methods (Sdp)mentioning

confidence: 99%

“…The edges represent units that can fail with known probabilities. In real problems, these probabilities are usually evaluated from statistical data [10]- [14]. In the exact methods there are two types for the computation of the network reliability.…”

Section: Introductionmentioning

confidence: 99%

Equivalent reliability polynomials modeling EAS and their geometries

Hassan

Udrişte

2015

Annals of West University of Timisoara - Mathematics and Computer Science

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“…A symbolic constraint for r i can then be generated using (5) to enumerate all possible failure events while traversing T from node i to the sources. However, such an exact computation, based on the enumeration of all possible component failure events, has exponential complexity on a fixed graph configuration [1]. The problem is further exacerbated when compiling a symbolic expression for a reconfigurable graph, since, in general, enumerating all possible configurations has also exponential complexity.…”

Section: Problem Formulationmentioning

confidence: 99%

“…SOLVEILP generates minimum cost architectures for the given set of interconnection constraints. The RELANAL-YSIS routine computes the probability of composite failure events at critical nodes, starting from the failure probabilities of the components, a problem known as K-terminal reliability problem in the literature [1]. To do so, we implement a modified depth-first search algorithm to traverse the graph G from node i (root) to the source nodes (leaves), by applying a path enumeration method, and by turning event relations as (5) into probability expressions.…”

Section: Ilp Modulo Reliabilitymentioning

confidence: 99%

“…In addition to the complexity of exact network reliability analysis, which is an NP-hard problem [1], techniques such as Fault Tree Analysis (FTA) or Reliability Block Diagrams (RBD) often rely on a set of system abstractions, which are hardly interoperable with system design flows [2]. For instance, in FTA, causal chains leading to some failure are depicted as a tree, inherently describing a hierarchical breakdown.…”

Section: Introductionmentioning

confidence: 99%

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Optimized Selection of Reliable and Cost-Effective Cyber-Physical System Architectures

Bajaj¹,

Nuzzo²,

Masin³

et al. 2015

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2015

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Abstract-We address the problem of synthesizing safetycritical cyber-physical system architectures to minimize a cost function while guaranteeing the desired reliability. We cast the problem as an integer linear program on a reconfigurable graph which models the architecture. Since generating symbolic probability constraints by exhaustive enumeration of failure cases on all possible graph configurations takes exponential time, we propose two algorithms to decrease the problem complexity, i.e. Integer-Linear Programming Modulo Reliability (ILP-MR) and Integer-Linear Programming with Approximate Reliability (ILP-AR). We compare the two approaches and demonstrate their effectiveness on the design of aircraft electric power system architectures.

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Design of reliable fiber‐based distribution networks modeled by multi‐objective combinatorial optimization

Haidine

2012

Int J Communication

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SUMMARYIn this work, we investigate the planning of hybrid fiber/very high bit rate digital subscriber line (HFV) access networks. This HFV variant is considered as an alternative to passive optical access network. It consists of implementing optical fibers in the access network part from the central office to the street cabinets, whereas the very high bit rate digital subscriber line technology is used in the last meter part, from street cabinets to subscribers. Firstly, we discuss the different tasks of this planning problem. We model this planning problem as a multi‐objective optimization problem, where different conflicting objectives have to be optimized at the same time. We consider network costs and network reliability. This problem is solved by two different approaches: the classical single‐objective optimization (SOO) and the multi‐objective optimization (MOO), which is a recent optimization approach that is gaining an increasing interest in practical optimization problems. MOO solves the problem by searching for different optimal trade‐offs between the optimization objectives. The performances of SOO and MOO are analyzed and compared with each other using three network instances. Copyright © 2012 John Wiley & Sons, Ltd.

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Exact Methods to Compute Network Reliability

Cited by 27 publications

References 34 publications

Equivalent reliability polynomials modeling EAS and their geometries

Equivalent reliability polynomials modeling EAS and their geometries

Optimized Selection of Reliable and Cost-Effective Cyber-Physical System Architectures

Design of reliable fiber‐based distribution networks modeled by multi‐objective combinatorial optimization

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