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— The calculation of network reliability in a proba-bilistic context has long been an issue of practical and academic importance. Conventional approaches (determination of bounds, sums of disjoint products algorithms, Monte Carlo evaluations, studies of the reliability polynomials, etc.) only provide approximations when the network's size increases, even… (More)

The two-terminal reliability, known as the pair connectedness or connectivity function in percolation theory, may actually be expressed as a product of transfer matrices in which the probability of operation of each link and site is exactly taken into account. When link and site probabilities are p and ρ, it obeys an asymptotic power-law behaviour, for… (More)

Caching is a key component for Content Distribution Networks and new Information-Centric Network architectures. In this paper, we address performance issues of caching networks running the RND replacement policy. We first prove that when the popularity distribution follows a general power-law with decay exponent α > 1, the miss probability is… (More)

The two-and all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan have been calculated exactly for arbitrary size as well as arbitrary individual edge and node reliabilities, using transfer matrices of dimension four at most. While the all-terminal reliabilities of these graphs are identical, the special case of identical edge (p)… (More)

The exact calculation of network reliability in a probabilistic context has been a long-standing issue of practical importance, but a diicult one, even for planar graphs, with perfect nodes and with edges of identical reliability p. Many approaches (determination of bounds, sums of disjoint products algorithms, Monte Carlo evaluations , studies of the… (More)

This paper shows how the steady-state availability and failure frequency can be calculated in a single pass for very large systems, when the availability is expressed as a product of matrices. We apply the general procedure to k-out-of-n:G and linear consecutive k-out-of-n:F systems, and to a simple ladder network in which each edge and node may fail. We… (More)

The development of jet nebulizers for medical purposes is an important challenge of aerosol therapy. The performance of a nebulizer is characterized by its output rate of droplets with a diameter under 5 µm. However the optimization of this parameter through experiments has reached a plateau. The purpose of this study is to design a numerical model… (More)

This paper deals with asymptotic expressions of the Mean Time To Failure (MTTF) and higher moments for large, recursive, and non-repairable systems in the context of two-terminal reliability. Our aim is to extend the well-known results of the series and parallel cases. We first consider several exactly solvable configurations of identical components with… (More)

- Annie Druault-Vicard, Christian Tanguy
- 2006

This paper shows how the steady-state availability and failure frequency can be calculated in a single pass for very large systems, when the availability is expressed as a product of matrices. We apply the general procedure to k-out-of-n:G and linear consecutive k-out-of-n:F systems, and to a simple ladder network in which each edge and node may fail. We… (More)

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