7 research outputs found
Exact Failure Frequency Calculations for Extended Systems
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
-out-of-:G and linear consecutive -out-of-:F systems, and to a
simple ladder network in which each edge and node may fail. We also give the
associated generating functions when the components have identical
availabilities and failure rates. For large systems, the failure rate of the
whole system is asymptotically proportional to its size. This paves the way to
ready-to-use formulae for various architectures, as well as proof that the
differential operator approach to failure frequency calculations is very useful
and straightforward
Exact two-terminal reliability of some directed networks
The calculation of network reliability in a probabilistic 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 when nodes do not fail
and all edges have the same reliability p. We consider here a directed, generic
graph of arbitrary size mimicking real-life long-haul communication networks,
and give the exact, analytical solution for the two-terminal reliability. This
solution involves a product of transfer matrices, in which individual
reliabilities of edges and nodes are taken into account. The special case of
identical edge and node reliabilities (p and rho, respectively) is addressed.
We consider a case study based on a commonly-used configuration, and assess the
influence of the edges being directed (or not) on various measures of network
performance. While the two-terminal reliability, the failure frequency and the
failure rate of the connection are quite similar, the locations of complex
zeros of the two-terminal reliability polynomials exhibit strong differences,
and various structure transitions at specific values of rho. The present work
could be extended to provide a catalog of exactly solvable networks in terms of
reliability, which could be useful as building blocks for new and improved
bounds, as well as benchmarks, in the general case
A memory efficient algorithm for network reliability
We combine the Augmented Ordered Binary Decision Diagram (OBDD-A) with the use of boundary sets to create a method for computing the exact K-terminal or all-terminal reliability of an undirected network with failed edges and perfect vertices. We present the results of implementing this algorithm and show that the execution time is comparable with the state of the art and the space requirement is greatly reduced. Indeed the space remains constant when networks increase in size but maintain their structure and maximum boundary set size; with the same amount of memory used for computing a 312 and a 31000 grid network
Computing performability for wireless sensor networks
The performability of a wireless sensor network (WSN) can be measured using a range of metrics, including reliability (REL) and expected hop count (EHC). EHC assumes each link has a delay value of 1 and devices have no delay or vice versa, which is not necessarily appropriate for WSNs. This paper generalizes the EHC metric into an expected message delay (EMD) that permits arbitrary delay values for both links and devices. Further, it proposes a method based on Augmented Ordered Multivariate Decision Diagram (OMDD-A) that can be used to compute REL, EHC and EMD for WSN with both device and link failures. Simulation results on various networks show the benefits of the OMDD-A approach
Exact solutions for the two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan
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 () and node ()
reliabilities shows that their two-terminal reliabilities are quite distinct,
as demonstrated by their generating functions and the locations of the zeros of
the reliability polynomials, which undergo structural transitions at