7,218 research outputs found
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
Energy-delay bounds analysis in wireless multi-hop networks with unreliable radio links
Energy efficiency and transmission delay are very important parameters for
wireless multi-hop networks. Previous works that study energy efficiency and
delay are based on the assumption of reliable links. However, the unreliability
of the channel is inevitable in wireless multi-hop networks. This paper
investigates the trade-off between the energy consumption and the end-to-end
delay of multi-hop communications in a wireless network using an unreliable
link model. It provides a closed form expression of the lower bound on the
energy-delay trade-off for different channel models (AWGN, Raleigh flat fading
and Nakagami block-fading) in a linear network. These analytical results are
also verified in 2-dimensional Poisson networks using simulations. The main
contribution of this work is the use of a probabilistic link model to define
the energy efficiency of the system and capture the energy-delay trade-offs.
Hence, it provides a more realistic lower bound on both the energy efficiency
and the energy-delay trade-off since it does not restrict the study to the set
of perfect links as proposed in earlier works
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
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