13,559 research outputs found
Reliability of Partial k-tree Networks
133 pagesRecent developments in graph theory have shown the importance of
the class of partial k- trees. This large class of graphs admits several
algorithm design methodologies that render efficient solutions for a large
number of problems inherently difficult for general graphs. In this thesis
we develop such algorithms to solve a variety of reliability problems on
partial k-tree networks with node and edge failures. We also investigate
the problem of designing uniformly optimal 2-trees with respect to the
2-terminal reliability measure.
We model a. communication network as a graph in which nodes represent
communication sites and edges represent bidirectional communication
lines. Each component (node or edge) has an associated probability of
operation. Components of the network are in either operational or failed
state and their failures are statistically independent. Under this model,
the reliability of a network G is defined as the probability that a given
connectivity condition holds. The l-terminal reliability of G, Rel1 ( G), is
the probability that any two of a given set of I nodes of G can communicate.
Robustness of a network to withstand failures can be expressed
through network resilience, Res( G), which is the expected number of distinct
pairs of nodes that can communicate. Computing these and other
similarly defined measures is #P-hard for general networks.
We use a dynamic programming paradigm to design linear time algorithms that compute Rel1( G), Res( G), and some other reliability and
resilience measures of a partial k-tree network given with an embedding
in a k-tree (for a fixed k).
Reliability problems on directed networks are also inherently difficult.
We present efficient algorithms for directed versions of typical reliability
and resilience problems restricted to partial k-tree networks without node
failures. Then we reduce to those reliability problems allowing both node
and edge failures.
Finally, we study 2-terminal reliability aspects of 2-trees. We characterize
uniformly optimal 2-trees, 2-paths, and 2-caterpillars with respect
to Rel2 and identify local graph operations that improve the 2-terminal
reliability of 2-tree networks
Topology design and performance analysis of an integrated communication network
A research study on the topology design and performance analysis for the Space Station Information System (SSIS) network is conducted. It is begun with a survey of existing research efforts in network topology design. Then a new approach for topology design is presented. It uses an efficient algorithm to generate candidate network designs (consisting of subsets of the set of all network components) in increasing order of their total costs, and checks each design to see if it forms an acceptable network. This technique gives the true cost-optimal network, and is particularly useful when the network has many constraints and not too many components. The algorithm for generating subsets is described in detail, and various aspects of the overall design procedure are discussed. Two more efficient versions of this algorithm (applicable in specific situations) are also given. Next, two important aspects of network performance analysis: network reliability and message delays are discussed. A new model is introduced to study the reliability of a network with dependent failures. For message delays, a collection of formulas from existing research results is given to compute or estimate the delays of messages in a communication network without making the independence assumption. The design algorithm coded in PASCAL is included as an appendix
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
Algorithms for Constructing Overlay Networks For Live Streaming
We present a polynomial time approximation algorithm for constructing an
overlay multicast network for streaming live media events over the Internet.
The class of overlay networks constructed by our algorithm include networks
used by Akamai Technologies to deliver live media events to a global audience
with high fidelity. We construct networks consisting of three stages of nodes.
The nodes in the first stage are the entry points that act as sources for the
live streams. Each source forwards each of its streams to one or more nodes in
the second stage that are called reflectors. A reflector can split an incoming
stream into multiple identical outgoing streams, which are then sent on to
nodes in the third and final stage that act as sinks and are located in edge
networks near end-users. As the packets in a stream travel from one stage to
the next, some of them may be lost. A sink combines the packets from multiple
instances of the same stream (by reordering packets and discarding duplicates)
to form a single instance of the stream with minimal loss. Our primary
contribution is an algorithm that constructs an overlay network that provably
satisfies capacity and reliability constraints to within a constant factor of
optimal, and minimizes cost to within a logarithmic factor of optimal. Further
in the common case where only the transmission costs are minimized, we show
that our algorithm produces a solution that has cost within a factor of 2 of
optimal. We also implement our algorithm and evaluate it on realistic traces
derived from Akamai's live streaming network. Our empirical results show that
our algorithm can be used to efficiently construct large-scale overlay networks
in practice with near-optimal cost
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
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