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A coherent model for the reliability of multiprocessor networks
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A coherent model for the reliability of multiprocessor networks
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Identifier
SITECE.00001
Title
A
coherent
model
for the
reliability
of
multiprocessor
networks
Personal author (1)
Boesch, Francis T.
Personal author (2)
Gross, Daniel
Personal author (3)
Suffel, Charles
Institute affiliation (1)
Stevens Institute of Technology. Dept. of Electrical Engineering and Computer Science
Institute affiliation (2)
Seton Hall University. Dept. of Mathematics and Computer Science
Publication year
1996
Technical report no.
9611
Abstract
There
is
extensive
literature
devoted
to
developing
a
mathematical
reliability
model
which
is
applied
to the
design
of
many
large
networks
. This
model
assumes
that a
graph
G
has
perfectly
reliable
nodes
, but
each
edge
has a
probability
of
operating
. The
reliability
R
is
defined
as the
probability
that there
is
an
operating
connected
spanning
subgraph
.
Analysis
problems
concern
the
determination
of
efficient
algorithms
to
find
R
.
It
is
known
that
calculating
R
is
NP
hard
for
general
graphs
, and that
it
remains
NP
hard
even
when
G
is
a
simple
undirected
planar
graph
and
each
edge
has the
same
probability
.
However
there are
classes
of
graphs
for
which
R
can
be
found
by a
polynomial
algorithm
.
Reliability
synthesis
problems
concern
finding
graphs
that are,
according
to
some
definition
, the
most
reliable
in the
class
of
all
graphs
having
a
given
number
of
edges
and
nodes
. In those
applications
such
as
multiprocessor
networks
where
the
edges
are
perfectly
reliable
but the
nodes
operate
with
known
probabilities
, the
obvious
analog
is
to
define
the
residual
node
reliability
as the
probability
that there
exists
a
spanning
connected
subgraph
on the
operating
nodes
.
However
this
suffers
by not
having
the
property
called
coherence
,
i.e.
,
it
is
possible
that
operating
subnetworks
generated
by
certain
operating
nodes
become
nonoperational
when
the
same
nodes
operate
but
some
additional
nodes
also
operate
.
Two
other
methods
for
treating
node
failures
have been
introduced
.
However
, the
first
of these
is
not a
reliability
model
, and the
second
does
not
handle
the
case
when
all
nodes
are
subject
to
failure
. In this
work
we
propose
a
new
definition
of a
reliability
function
to
handle
the
case
of
node
failures
.
We
show
that
it
is
coherent
, and
we
determine
many
of its
properties
.
Several
analysis
and
synthesis
results
are
presented
.
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