states that the system
can be in, and defines
the speed at which transitions
between those states take
place. As such, Markov
models consist of comprehensive
representations of possible
chains of events, i.e.,
transitions, within systems,
which in the case of reliability
and availability analysis
correspond to sequences
of failures and repair….
The Markov model is analyzed
in order to determine such
measures as the probability
of being in a given state
at a given point in time,
the amount of time a system
is expected to spend in
a given state, as well
as the expected number
of transitions between
states, for instance representing
the number of failures
and repairs.”

But the true value of
Markov computations comes
in applying it at the design
stage. Markov mixing process
in complex systems reveals
little depressions of stability
- think of marbles on a
rubber sheet; stable depressions
in the sheet form dry lake
beds where the marbles
will collect. Even if the
sheet is slightly shaken,
the marbles will bounce
and role around, but most
will stay inside their
depressions – local
zones of stability. This
can allow richly interacting
networks of only moderately
high component reliability
to be of higher reliability
working together than each
component devices achieves
alone. In fact this is
the real world of good
network design. While few
network designers actually
use Markov mathematics
explicitly, their decisions
taken from a perspective
of the complex network
as a whole, with all of
its interacting and redundant
systems, frequently create
Markov spaces.

Other approaches should
be in the designer’s
tool-kit. Decision Analysis
is can help determine the
consequences of any specific
design choice on the system
and ability to meet utilitarian
goals. But there are graphical
ways of representing this
and simplifying design.
Perhaps more frequently
used would be Reliability
Block Diagram (RBD), Event
Tree Analysis, or a Fault
Tree diagram.

**It all works
together**

“Downtime usually
translates into significant
productivity and revenue
losses for many enterprises.
Maximizing network uptime
requires the use of operational
best practices and redundant
network designs in conjunction
with high-availability
technologies within network
elements.” [__Cisco__]

Availability is of course
only one part of the complex
concept of Carrier-grade.
Several other “ilities”:
Reliability/Dependability,

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