Information Technology Reference
In-Depth Information
the system MTTF. In other words, we need to derive the system MTTF in terms of the failure
rate, repair rate, total number of redundancies, initial number of redundancies transmitted,
and the detection delay in order to choose the appropriate system parameters to meet a given
system MTTF requirement.
13.4.1 System Reliability
Again we model the system as a continuous-time Markov chain with state denoted by (
h
,
k)
,
where
h
is the number of failed servers and
k
is the number of redundancies activated for
transmission. Let
K
max
be the total number of redundancies in the system and
K
min
be the
excess number of redundancies to be transmitted. Figure 13.3 illustrates an example with
K
min
=
4. In general, there are three types of state transition. Specifically, the
system will transit from state (
h
,
k)
to state (
h
2 and
K
max
=
λ
h
when an additional server
fails. After the failure is detected, with a mean detection time of 1/
+
1
,
k
) at a rate of
ω
, the system will activate a
new redundancy transmission and transit to state (
h
1), thus bringing the number of
excess redundancies back to
K
min
. When a failed server is repaired at a rate of
+
1
,
k
+
µ
h
in state (
h
,
k)
,
then the system will transit from state (
h
,
k
) to state (
h
−
1
,
k
)if(
k
−
h
)
≤
K
min
. Otherwise,
i.e., (
k
1) by deactivating one
redundancy currently being transmitted. This again brings the number of excess redundancies
back to
K
min
.
Note that there is a subtle problem associated with this model. In FEC, since all the servers
in the system are operating, server failure will only occur in servers actively transmitting video
−
h
)
=
K
min
, it will transit from state (
h
,
k)
to state (
h
−
1
,
k
−
λ
0
λ
1
λ
2
0,2
1,2
2,2
3,2
3,2
3,2
µ
1
µ
2
1
2
ω
ω
λ
1
λ
2
λ
3
µ
1
1,3
2,3
3,3
4,3
4,3
4,3
µ
2
µ
3
2
3
ω
ω
λ
2
λ
2
λ
3
λ
4
µ
2
3
2
2,4
3,4
4,4
5,4
5,4
5,4
µ
3
µ
4
4
:
: state with
h
servers failed and
k
level of redundancy
h
,
k
λ
h
: aggregate server failure rate with
h
server failed
µ
h
: aggregate repair rate with
h
server failed
ω
: detection rate
Figure 13.3
A Markov chain for PRT with
K
min
=
2 and
K
max
=
4
Search WWH ::
Custom Search