Database Reference
In-Depth Information
discussion on determining the data reliability assurance
RA
(1
k
in
Chapter 6
. In each
storage duration
SD
k
, the data reliability assurance should always be no smaller than
RA
(1)
k
. Then we have:
RA
(1)
RA t
t
()
1
-
k
≥
1
-
1
Note that value “1” on the denominator of the left-hand side indicates the unit stor-
age duration of 1 year. The preceding inequation can be transformed to:
RA t
() 1 1
≥− −
RAt
(1))
(5.3)
k
According to Rule 2, the data reliability assurance for data file stored with single
replica or two replicas can be derived as shown in equations (5.4) and (5.5), which are:
−
RA t e
λ
t
With single replica,
()
=
(5.4)
1
−
λ
t
−
λ
t
With two replicas,
RA t
( )1(1
=− −
e
)(1
−
e
)
(5.5)
1
2
Inequation
(5.3)
is the key for building the relationship between the data reliability
requirement and the storage duration of data files. After combining inequation
(5.3)
and equation
(5.4)
, we have:
−
λ
1
(
e
+−
t
1)
RA
(1)
≤
k
t
For the storage with one replica, because the redundancy level cannot be changed,
we have
RA
(1)
=
RR
(1)
. Therefore:
k
−
λ
1
(
e
+−
t
1)
RR
(1)
≤
(5.6)
t
Inequation
(5.6)
shows the relationship between the data reliability requirement
and the storage duration of data fi
le
with a single replica. Assume that
t
is the expected
storage duration of the data file,
λ
1
is the average disk failure rate of the correspond-
ing disk storing the replica, if inequation
(5.6)
holds, then a single replica suffices to
provide data reliability assurance that meets the data reliability requirement. Other-
wise, if this inequation does not hold, the storage with single replica may jeopardize
the data reliability requirement, and hence creating another replica is necessary.
After combining inequation
(5.3)
and equation
(5.5)
, we have:
(1)1
(1
≤−
−
e
−
λ
t
)(1
−
e
−
λ
t
)
1
2
RA
k
t
This inequation shows the relationship between the data reliability requirement
and the storage duration of data file with two replicas. The right-hand side of the
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