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variable disk failure rate for multiple replicas is proposed. In this model, due to the
assumption that each disk could theoretically have its own failure rate pattern, we
assume that the disk failures are independent. Assume that replicas of the same data
file are stored in different disks. The data reliability with multiple replicas can be
derived from equation
(4.3)
:
k
∏
RT
()1
=− −
(1
e
−
λ
T
)
(4.3)
i
k
k
i
=
1
In equation
(4.3)
, the data reliability level with multiple replicas is described based
on permutations
a
nd combinations principles. In this equation,
k
represents the num-
ber of replicas,
λ
i
is the weighted average failure rate of the disk storing replica
r
i
,
T
k
is the storage duration of the data file with
k
replicas. The right-hand side of the
equation describes the probability that at least one of the
k
replicas survives during the
storage duration of
T
k
. equation
(4.3)
reveals the relationship among data reliability
level, the number of replicas, failure rates of disks, and the storage duration of the data
file. If the number of replicas and the failure rates of disks are known, the relationship
between storage duration and data reliability can then be derived. It can be seen that
equation
(4.2)
is a special case of equation
(4.3)
when
k
= 1.
4.3 Summary
In this chapter, we first determined several properties in our data reliability model,
which includes the reliability metrics used for describing disk and data reliability lev-
els, the model type used in our data reliability model design and the style of the disk
failure rate pattern used for describing the disk reliability. Afterward, we presented
our novel generic data reliability model in detail. Based on this model, the relation-
ship among data reliability levels, the number of replicas, failure rates of disks, and the
storage durations of the data are able to be well described, where calculations among
these parameters are defined.
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