Xiao Liu PhD Thesis.pdf - Faculty of Information and Communication ...

samples from the scientific workflow system logs which are above D ( a i ) or below
d ( a i ) are hence discarded as outliers. The actual runtime duration at a i is denoted
as R ( a i ) . Now, we propose the definition of probability based temporal consistency
which is based on the weighted joint distribution of activity durations. Note that,
since our temporal framework includes both build-time components and runtime
components to support the lifecycle of scientific workflow systems. Accordingly,
our probability based temporal consistency model also includes both definitions for
build-time temporal consistency and runtime temporal consistency.
Definition 5.2: (Probability based temporal consistency model).
At build-time stage, U (SW ) is said to be:
n
1) Absolute Consistency (AC), if ∑ wi ( µ i + 3σ
i ) < U ( SW ) ;
i=
1
n
2) Absolute Inconsistency (AI), if ∑ wi ( µ i − 3σ
i ) > U ( SW ) ;
i=
1
3) α%
Consistency ( α%
C), if ∑ w ( µ + λσ ) u(
SW ) .
n
i=
1
At runtime stage, at a workflow activity
i i i =
a p ( 1 < p < n ), U (SW ) is said to be:
p
n
1) Absolute Consistency (AC), if ∑ R(
ai ) + ∑ wi
( µ i + 3σ
i ) < U ( SW ) ;
i=
1 j=
p+
1
p
n
2) Absolute Inconsistency (AI), if ∑ R(
ai ) + ∑ wi
( µ i − 3σ
i ) > U ( SW ) ;
i=
1 j=
p+
1
p
n
i i i i =
j=
p+
1
3) α%
Consistency ( α%
C), if ∑ R(
a ) + ∑ w ( µ + λσ ) U ( SW ) .
Here
i=
1
w i stands for the weight of activity a i , λ ( − 3 ≤ λ ≤ 3 ) is defined as the
α % confidence percentile with the cumulative normal distribution function of
−(
x−µ
2
1
i )
µ + λσ
F( µ + λσ ) =
2σ
2
∫ i i
i i
−∞
l i • dx = α%
( 0 < α < 100 ).
σ 2π
Note that the build-time model will mainly be used in Component 1 and its
runtime counterpart will mainly be used in Component 2 and Component 3 of this
thesis. Meanwhile, as explained in [56], without losing generality, the weights of
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