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

The probability consistency range where light-weight temporal violation
handling is statistically effective is defined as (0.13%, 99.87%). At scientific
workflow runtime, based on temporal QoS contracts, light-weight temporal violation
handling is only triggered when the probability of current temporal consistency state
is within the range of (0.13%, θ % ) where θ % is the bottom-line temporal
consistency state.
Figure 6.1 Statistically Recoverable Temporal Violations
6.2.2 Minimum Probability Time Redundancy
After we have identified the effective probability consistency range for temporal
violation handling, the next issue is to determine at which activity point to check for
the temporal consistency so that a temporal violation can be detected in the first
place. Here, a necessary and sufficient checkpoint selection strategy is proposed.
First, the definitions of probability time redundancy and minimum probability time
redundancy are presented.
Definition 6.1 (Probability Time Redundancy for Single Workflow Activity).
At activity point
a p between a i and
a j ( i ≤ j ), let U ( a i , a j ) be of β % C with
the percentile of λ β which is above the threshold of θ % with the percentile of λ θ .
Then the probability time redundancy of U ( a i , a j ) at a p is defined as
PTR U ( a , a ), a ) = a , a ) −[
R(
a , a ) + θ ( a , a )] . Here,
( i j p
j
k
k = p+
1
θ ( a + 1,
) = ∑ ( µ + λθ σ ) .
p a j
k
u ( i j i p p+
1 j
95