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

Therefore, it can be expressed as
n
n n n
2 2
u( WS)
= ∑ wi
µ i + λ ∑ wi
σi
= ∑ wi
µ i + λ ∑ wiσ
i − ∆t2
(Equation Ⅰ) where ∆ t2
i=
1 i=
1 i=
1 i=
1
⎛ n n ⎞
equals ⎜
2 2
λ ∑ w − ∑ ⎟
⎜ i σi
wi
σi
. Furthermore, if we denote
⎟
⎝i=
1 i=
1 ⎠
⎛ n n ⎞
⎜
2 2
∑ w − ∑ ⎟
⎜ i σi
wi
σ i as
⎟
⎝i=
1 i=
1 ⎠
B then we can have
⎛ n n
t wi
i ⎟ ⎞
∆ 1 =
⎜ ∑ ∑σ B and ∆t
2 = λB
⎝i= 1 i=
1 ⎠
. Since in real world
scientific workflows,
⎛ n
⎜ ∑
⎝i=
w i
1
n
⎟ ⎞
n
∑σ i is smaller than 1 due to ∑σ i is normally
= 1 ⎠
i=
1
i
n
much bigger than ∑ w i , meanwhile, λ is a positive value smaller than 1 (1 means a
i=
1
probability consistency of 84.13% which is acceptable for most users) [87], ∆ t1
and
∆ t 2 are all relatively small positive values compared with the major component of
Equation Ⅰ and Equation Ⅰ above. Evidently, we can deduce
n
n n
n n
that ∑ wiu( ai
) = ∑ wi
µ i + λ ∑ wiσ
i − ∆t1
≈ ∑ wi µ i + λ ∑ wiσ
i − ∆t2
= u(
WS ) .
i= 1 i=
1 i=
1
i=
1 i=
1
Therefore, the sum of weighted fine-grained temporal constraints is approximately
the same to the coarse-grained temporal constraint and thus our claim holds.
5.4 Case Study
In this section, we evaluate the effectiveness of our probabilistic strategy for setting
temporal constraint by illustrating a case study on a data collection workflow
segment in a weather forecast scientific workflow. The process model is the same as
depicted in Figure 5.7. The entire weather forecast workflow contains hundreds of
data intensive and computation intensive activities. Major data intensive activities
include the collection of meteorological information, e.g. surface data, atmospheric
humidity, temperature, cloud area and wind speed from satellites, radars and ground
observatories at distributed geographic locations. These data files are transferred via
various kinds of network. Computation intensive activities mainly consist of solving
complex meteorological equations, e.g. meteorological dynamics equations,
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