Information Technology Reference
In-Depth Information
Theorem 5.7.
The association algorithm can limit the SSE with the
optimal QoS to be achieved only when an SSE corresponds to an SFC.
Proof:
From Lemma 5.1, the SSE with the optimal QoS is a CP. Then we
finish our proof by contradiction. We suppose that there exists a CP with
the optimal QoS that does not correspond to an SFC.
By Theorem 5.2, there exists a transition that can be enabled under
M
.
According to the structural characteristics of the SC-net, no transition in CP
under
M
can be enabled if every nonleaf place
p
2
P
satisfies
M
ð
p
Þ¼
0.
Then there exists at least one nonleaf place
p
2
P
satisfying
M
ð
p
Þ >
0.
According to Step 1 in the association algorithm, there are two cases.
1.
If the
j
th QoS attribute is cost, after aggregation through
V
m
M
,
V
j
a
will be too large; and
2.
If the
j
th QoS attribute is benefit, after aggregation through
V
m
M
,
V
j
a
will be too small.
can
achieve the optimal value neither in case (a) nor in case (b). Therefor
e,
the conclusion holds.
Considering the objective function stated in (2) and (3),
V
j
a
Note that the approach we apply in Step 1 in the association
algorithm is analogous to the “big M method,” which is widely used
in linear programming to force an artificial variable to be zero [128].
5.4.2 Web Service Configuration under Multiple
QoS Objectives
If a Web service user has multiple QoS objectives, the optimal
configuration problem can be treated as multi-attribute decision-making
(MADM) [129], in which alternatives are the candidate SFCs to be
evaluated and attributes are the QoS measures of SFCs under consider-
ation. Simple additive weighting (SAW) [130] is an important method
for MADM. We adopt SAW as follows. We first normalize every QoS
attribute
j
to allow a comparable scale for all cost and benefit
QoS attributes. Then we apply a weight
w
j
for the
j
th QoS attribute to
represent relative importance or value trade-offs of different attributes.
Finally, we calculate
f
c
j
to
G
¼
P
q
j¼
1
G
j
w
j
for each candidate configura-
tion. The greater the
f
value, the more preferred the SFC. Through
