Information Technology Reference
In-Depth Information
objective function by adjusting the values of the variables under
constraints. The results are the optimal value of the objective function
and the values of variables at this optimum. The objective function and
the constraints are both linear.
The
can be treated as the
variable vector for the linear programming problem. The state-shift
equation, that is,
M
x
ð
m
þ
n
Þ
1 column vector
a ¼
M
0
, can be taken as the constraints.
A Web service user may have single or multiple QoS objectives. For
example, a user may want the total cost minimized with the configura-
tion availability maximized. From Theorem 5.1, for the
j
th QoS
attribute, we have
½
E
-
A
a ¼
c
j
¼
V
j
a
(5.1)
5.4.1 Web Service Configuration under Single
QoS Objective
If the
j
th QoS attribute is cost, the search problem of optimal configu-
ration is formulated as follows:
Minimize
c
j
¼
V
j
a
(5.2)
If the
j
-th QoS attribute is benefit, it is formulated as follows:
Maximize
c
j
¼
V
j
a
(5.3)
Both are subject to the same constraints:
E
-
A
½
a ¼
M
0
and
a
0,
and
M
0
¼ð
M
x
T
where
a ¼
1
;
0
;
0
;
0
;
0
;
...
;
0
Þ
Lemma 5.1.
The SSE with the optimal QoS is a CP.
Proof:
From Theorem 5.6, the set of basis solutions of a state-shift
equation of the SC-net is identical to the set of solutions that correspond
to realizable configuration processes. Since the optimal value of the
objective function of the linear programming occurs with a basis solution,
the SSE with the optimal QoS is a CP.
