Information Technology Reference
In-Depth Information
SSEs
SFCs
CPs
Figure 5.4
Relationship among the set of solutions correspondent to SSEs, CPs, and
SFCs. SSE, a subgraph in SC-net that corresponds to a solution of the state-shift equation;
CP, a subgraph in SC-net that corresponds to a realizable configuration process; SFC,
service dependency configuration.
and the other elements are all 0. SSE
2
satisfies the condition of case (2),
we can extract the subgraph
,andwe
can then generate two column vectors of which only the element
corresponding to the Web service place
p
1
is 1, and the other elements
are all 0. In both cases, the solution is not a basis solution.
fð
P
;
T
Þj
P
¼f
p
1
;
p
3
4
g;
T
¼f
t
3
gg
Theorem 5.6.
A solution corresponds to a CP if and only if it is a basis
solution
.
Proof:
From Theorems 5.4-5.5, it is obvious.
From Theorem 5.2, the set of places of a CP in which no transition can
be enabled under
M
is a candidate SFC, whereas Theorem 5.6 represents
that the set of the CPs is correspondent to the set of the basis solutions of
E
-
A
½
M
0
. Relationship among the set of solutions correspondent to
SSEs, CPs, and SFCs is shown in Figure 5.4. We can conclude that 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. If
we formulate nonfunctional objectives in a way that can restrict the
search space of the set of solutions correspondent to CPs with optimal
QoS to the set of solutions correspondent to the SFCs, we can then search
the optimal QoS configuration by a linear programming technique.
a ¼
5.4 OPTIMAL WEB SERVICE CONFIGURATION
A linear programming problem is a kind of problem that has three
inputs, that is, a set of variables, an objective function, and a set of
constraints
[128].
Linear
programming
attempts
to
optimize
the
