Information Technology Reference
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(ii)
every atomic Web service in
S
is denoted by a leaf place;
(iii)
every other Web service
s
S
excluding those mentioned in
items 1 and 2 is mapped to a place set
P
s
2
P
. Every Web
service place
p
P
s
has the same function and nonfunctional
attributes and can be treated as the duplication of
s
. The
number of duplications is equal to the reusability frequency of
s
in the configuration;
2
(iv)
each nonleaf place has only one input arc and at least one
output arc;
(v)
each transition has only one input arc and at least one output
arc; and
t
j >
(vi)
8
t
2
T
,if
j
1 there is an AND relationship among places
in
t
.
t
j¼
1,
t
p
j >
8
t
2
T
, and if
j
¼
p
and
j
1, there is an
p
Þ
.
OR relationship among transitions in
ð
Note that the proposed SC-net falls into the class of disassembly
Petri nets [80]. Based on the definition of the SC-net, we state SFC and a
realizable configuration process.
p
0
; zÞ
Definition 5.5.
z
is denoted
C
ð
An SFC at time
such that (a)
p
0
2
p
0
; zÞ
, and (b)
8
p
0
; zÞ
,if
p
6¼
1
,
9
p
and
8
p
00
2
t
,
C
ð
p
2
C
ð
t
2
p
00
2
p
0
; zÞ
.
C
ð
Definition 5.6.
A realizable configuration process is a sequence of
transition firings from the initial marking
M
0
to a current marking
M
.
M
is called a realizable configuration state.
If we denote system A, subsystems X, Y, B, C, and D, module
components E and F by
p
0
and
p
3
9
, respectively, we can obtain an
SC-net in Figure 5.3 for the configuration of system A in Figure 5.1.
There are three candidate configurations, that is,
C
1
ð
p
0
; zÞ¼f
p
0
;
p
1
;
p
0
; zÞ¼f
p
0
;
p
0
; zÞ¼f
p
0
;
p
3
4
g
.
The firing transitions determine the configuration processes, for exam-
ple,
M
0
½
,
C
2
ð
p
2
;
p
5
8
g
,
and
C
3
ð
p
2
;
p
5
7
;
p
9
g
p
0
; zÞ
t
1
>
M
1
½
t
3
>
M
2
corresponds to
C
1
ð
whereas
M
0
½
t
2
>
p
0
; zÞ
M
3
½
. Note that since the
subgraph in the dotted trapezoid denotes the configuration information
for subsystem C, if C can be referenced by other services, the subgraph
can also be reused for configuration description according to the
property 3 of Definition 5.3.
t
4
>
M
5
½
t
5
>
M
6
corresponds to
C
2
ð
