Graphics Programs Reference
In-Depth Information
Table 8.3: P-invariants of the GSPN model of Fig.
8.10
+ M(inM
1
)
+ M(outM
1
)
M(idleM
1
)
=
+ M(inM
2
)
+ M(inM
2
)
M(outM
2
)
M(idleM
2
)
+
M(outM
2
)
+
=
+ M(inM
3
)
+ M(outM
3
)
M(idleM
3
)
=
+ M(wait
1
)
+ M(in
S1
)
M(in
S1
)
M(free
S1
)
+
=
+ M(in
S2
)
+ M(in
S2
)
M(free
S2
)
=
+ M(wait
2
)
+ M(wait
2
)
M(in
S3
)
M(free
S3
)
+
M(in
S3
)
+
=
+ M(in
S4
)
+ M(in
S4
)
M(free
S4
)
=
+ M(wait
3
)
+ M(in
S5
)
M(in
S5
)
M(free
S5
)
+
=
+ M(outLU
a
)
M(outLU
b
)
M(load)
+ M(type)
+
+ M(wait
1
)
+ M(in
S1
)
+ M(in
S2
)
+ M(wait
2
)
+ M(in
S3
)
+ M(in
S4
)
+ M(in
S5
)
+ M(in
S1
) + M(in
S2
)
+ M(wait
2
)
+ M(in
S3
)
M(in
S4
)
+
+ M(wait
3
)
+ M(in
S5
)
M(inM
1
)
+
+ M(outM
1
)
+ M(inM
2
)
M(outM
2
)
+
+ M(inM
2
)
+ M(outM
2
)
M(inM
3
)
+
M(outM
3
)
+
= N
time is selected to be processed on that machine. This is represented in the
net by means of the four inhibitor arcs connected to transitions inM
3
and
inM
2
.
8.3.1
Structural analysis of the push production systems
In this section we show how the structural analysis methods can be used
to check whether the models correctly represent the studied systems and
whether the system behaviour is correct.
P-invariants analysis allows us to conclude that both GSPN models built
in this section are bounded, since both of them are covered by P-semiflows.
Here we give a list of P-invariants for each model and provide their inter-
pretation.
The GSPN model of Fig.
8.10
(continuous transport system) has nine mini-
mal P-semiflows from which it is possible to derive the P-invariants listed in
Table
8.3.
The first three invariants ensure that each machine can process
at most one part at a time. The following five invariants ensure that at most
one part can be present in one section of the continuous transport system at
any time. The last invariant ensures that the total number of parts circu-
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