Graphics Programs Reference
In-Depth Information
Table 8.4: P-invariants of the GSPN model of Fig.
8.12
+ M(busyLU
a
)
+ M(busyLU
b
)
M(idleLU)
= 1
+ M(busyM
1
)
M(idleM
1
)
= 1
+ M(busyM
2
)
+ M(busyM
2
)
M(idleM
2
)
= 1
+ M(busyM
3
)
+ M(busyM
3
)
M(idleM
3
)
= 1
+ M(mv
LU−1
)
+ M(mv
1−23
)
+ M(mv
23−LU
)
M(idleAGV )
+ M(mv
LU−23
)
+ M(mv
23−LU
)
= 1
M(inLU
a
)
+ M(busyLU
a
)
+ M(outLU
a
)
+ M(mv
LU−1
)
+ M(inM
1
)
+ M(busyM
1
)
+ M(outM
1
)
+ M(mv
1−23
)
+ M(inM
23
)
+ M(busyM
2
)
+ M(busyM
3
)
+ M(outM
23
)
+ M(mv
23−LU
)
= N
M(inLU
b
)
+ M(busyLU
b
)
+ M(outLU
b
)
+ M(mv
LU−23
)
+ M(inM
23
)
+ M(busyM
2
)
+ M(busyM
3
)
+ M(outM
23
)
+ M(mv
23−LU
)
= M
lating in the system is constant and equal to N. This is consistent with our
approach of modelling a closed system: every time a part exits the system
through the LU station, it is replaced with a raw part to be processed.
The model of Fig.
8.12
(AGV transport system) is covered by seven P-
semiflows that allow the derivation of the P-invariants listed in Table
8.4.
The first four invariants ensure mutual exclusion for the usage of the three
machines and the LU station. The fifth invariant ensures that only one
transport can happen at a time (due to the presence of a unique AGV).
The last two invariants mean that there is a fixed number (N) of type a
parts and a fixed number (M) of type b parts in the system, respectively.
Notice that in the previous model these two invariants are replaced by a
unique invariant due to the fact that in the GSPN model of Fig.
8.10
when
a part of any type exits the system, it is not necessarily replaced by a part
of the same type due to the probabilistic choice implemented through the
free-choice conflict comprising transitions part
a
and part
b
.
Let's now discuss the T-invariants obtained for the two models.
The GSPN model of the continuous transport system is covered by two T-
invariants, corresponding to the (deterministic) flow of parts of each type.
The GSPN model of the AGV transport system is covered by four T-
invariants, corresponding to the four working schedules (two for each part
type) the parts can undergo.
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