Graphics Programs Reference
In-Depth Information
Table 8.6: ECS definition of the model with modified priority definition
transition
weight
priority
ECS
waitAGV
1
1
1
1
waitAGV
2
1
1
1
waitAGV
3
1
1
1
part
a
20
2
2
part
b
80
2
2
inM
2
1
1
3
inM
2
1
1
4
inM
3
1
1
5
inM
3
1
1
6
inM
2
, lead to the same new marking, but the second sequence requires a
conflict resolution between part
b
and inM
2
that is not solved in the first
sequence. The reason is that transition inM
3
is in causal connection with
inM
2
.
As a matter of fact, such a situation can never arise, due to the parametric
initial marking and the priority structure of the model: in this model, tran-
sitions part
a
and part
b
are never enabled together with transitions inM
2
,
inM
2
, inM
3
or inM
3
. However, to eliminate any possibility for confusion
to arise, the modeller might assign a higher priority level to part
a
and part
b
.
Table
8.6
shows the new ECS definition obtained from the modified model.
To reduce both the time and memory required to obtain the desired result,
a new model has been devised that gives good upper and lower bounds on
the system throughput and has a considerably reduced state space. The
new GSPN model is depicted in Fig.
8.15.
The lower bound net is obtained
by merging in a unique transition three operations: the transport of a fin-
ished part to the LU station, its unloading, the loading of a raw piece and
its transportation to the first machine in the working schedule: all these
operations are performed never releasing the AGV thus reducing the po-
tential concurrency in the model. The upper bound instead is obtained by
assuming a 0 time duration for the load/unload operation. The structure of
the upper/lower bound GSPN models is exactly the same; they only differ
in the rate of transition mv LU mv. Observe that, as a consequence, the
reachability graph must be built only once for a given value of N, then two
different Markov chains are derived from the common tangible reachability
graph using the different rates for transition mv LU mv. The bounds ob-
tained from these two models are plotted in Fig.
8.16
and are compared with
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