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n i 0
n o c o
IE
OE
UL
L
n i 0
n o 0
NW
L
WD
WD
UL
n i 0
n i 0 || n o c o
n i c i
L
n o c o
n i 0
n o 0
L
WD
UL
IN
WD
ON
UL
WD
W
n o c o
LWD
WD UL
n i c i
n o c o
WD
n i 0 && n o c o
IF
OF
Figure 9.1 The automata of the input buffer, the production unit and the output
buffer
finite capacity. Parameters c i
and c o
represent their capacity, while n i
and
n o
represent the current number of pieces respectively. The model of the
production unit has two states, WORKING ( W ) and NOT WORKING ( NW ); the
model of the input buffer has three states, EMPTY ( IE ), NOT EMPTY NOT FULL
( IN ), and FULL ( IF ); similarly, the model of the output buffer has three states
( OE , ON and OF ).
Three events determine the dynamics of these automata:
WORKDONE ( WD ) is notified when the production unit completes the
machining of a piece and places it in the output buffer. If the input buffer
is empty or the output buffer is full, the production unit enters the NW
state.
LOADED ( L ) is notified when a new piece is loaded from the inventory to
the input buffer. This event may fire the transition of the production unit
from the NW to the W state.
UNLOADED ( UL ) is notified when a piece is unloaded from the output
buffer to the AGV. This event may fire the transition of the production
unit from the NW to the W state.
At any instant of time the machine current state is the union of the
current states of the three automata depicted in Figure 9.1. If we compute
the Cartesian product of these states, we come up with a new automaton
characterized by eighteen states, three events and a large number of possible
state transitions. In reality, five out of those eighteen states are inadmissible
because they represent situations like:
The machine is working when the output buffer is full.
The machine is not working when the output buffer is not full.
Note that the state ( IN - W - OF ) is inadmissible because it corresponds to
the situation where the production unit is machining a piece but there is no
room in the output buffer to place it when the work is done. Of course, it
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