Graphics Programs Reference
In-Depth Information
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p
in
t
1
p
1
t
2
p
2
T
1−2
p
3
T
3
p
out
p
4
p
control
Figure 7.7: The interruptible GSPN model of an Erlang-3 server
to signal that the subnet is busy and a token is put back in place p
in
to
mean that the original request (arrival of a token in place p
in
) is undergoing
service, but has not been completed yet. At the same time, the first delay
stage starts with the firing of t
2
, but no token is removed from place p
in
. The
control place p
4
is introduced in order to insure a single-server semantics for
timed transition T
1−2
. Transition T
1−2
plays the role of transitions T
1
and T
2
in the net of Fig.
7.5
and is fired twice to implement the first two stages of the
Erlang-3 distribution. When two tokens are finally accumulated in place p
3
,
timed transition T
3
becomes enabled and its firing corresponds to the end of
the overall delay that indeed lasted for three exponential stages. Only when
transition T
3
fires, the token deposited in p
in
is removed to mean that the
whole subnet completed its evolution. In this case a conflict arising because
of a race between (macro-)transitions with Erlang type distributions would
be decided only on the basis of which of the transitions actually completed
its work (fired) first.
The computation of the P and T semi-flows for the GSPN systems of Figs.
transition) allows the equivalence of the two representations to be established
in a formal manner. In particular, looking at the T semi-flows of the two
nets we can notice that for the subnets to transfer a token from the input
place (place p
in
) to the output place (place p
out
) the firing of three timed
transitions is needed in both cases. Moreover, the use of the semi-flows shows
withdrawn, leaving the net in its original (idle) state.
As we briefly discussed at the beginning of this section, the age memory
policy needs to be specified in the case of generally distributed firing times
because of different possible attitudes with respect to the work performed
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