Graphics Programs Reference
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p
1
p
1
p
3
p
4
T
1
p
3
p
2
p
4
T
a1
T
a12
T
a21
T
a2
T
a0
t
1
t
2
p
5
p
6
p
2
p
5
p
6
t
1
t
2
(a)
(b)
Figure 6.13: Removing immediate transitions: the non-free-choice case
In any case, at most one of the two immediate transitions can fire (only one
token is in p
2
after the firing of T
a
). The probability that, for example, t
1
is the transition that actually fires is different in the two cases where t
1
is
enabled alone, or together with t
2
: we have therefore to distinguish the two
cases. A similar consideration holds for t
2
, so that we have two more cases,
plus the additional case in which the firing of the timed transition cannot be
followed by that of any immediate transition. We hence have five possible
situations:
1. T
a
is followed by t
1
when only t
1
is enabled (transition T
a1
with rate
w
a
);
2. T
a
is followed by t
1
when both t
1
and t
2
are enabled (transition T
a12
with rate w
a
w
1
/(w
1
+ w
2
));
3. T
a
is followed by t
2
when only t
2
is enabled (transition T
a2
with rate
w
a
);
4. T
a
is followed by t
2
when both t
2
and t
1
are enabled (transition T
a21
with rate w
a
w
2
/(w
1
+ w
2
));
5. T
a
is not followed by any immediate transition (transition T
0
with rate
w
a
).
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