TIME IN PETRI NETS - Modelling with Generalised Stochastic Petri Nets - page 66

p 1 p 2

T 1

Figure 3.13: Timed transition with enabling degree 3

present in both input places. Borrowing from queueing network terminology,
we can consider the following different situations.

1. Single-server semantics: a firing delay is set when the transition
is first enabled, and new delays are generated upon transition firing
if the transition is still enabled in the new marking. This means that
enabling sets of tokens are processed serially, and that the temporal
specification associated with the transition is independent of the en-
abling degree, except for special marking dependency functions that
will be discussed in Chapter 6.

2. Infinite-server semantics: every enabling set of tokens is processed
as soon as it forms in the input places of the (timed) transition. Its
corresponding firing delay is generated at this time, and the timers
associated with all these enabling sets run down to zero in parallel.
Multiple enabling sets of tokens are thus processed in parallel. We can
say that the overall temporal specifications of transitions with this
semantics depend directly on their enabling degrees.

3. Multiple-server semantics: enabling sets of tokens are processed as
soon as they form in the input places of the transition up to a maximum
degree of parallelism (say K). For larger values of the enabling degree,
the timers associated with new enabling sets of tokens are set only
when the number of concurrently running timers decreases below the
value f K. The overall temporal specifications of transitions with this
semantics depend directly on their enabling degrees up to a treshold
value K,

2 .

2 Observe that in this case the single server semantics actually implies a more restricted
meaning than in queueing networks, where the presence of one server may be associated
with a variable service speed.