TIME IN PETRI NETS - Modelling with Generalised Stochastic Petri Nets - page 62

value and will continue later on the count-down.

• Restart. The timer associated with the transition is restarted, i.e.,
its present value is discarded and a new value will be generated when
needed.

To model the different behaviours arising in real systems, different ways of
keeping track of the past are possible by associating different continue or
restart mechanisms with timed transitions. We discuss here three alterna-
tives:

• Resampling. At each and every transition firing, the timers of all
the timed transitions in the timed PN system are discarded (restart
mechanism). No memory of the past is recorded. After discarding all
the timers, new values of the timers are set for the transitions that are
enabled in the new marking.

• Enabling memory. At each transition firing, the timers of all the
timed transitions that are disabled are restarted whereas the timers
of all the timed transitions that are not disabled hold their present
value (continue mechanism). The memory of the past is recorded with
an enabling memory variable associated with each transition. The
enabling memory variable accounts for the work performed by the
activity associated with the transition since the last instant of time its
timer was set. In other words, the enabling memory variable measures
the enabling time of the transition since the last instant of time it
became enabled.

• Age memory. At each transition firing, the timers of all the timed
transitions hold their present values (continue mechanism). The mem-
ory of the past is recorded with an age memory variable associated with
each timed transition. The age memory variable accounts for the work
performed by the activity associated with the transition since the time
of its last firing. In other words, the age memory variable measures
the cumulative enabling time of the transition since the last instant of
time when it fired.

The three memory policies can be used in timed PN models for different
modelling purposes. In the first case (resampling) the work performed by
activities associated with transitions that do not fire is lost. This may be
adequate for modelling, for example, competing activities of the type one
may find in the case of the parallel execution of hypothesis tests. The pro-
cess that terminates first is the one that verified the test; those hypotheses
whose verification was not completed become useless, and the correspond-
ing computations need not be saved.

The practical and explicit use of this