As we have seen Petri Nets can be used to model dynamic systems. Time is an important part of such systems. Therefore is has been of interest to extend Petri Nets so that they can model real time systems.There are several ways in which time can be included. Our timed Petri Nets are derived from classical Petri Nets by associating a firing duration drawn from some random distribution (not excluding a constant value), with each transition in the net. The transition is disabled from occurring for the duration time, but is fired immediately after becoming enabled.
Such timed Petri Nets can be used for performance evaluation of the systems they model.
The time is modeled in the net by inscribing the density function of the distribution in the transition box.
___________________ |Arrival Generation | | _______ | | (•)<-->|_t_=_5_|----->( ) | G Gen | Q |___________________|In the net above the time delay (execution time) of the transition Gen is 5 time units. The working of the generator is the following: In the initial state of the net Gen is enabled and will therefore immediately fire, i.e., the token in G is consumed. Then there is a delay of 5 time units before the firing is complete and tokens are deposited into G and Q. Now Gen is again enabled and will again fire. Because of G only one generation at a time is active. If missing, infinitely many generations would start, because Gen is then always enabled.The time between firings is thus 5 time units, which means that the time inscribed in the generating transition shall be interpreted as the inter-arrival time of items generated.
If we make the inscription t = nexp(5) in the transition Serv of the Service refinement it would mean that the service times are distributed according to the negative exponential distribution with mean duration of 5 time units. The variation of the negative exponential distribution is from zero to infinity.