Exact(3)
So, we developed a method allowing generation of firing sequences from an initial marking to a final marking.
It associates to each pair (place, transition) or (transition, place) the weight of the corresponding arc in the net; ▪ M init : P → N+ is an initial marking in R (tokens contained in the initial places).
In order to find out the reachability of the proposed model, it is necessary to locate a sequence of events or transitions which would transform an initial marking to a final marking by representing the required functioning behavior of the network.
Similar(57)
In this paper, we obtain a purely structural characterization of SΠ-nets for which a product-form solution exists for any value of probabilistic parameters of the SPN and for any initial marking.
A place belonging to a P-invariant is obviously bounded, i.e. the number of tokens on each place is finite in any reachable marking, and CPI causes structural boundedness, i.e. boundedness for any initial marking.
Second, the net Net(p) associated to a process p is statically reduced: this ensures that Net(p) and Net((pp)) are the same unmarked net, but with a different initial marking; on the contrary, in [18] Net(p) was only dynamically reduced.
Figure 5 A simple PN with initial marking [ 29 ].
Consequently, a structural deadlock needs a non-empty initial marking.
Check whether each P-invariant gets a non-zero initial marking (concentration).
This has to be done with care, as a badly chosen initial marking can result in so called "deadlocks", i.e. when none of the transitions can be fired anymore.
Given a marking I called the initial marking, we define a marking M t) called the marking at time t and a marking M r (t) called the reserved marking at time t for t ≥ 0 in the following way.
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