PETRI NETS WITH sPRIORITY - Modelling with Generalised Stochastic Petri Nets - page 88

p 1

t l

_2

π l = 1

p 2

t k

π k = 2

p 3

t m

π m = 1

Figure 4.7: An example of ΠME relation

priority levels 0, 1, and 2. Seven markings enable priority 0 transitions, three
markings enable priority 1 transitions (namely M 2 , M 3 , and M 7 ), and three
enable priority 2 transitions (namely M 1 , M 6 , and M 10 ). In Fig. 4.8 and
Fig. 4.9, markings at priority level 1 have a ∗ superscript, while markings
at priority level 2 have a ∗∗ superscript.

Reduced reachability graphs — Often, when performing the analysis
of a priority PN model, we are interested only in a part of the model be-
haviour, such as the enabling and firing of transitions with priority level less
than or equal to a given threshold. This is in particular the case when the
priority PN model describes the underlying logic of a timed PN model, in
which higher priority transitions are immediate and fire in zero time, while
the enabling of lowest priority transitions lasts for non-negligible amounts
of time. In such cases, it is convenient to introduce the construction of a
reduced reachability graph up to priority level L (denoted L-RRG), in which
all markings enabling transitions of priority greater than L “vanish”. The
indirect conflict between transitions at priority level L can be directly rec-
ognized by the analysis of the L-RRG as if it was a regular conflict on
that graph. In the GSPN framework, the 0-RRG is usually called Tangible
Reachability Graph (TRG), because its nodes are the tangible markings.
Figs. 4.10 and 4.11 depict the 1-RRG and the 0-RRG, respectively, associ-
ated with the readers & writers PN model with priority. Notice the labelling
of the arcs representing sequences of higher priority transition firings that
substitute higher priority sequences of markings. These sequences should
contain an indication of the higher priority transition firings, together with