Graphics Programs Reference
Figure 3.17: Timed PN model of the readers & writers system
A Timed PN Model Example
To conclude this chapter, we illustrate the timed PN model resulting from
the introduction of temporal specifications in the readers & writers example
discussed earlier in this topic.
The timed PN model of the readers & writers system is shown in Fig. 3.17.
The model comprises three timed and four immediate transitions. Timed
transitions are used to represent the reading and writing actions as well as
the local activities performed by processes between two subsequent accesses
to the database. Immediate transitions are used to implement the decision
of which action a process wants to perform on the data base and to imple-
ment the coordination among reading and writing activities. The complete
specification of the three timed transitions is the following:
• T 1 models the process activity not related to the data base access.
The memory policy for T 1 is age memory (observe that the enabling
memory policy can also be chosen, since the transition is not in con-
flict with other transitions). The timing semantics of the transition is
• T 6 models the data base read activity. The memory policy for T 6 is age
memory (also in this case the enabling memory policy produces the
The timing semantics of the transition is infinite-
• T 7 models the data base write activity. The memory policy for T 7 is age
memory (once more, the enabling memory policy is equivalent). The
timing semantics of the transition is single-server (however, the initial
marking of the model - 1 token in place p 5 - prevents the enabling
degree of transition T 7 from exceeding 1, thus making inessential the
difference between single-server and multiple-server specifications).
The pair of conflicting immediate transitions t 2 and t 3 allows the selection
between a read and a write request. The two immediate transitions t 4 and
t 5 allow the start of either a read or a write access.
The main reason for the introduction of temporal specifications into PN
models is the interest for the computation of performance indexes. Con-
sider for example the multiprocessor system modelled by the PN system in
Fig. 3.5. In this case, it may be of interest to answer the following questions: