ANALYSIS OF GSPN MODELS - Modelling with Generalised Stochastic Petri Nets - page 131

p 1

µ 2 T 2 µ 1 T 1

p 2 t 1 p 3

α

β t 2

Figure 6.10: A GSPN system with multiple paths between tangible markings

Table 6.10: Specification of the transitions of the SPN of Fig. 6.10

transition rate semantics

T 1 µ 1 single-server

transition weight priority ECS

T 2 µ 2 single-server

t 1 α 1 1

t 2 β 1 1

size of the set of tangible markings). However, this method requires the
computation of the steady-state probability of each vanishing marking that
does not increase the information content of the final solution since the time
spent in these markings is known to be null. Moreover, vanishing markings
not only require useless computations, but, by enlarging the size of the tran-
sition probability matrix U, tend to make the computation of the solution
more expensive and in some cases even impossible to obtain.
In order to restrict the solution to quantities directly related with the compu-
tation of the steady-state probabilities of tangible markings, we must reduce
the model by computing the total transition probabilities among tangible
markings only, thus identifying a Reduced EMC (REMC).
To illustrate the method of reducing the EMC by removing the vanishing
markings, consider first the example of Fig. 6.10. This system contains
two free-choice conflicts corresponding to transitions T 1 , T 2 , and t 1 , t 2 ,
respectively. The transition characteristics are specified in Table 6.10. From
the initial marking M i = p 1 , the system can move to marking M j = p 3
following two different paths. The first corresponds to the firing of transition