Graphics Programs Reference

In-Depth Information

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

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