GSPN BASICS - Modelling with Generalised Stochastic Petri Nets - page 107

Table 5.2: Characteristics of the immediate transitions in the example

GSPN model

transition weight priority ECS

t read 8 2 1

t write 2 2 1

t start r 1 3 2

t start w 1 4 3

t start LAN r 1 1 4

t start LAN w 1 1 4

t think 9 1 5

t reaccess 1 1 5

conflict sets that are either free-choice or non-free-choice. Note also that
only the relative values of weights associated with immediate transitions are
important: if all weights are multiplied or divided by an arbitrary constant,
the model behaviour does not change.

5.6 Some Fine Points

Let us return to the points we raised in the previous sections, but left unan-
swered. These are:

1. the need for an explicit priority of immediate over timed transitions;

2. the irrelevance of the distinction between resampling, enabling mem-
ory, and age memory;

3. the impossibility for two timers to expire at the same time.

All three points relate to the properties of the negative exponential pdf.
This distribution characterizes a continuous random variable, hence it is a
continuous function defined in the interval [0, ∞ ), that integrates to one.
The lack of discontinuities in the function makes the probability of any spe-
cific value x being sampled equal to zero (however, obviously, the probability
that a value is sampled between two distinct values x 1 ≥ 0 and x 2 > x 1 is
positive). The particular shape of the negative exponential pdf is such that
the memoryless property [37] holds, as explained in Appendix A. This means
that, if the exponentially distributed random variable models a lifetime, at
any time instant the residual life has the same negative exponential pdf as
the entire lifetime.
Let us look now at the three previous points in order.