GSPN REPRESENTATION OF PHASE-TYPE DISTRIBUTIONS - Modelling with Generalised Stochastic Petri Nets - page 170

tative analysis of the problem as it hides the complexity of the firing time
distribution of the timed transition CPU as well as of its associated memory
policy, which do not affect the qualitative properties of the model. At the
moment of the performance analysis, the three models can then be used to
study the effects that the time specifications may have on the e ciency of
the system.

7.2.2 Numerical evaluation

The importance of the higher moments of certain firing time distributions
and of the firing memory policies is shown experimentally by comparing the
results of the evaluation of the models of Figs. 7.3, 7.10, and 7.11.
Tables 7.7 and 7.8 contain the parameters of the model of Fig. 7.11 that
can be used for the evaluation of the three models. All these models have
the same mean firing delay for each CPU service. The difference is that
in the model of Fig. 7.3 the second moment of the CPU service time is
neglected, thus reducing the representation of the firing time to an expo-
nential distribution. The models of Figs. 7.10 and 7.11 account instead for
the second moment of the distribution. They differ because in Fig. 7.10 an
age memory policy is assumed, while in the other case the memory policy
is of the enabling type.
Table 7.9 reports some performance measures obtained from the evaluation
of these models. The results focus on the effects that the different modelling
assumptions have on the performance of the system as seen from the regular
customers. The system throughput and response time computed with re-
spect to place think, represent the quantities that summarize the behaviour
of the system as seen from the customers. The CPU utilization can instead
be seen as an indication of system resource exploitation that is of some
interest for a possible system manager. The numerical results show that
the model with the negative exponential distribution provides performances
that are bracketed by those of the other two models, the age memory being
the policy that provides the best performance. It is interesting to observe
that replacing in this model the exponential distribution of the CPU fir-
ing time with an Erlang-3 with age memory has only a marginal effect on
the performance of the system (less than 2.5% improvement of the system
throughput), while the assumption of an Erlang-3 distribution with enabling
memory yields a considerable loss of performance from the point of view of
the regular customers (about 25% decrease in system throughput). The fact
that the CPU utilization increases when the Erlang-3 distribution is speci-
fied in the model can be explained by observing that in the case of the age
memory policy the system is more e cient and an increase in throughput
corresponds to a better system exploitation. In the case of the enabling
memory policy, the increase in CPU utilization does not correspond to an
improvement of the e ciency of the system because of the amount of work