GSPN REPRESENTATION OF PHASE-TYPE DISTRIBUTIONS - Modelling with Generalised Stochastic Petri Nets - page 171

Table 7.9: Performance figures computed for the Central Server Models of
Figs. 7.3, 7.10, and 7.11

CPU service time System System CPU

distribution throughput resp. time utilization

Erlang-3 with Age Memory 0.049082 112.2444 0.99874

Negative Exponential 0.047969 115.0805 0.97961

Erlang-3 with Enabling Memory 0.036253 155.4944 0.99670

that is lost due to the interruptions.
This shows that in many situations the possibility of specifying timed tran-
sitions with non-exponential firing time distributions can be important and
that confining the impact of this specification at the solution level is essen-
tial to keep under control the complexity of the analysis techniques used to
study these models.

7.3 General Phase-Type Distributions

The basic idea used for developing a convenient representation of Erlang-r
firing time distributions is exploited in [ 13] to construct subnets whose pas-
sage times have general PH distributions still showing the property of being
easy to embed in standard GSPN models with the same type of substitution
rules sketched for the Erlang-3 distribution. In particular, all the expan-
sions reported in [13] present the important characteristic of being of the
one-in/one-out type and of having a compact structure capable of accommo-
dating distributions of the same type, but with different parameters within
the same GSPN layout. This compact representation is especially impor-
tant to allow the implementation of the memory policies in a self-contained
manner.
With the use of this technique it is conceivable to devise algorithms that
automatically perform the substitution of a standard timed transition with
negative exponential firing time distribution, with a subnet implementing a
general PH distribution, producing a detailed version of the model that is
used for performance analysis, but is completely transparent to the user. In
this way, the analyst could be relieved from the burden of understanding the
meaning of the many arcs that must be added to implement the memory
policies and could concentrate on the more important tasks of capturing the
relevant feature of the system with the model and of interpreting the exact
meanings of the results of the analysis.