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## Performance Evaluation of Parallel Systems by Using Unbounded Generalized Stochastic Petri Nets.

Granda, M.;
Drake, J.M.;
Gregorio, J.A.
In:
1: *IEEE Transactions on Software Engineering, 18*.
1992.

Abstract:
This paper presents methods of calculating efficiently the performance
measures of parallel systems by using unbounded generalized stochastic
Petri nets. One of the main limitations of the use of Petri nets for
modeling and evaluating the performance of complex parallel systems is the
explosion in the number of states to be analyzed. This is what occurs when
unbounded places appear in the model. The state space of such nets is
infinite, but it is possible to take advantage of the natural symmetries
of the system to aggregate the states of the net and construct a finite
graph of lumped states which can easily be analyzed. With the methods
developed in this paper, the unbound places introduce a complexity similar
to that of safe places of the net. These methods can be used to evaluate
models of open parallel systems in which unbounded places appear; systems
which are k-bounded but are complex and have large values of k can also be
evaluated in an approximate way by means of simpler unbounded models. From
the steady-state solution of the model, it is possible to obtain
automatically the performance measures of parallel systems represented by
this type of nets, such as the time devoted to the execution of each task,
the time during which each processor of the system is operating or the
memory necessary for the execution of a job in a multiprocessor
architecture.

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