In this paper we present and compare two diier-ent approaches for the transient solution of Markov regenerative stochastic Petri Nets: the method based on Markov regenerative theory and the method of supplementary variables. In both cases the equations that govern the marking process of the non-Markovian stochastic Petri net are presented and then solved either in time-domain or using a Laplace...

We consider asynchronously composed I/O-Petri nets (AIOPNs) with built-in communication channels. They are equipped with a compositional semantics in terms of asynchronous I/O-transition systems (AIOTSs) admitting infinite state spaces. We study various channel properties that deal with the production and consumption of messages exchanged via the communication channels and establish useful rela...

This paper addresses the computation of lower bounds for the steady-state throughput of stochas-tic Petri nets with immediate and exponentially distributed service times of transitions. We try to deeply bridge stochastic Petri net theory to untimed Petri net and queueing networks theories. Previous results for general service time distributions are improved for the case of Markovian nets by con...

Some insight on the meaning of \modeling power" for Stochastic Petri Net models is given. Extensions characterizing a Stochastic Petri Net are categorized as logical or stochas-tic. Three logical constructs are shown to be equivalent: inhibitor arcs, transition priorities, and enabling functions associated with the transitions. A direct transformation of Petri Nets with inhibitor arcs into Petr...

This paper presents an efficient method to evaluate the performance of an extended stochastic Petri net by simple algebraic operations. The reachability graph is derived from an extended stochastic Petri net, and then converted to a timed stochastic state machine, using a semi-Markov process. The n-th moments of the performance index are derived by algebraic manipulations with each of the n-th ...

The complexity of gene regulatory network models stems from the fact that the models should be able to represent continuous, discrete as well as stochastic aspects of gene regulation. Hybrid stochastic Petri nets are the models, which can fairly incorporate all these aspects while keeping the model as simple as possible for biologists. This paper constructs an Hybrid Petri net model of the fiss...

There are widely used analysis techniques for stochastic Petri nets with phase type (PH) distributed firing times. These techniques are based on the generation of an expanded Markov chain that describes the behaviour of the marking process and additionally the phase processes of the involved PH distributions. In this paper we investigate the use of a similar approach when the firing time distri...

In this paper we evaluate the performance of design alternatives for Web proxy cache architectures. Our performance study employs deterministic and stochastic Petri nets (DSPN) as stochastic modeling formalism because DSPN provide an illustrative graphical representation. The presented DSPN models address in particular the sensitivity of the performance of proxy cache architectures on the traff...

AbstmctThe original proposals of several stochastic Petri net modeling techniques and of generalized stochastic Petri nets (GSPN) in particular were based mainly on the characteristics of their underlying stochastic processes. This led to the use of GSPN only as a shortened notation for the description of stochastic models. Although already quite useful in practice, this approach did not fully ...