I n this paper we characterize a class of stochastic Petri nets that can be solved using matrix geometric techniques. Advantages of such a n approach are that very efficient mathematical technique become available for practical usage, as well as that the problem of large state spaces can be circumvented. W e first characterize the class of stochastic Petri nets of interest by formally defining ...

Generalizedd StochasticPetriNetsprovidethe modeller withh immediate transitions, but aa model will be correct only if the modeller cann specify how too solve the firingg conflicts betweenn these transitions. This task is usually cumbersome andd may be impossible for large nets. Inn confusion-free nets, these conflict sets are subsets of equivalence classes of aa structural conflict relation, wh...

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...

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...

Ordinary t-timed modular Petri Nets are used for modeling, analysis, synthesis and performance evaluation of random topology dedicated production systems. Each system is first decomposed into production line, assembly, disassembly and parallel machine modules followed by derivation of their modular Petri Net models. Two sets of modules, generic and generalized respectively, are derived correspo...

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...