This paper presents an extension of the Generalized Stochastic Petri Net (GSPN) formalism that enables the computation of first passage time distributions. The tagged customer technique typical of queuing networks is adapted to the GSPN context by providing a formal definition and an automatic computation of the groups of tokens that can be identified as customers, i.e. classes of homogeneous entities behaving in a similar manner. Passage times are identified through the concept of events that correspond to the firing of transitions placed at the boundaries of a subnet. The extended model obtained with this specifications is translated into an ordinary GSPN by isolating a customer from the group and highlighting its path through the net thus obtaining a representation suited for the passage time analysis. Proofs are provided to show the equivalence between these models with respect to their steady state distributions. An important and original aspect treated in this paper is the possibility of specifying several scheduling policies of tokens at places, an information not present in ordinary GSPN models, but that is vital for the precise computation of first passage time distributions as shown by a few results computed for a simple Flexible Manufacturing application.

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The global multilevel priority de nition in GSPN, while being most convenient with many respects, poses some modelling problems related with confusion and indirect con icts, which may lead to undesired e ects in the de nition of the underlying stochastic process. While some of these problems have been recognized and dealt with in previous works on the de nition of GSPN, through the introduction of extended c on ict sets, some others, that will be illustrated in this paper, were not covered. To overcome all these problems, in this paper a syntactical subclass of GSPN, called detached priorities GSPN dpGSPN, is proposed. In dpGSPN no confusion or indirect con icts are p ossible, and according to our experience, modelling power is not substantially sacri ced. To facilitate the modelling, a possible method to derive a suitable global priority de nition from local information is outlined.

Structural properties of Petri Nets (PN) have an important role in the process of model validation and analysis. When dealing with high level Petri nets (HLPN) structural analysis still poses many problems and often tools go through the unfolding of the HLPN model and apply PN structural analysis techniques to the unfolded model: with this approach the symmetries present in the models are completely ignored and cannot be exploited. Structural properties of HLPN can be defined as relations among node instances using symbolic and parametric expressions; the computation of such expressions from the model structure and annotations requires the development of a specific calculus, as the one proposed in the literature for Symmetric Nets (SN). When dealing with Stochastic SN (SSN), comprising stochastic timed transitions and immediate transitions, structural analysis becomes a fundamental step in net-level definition of probabilistic parameters. Moreover some structural relations allow to automatize the derivation of symbolic Ordinary Differential Equations for the solution of SSN models with huge state space. The goal of the present paper is to summarize the language defined to express SNs' structural relations, to complete the formalization of some interesting structural properties as expressions of the calculus, and to provide examples of their use. The algorithms required to support the calculus for symbolic structural relations computation have been recently completed and implemented in a tool called SNexpression.

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