High-level Petri nets (HLPNs) are an expressive formalism well supported by a number of tools that automate the editing and the interactive simulation of models and some kinds of analytical techniques, mainly based on state-space exploration. Structural analysis of HLPNs is, however, a challenging task not yet adequately supported and it is often accomplished via the unfolding of an HLPN into a corresponding low-level Petri Net. An approach to derive a system of Ordinary Differential Equations (ODEs) from a Stochastic Symmetric Net (SSN) has been proposed a few years ago, based on the net's unfolding and subsequent grouping of similar equations. This method has been recently improved by providing an algorithm that directly derives a compact ODE system (from a partially unfolded net) in a symbolic way, through algebraic manipulation of SSN annotations. In this paper, we present the automation of the calculus of Symbolic ODEs (SODEs) for SSN models as a new module of SNexpression, a tool for the symbolic structural analysis of Symmetric Nets. An application of the tool/technique to a variant of a SIRS epidemic model including antibiotic resistance is also described.

In this paper we propose a methodology for the modeling and analysis of ad hoc networks composed by a large number of nodes moving among geographical regions. This methodology uses compositional construction of stochastic Petri nets (SPN) for building the model which allows for specifying the model and the required performance indices at a high level of abstraction. As our aim is to consider real scenarios with several geographical regions and non-trivial user behavior in each region, the size of the state space of the model can easily grow too large to analyze with exact analytical approaches or even with simulation. For this reason, we propose to carry out the analysis by constructing the mean field approximation of the behavior of the SPN. The approximation is provided by a set of ordinary differential equations (ODE) that can be derived automatically from the SPN and can be solved numerically with low computational effort even for large models. The methodology is illustrated on a case study, modeling application spreading in a mobile environment. It will be shown that the approximate results obtained by the mean field approach capture well the behavior of the system.

The increasing demand for customer centric evaluation of systems, mostly related with the assessment of the quality of service that they can deliver, requires the development of techniques properly designed to model and to study the movement of specific entities generically referred to as "customers". Stochastic Well-Formed Net(SWN) are naturally suited for the representation of systems in which "customers" of different categories compete for the use of common resources. Color classes of SWN are easily associated with these different categories, leaving to the peculiar features of the formalism the possibility of exploiting all the symmetries existing into the representation for the efficient and effective computation of the measures of interest. Within this application context, the computation of first passage time distribution measures in Stochastic Well-Formed Net (SWN) is becoming of primary interest. Customers however are not primitive entities in the formalism and an approach similar to that previously developed for Generalized Stochastic Petri Nets (GSPN) is suggested to overcome this problem in which P-semiflows are used to identify the circulating "customers". In this paper we propose an original algorithm for computing some P-semiflows of colored PNs (in particular of SWNs) in parametric form by exploiting the peculiarities of the objective of this investigation, and extend the customer centric first passage time computation approach previously developed for GSPNs, to make it suitable for SWN models. Moreover, the paper proposes an enhancement of the SWN notation in order to provide a way to ease the modeler in the specification of customer scheduling policies that may affect the computation of first passage time distributions. This extension, inspired by Queueing Petri Nets, adds to SWN some "syntactic sugar" that allows to include in the model queueing places which are automatically replaced by appropriate submodels, before solving the model.

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.

Generalized stochastic Petri nets (GSPN), with immediate transitions, are extensively used to model concurrent systems in a wide range of application domains, particularly including software and hardware aspects of computer systems, and their interactions. These models are typically used for system specification, logical and performance analysis, or automatic code generation. In order to keep modeling separate from the analysis and to gain in efficiency and robustness of the modeling process, the complete specification of the stochastic process underlying a model should be guaranteed at the net level, without requiring the generation and exploration of the state space. In this paper, we propose a net-level method that guides the modeler in the task of defining the priorities (and weights) of immediate transitions in a GSPN model, to deal with confusion and conflict problems. The application of this method ensures well-definition without reducing modeling flexibility or expressiveness.