Massimiliano De Pierro

The GreatSPN tool: recent enhancements

GreatSPN is a tool that supports the design and the qualitative and quantitative analysis of Generalized Stochastic Petri Nets (GSPN) and of Stochastic Well-Formed Nets (SWN). The very first version of GreatSPN saw the light in the late eighties of last century: since then two main releases where developed and widely distributed to the research community: GreatSPN1.7 [13], and GreatSPN2.0 [8]. This paper reviews the main functionalities of GreatSPN2.0 and presents some recently added features that significantly enhance the efficacy of the tool.

On the Use of Stochastic Petri Nets in the Analysis of Signal Transduction Pathways for Angiogenesis Process

In this paper we consider the modeling of a selected portion of signal transduction events involved in the angiogenesis process. The detailed model of this process contains a large number of parameters and the data available from wet-lab experiments are not sufficient to obtain reliable estimates for all of them. To overcome this problem, we suggest ways to simplify the detailed representation that result in models with a smaller number of parameters still capturing the overall behaviour of the detailed one. Starting from a detailed stochastic Petri net (SPN) model that accounts for all the reactions of the signal transduction cascade, using structural properties combined with the knowledge of the biological phenomena, we propose a set of model reductions.

A high level language for structural relations in well-formed nets

Well-formed Nets (WN) structural analysis techniques allow to study interesting system properties without requiring the state space generation. In order to avoid the net unfolding, which would reduce significantly the effectiveness of the analysis, a symbolic calculus allowing to directly work on the WN colour structure is needed. The algorithms for high level Petri nets structural analysis most often require a common subset of operators on symbols annotating the net elements, in particular the arc functions. These operators are the function difference, the function transpose and the function composition. This paper focuses on the first two, it introduces a language to denote structural relations in WN and proves that it is actually closed under the difference and transpose.

First Passage Time Computation in Tagged GSPNs with Queue Places

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.

A Mean Field Based Methodology for Modeling Mobility in Ad Hoc Networks

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.

Deriving Symbolic Ordinary Differential Equations from Stochastic Symmetric Nets Without Unfolding

This paper concerns the quantitative evaluation of Stochastic Symmetric Nets (SSN) by means of a fluid approximation technique particularly suited to analyse systems with a huge state space. In particular a new efficient approach is proposed to derive the deterministic process approximating the original stochastic process through a system of Ordinary Differential Equations (ODE). The intrinsic symmetry of SSN models is exploited to significantly reduce the size of the ODE system while a symbolic calculus operating on the SSN arc functions is employed to derive such system efficiently, avoiding the complete unfolding of the SSN model into a Stochastic Petri Net (SPN).