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.

A Tool for the Automatic Derivation of Symbolic ODE from Symmetric Net Models

Marco Beccuti;Lorenzo Capra;Massimiliano De Pierro;Laura Follia;Simone Pernice
2019

Abstract

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.
2019 IEEE 27th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS)
Rennes, France
October 22-24, 2019
2019 IEEE 27th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS)
IEEE Computer Society
36
48
978-1-7281-4950-9
Color;Tools;Petri nets;Stochastic processes;Mathematical model;Computational modeling;Analytical models;High-Level Petri Nets, Symmetric Nets, Symbolic structural relations, Ordinary Differential Equations
Marco Beccuti, Lorenzo Capra, Massimiliano De Pierro, Giuliana Franceschinis, Laura Follia, Simone Pernice
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1725811
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