Bounds Computation for Symmetric Nets

Benoît Barbot 1 Marco Beccuti 2 Giuliana Franceschinis 3 Serge Haddad 4 Claudine Picaronny 4
4 MEXICO - Modeling and Exploitation of Interaction and Concurrency
LSV - Laboratoire Spécification et Vérification [Cachan], ENS Cachan - École normale supérieure - Cachan, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8643
Abstract : Monotonicity in Markov chains is the starting point for quantitative abstraction of complex probabilistic systems leading to (upper or lower) bounds for probabilities and mean values relevant to their analysis. While numerous case studies exist in the literature, there is no generic model for which monotonicity is directly derived from its structure. Here we propose such a model and formalize it as a subclass of Stochastic Symmetric (Petri) Nets (SSNs) called Stochastic Monotonic SNs (SMSNs). On this subclass the monotonicity is proven by coupling arguments that can be applied on an abstract description of the state (symbolic marking). Our class includes both process synchronizations and resource sharings and can be extended to model open or cyclic closed systems. Automatic methods for transforming a non monotonic system into a monotonic one matching the MSN pattern, or for transforming a monotonic system with large state space into one with reduced state space are presented. We illustrate the interest of the proposed method by expressing standard monotonic models and modelling a flexible manufacturing system case study.
Type de document :
Pré-publication, Document de travail
2018
Liste complète des métadonnées

Littérature citée [15 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01726011
Contributeur : Benoît Barbot <>
Soumis le : mercredi 7 mars 2018 - 17:12:48
Dernière modification le : samedi 10 mars 2018 - 01:17:37
Document(s) archivé(s) le : vendredi 8 juin 2018 - 15:17:33

Fichier

main.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01726011, version 1

Citation

Benoît Barbot, Marco Beccuti, Giuliana Franceschinis, Serge Haddad, Claudine Picaronny. Bounds Computation for Symmetric Nets. 2018. 〈hal-01726011〉

Partager

Métriques

Consultations de la notice

149

Téléchargements de fichiers

47