Structural, temporal and stochastic properties of unbounded free-choice Petri netsReportar como inadecuado

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1 MISTRAL - Modeling of Computer Systems and Telecommunication Networks : Research and Software Development CRISAM - Inria Sophia Antipolis - Méditerranée

Abstract : In this paper, we show how a decomposition of a free choice Petri net into a ``routing- network and marked graph subnetworks i.e. linear subnetworks in the $\max, +$ setting leads to new methods and algorithms to test structural as well as temporal properties of the net. Although several results hold for general free choice nets, the paper primalily focuses on the class of single input-free choice nets, defined here. We show how this decomposition in linear subnets allows one to: in the untimed case check liveness in polynomial time; in the timed case establish evolution equations which allow to represent the system as a coupling of two linear systems, a $\min,+$-linear system, and a quasi $+,\times$-linear one; in the stochastic case check stability, i.e. the fact that the marking remains bounded in probability. The main tools for proving these properties are graph theory, idempotent algebras and ergodic theory.


Autor: François Baccelli - Bruno Gaujal Serguei Foss



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