Perfect simulation of stochastic hybrid systems with an application to peer to peer systems

In this paper we present a rather general hybrid system made of deterministic differential equations and random discrete jumps. We then show how to construct a simulation of such a stochastic hybrid system that provides perfect samples of its asymptotic behavior. The applicability of the method is illustrated by showing how this framework can be used to model the Squirrel peer to peer system and by reporting a simulation study based on this approach. This paper provides both a general framework on how to carry simulation based experimental studies of large and complex hybrid systems and its application in the Squirrel model demonstrating how versatile and powerful this approach can be over a typical example. Key-words: backward coupling, stochastic hybrid systems, simulation, P2P systems, fluid models § Supelec, Metz. This work was done while this author was visiting the Laboratory ID-IMAG under an INRIA internship ∗ INRIA. Email: [email protected] † Lab. ID-IMAG (CNRS, INPG, INRIA, UJF) 51, Av. J. Kunztmann, Montbonnot, France ‡ Université Joseph Fourier. Email: [email protected] Simulation Parfaite de systèmes hybrides stochastiques avec application à un système pair-à-pair Résumé : Dans cet article nous définissons un système hybride assez général composé d’équations différentielles déterministes et de saut aléatoires discrets. Nous montrons ensuite comment construire une simulation parfaite d’un tel système hybride, qui fournit des échantillons distribués exactement selon la mesure stationnaire. Nous illustrons ensuite cette méthode en proposant une évaluation de performances du système pair-à-pair Squirrel modélisé par un système hybride. Mots-clés : Couplage vers l’arrière, systèmes hybrides stochastiques, simulation, systèmes pairà-pair, modèles fluides Perfect simulation of hybrid systems 3