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

Bruno Gaujal 1 Florence Perronnin 1, * Remi Bertin 1, 2, *
* Corresponding author
1 MESCAL - Middleware efficiently scalable
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
Abstract : In this paper we present a class of hybrid systems 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 based on the extension to continuous state-space of coupling-from-the-past techniques introduced by Foss and Tweedie (Stoch Models 14:187-204, 1998) and using suitable envelope trajectories to tackle non-monotonicity. 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 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.
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Bruno Gaujal, Florence Perronnin, Remi Bertin. Perfect simulation of a class of stochastic hybrid systems with an application to peer to peer systems. Discrete Event Dynamic Systems, Springer Verlag, 2008, Special Issue on Hybrid Systems, 18 (2), pp.211-240. ⟨10.1007/s10626-008-0042-7⟩. ⟨hal-00874342⟩

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