# Perfect Simulation of a Class of Stochastic Hybrid Systems with an Application to Peer to Peer Systems

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## 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.

## Keywords

Hybrid stochastic systems Perfect simulation Peer to peer systems## Notes

### Acknowledgements

We would like to thank the three reviewers of this paper whose in-depth study of our work and constructive comments helped us greatly in improving the quality of this paper.

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