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.