Differential Analysis of Interacting Automata with Immediate Actions

The stochastic modelling of software systems with activities of durations that are separated by many orders of magnitude typically leads to numerical complications, due to stiffness. To avoid explicit state-space generation—a prerequisite to tackle this problem via suitable manipulations or aggregations—in this paper we present an accurate and scalable fluid approximation. It is expressed as a compact piecewise linear system of ordinary differential equations, which have discontinuous right-hand sides as a result of the incorporation of immediateness. We study the nature of this approxi- mation in a general high-level framework of interacting automata. On a case study of client/server interaction, our approach is ca two times faster than the analysis conducted on the stiff equations where immediate actions are explicitly modelled.