Fluid approximation of broadcasting systems

Nature-inspired paradigms have been proposed to design and forecast behaviour of open distributed systems, such as sensor networks and the internet of things. In these paradigms system behaviour emerges from (complex) interactions among a large number of agents. Modelling these interactions in terms of classical point-to-point communication is often not practical. This is due to the large scale and the open nature of the systems, which means that partners for point-to-point communication may not be available at any given time. Nevertheless the need for efficient formal verification of qualitative and quantitative properties of these systems is of utmost importance, especially given their proposed pervasive and transparent nature. CARMA is a recently proposed formal modelling language for open distributed systems, which is equipped with a broadcast communication in order to meet the communication challenges of such systems. The inclusion of quantitative information about the timing and probability of actions gives rise to models suitable for analysing questions such as the probability that information will achieve total coverage within a system, or the expected market share that might be gained by competing service providers relying on viral advertising. The ability to express models is not the only challenge, because the scale of the systems we are interested in often defies discrete state-based analysis techniques such as stochastic simulation. This is the problem that we address in this paper as we consider how to provide an efficient fluid approximation, supporting efficient and accurate quantitative analysis of large scale systems, for a language that incorporates broadcast communication.