Investigating fluid-flow semantics of asynchronous tuple-based process languages for collective adaptive systems

Recently, there has been growing interest in nature-inspired interaction paradigms for Collective Adaptive Systems, for modelling and implementation of adaptive and context-aware coordination, among which the promising pheromone-based interaction paradigm. System modelling in the context of such a paradigm may be facilitated by the use of languages in which adaptive interaction is decoupled in time and space through asyn- chronous buffered communication, e.g. asynchronous, repository- or tuple- based languages. In this paper we propose a differential semantics for such languages. In particular, we consider an asynchronous, repository based modelling kernel-language which is a restricted version of LINDA, extended with stochastic information about action duration. We provide stochastic formal semantics for both an agent-based view and a population-based view. We then derive an ordinary differential equation semantics from the latter, which provides a fluid-flow deterministic approximation for the mean be- haviour of large populations. We show the application of the language and the ODE analysis on a benchmark example of foraging ants.