Higher Moment Analysis of a Spatial Stochastic Process Algebra

We introduce a spatial stochastic process algebra called MASSPA, which provides a formal behavioural description of Markovian Agent Models, a spatial stochastic modelling framework. We provide a translation to a master equation which governs the underlying transition behaviour. This provides a means of simulation and thus comparison of numerical results with simulation that was previously not available. On the theoretical side, we develop a higher moment analysis to allow quantities such as variance to be produced for spatial stochastic models in performance analysis for the first time. We compare the simulation results against resulting ODEs for both mean and standard deviations of model component counts and finish by analysing a distributed wireless sensor network model.