Stochastic process algebra and stability analysis of collective systems

Collective systems consist of large numbers of agents that coordinate through local behaviour, adapt to their environment and possibly give rise to emergent phenomena. Their formal analysis requires advanced scalable mathematical approximation techniques. We show how Stochastic Process Algebra (SPA) can be combined with numeric analysis tools for the analysis of emergent behavioural aspects of such systems. The approach is based on an automatic transformation of SPA models into ordinary differential equations in a format in which numeric and symbolic computing environments can be used to perform stability analysis of the system. The potential of the approach is illustrated by a crowd dynamics scenario in which various forms of behavioural and topological asymmetry are introduced. These are cases in which analytical approaches to stability analysis are in general not feasible.The analysis also shows some surprising aspects of the crowd model itself.