Massink M, Latella D, Bracciali A & Hillston J (2011) Modelling Non-linear Crowd Dynamics in Bio-PEPA. In: Giannakopoulou D & Orejas F (eds.) Fundamental Approaches to Software Engineering. Lecture Notes in Computer Science, 6603. 14th International Conference on Fundamental Approaches to Software Engineering, FASE 2011, Saarbrucken, Germany, 26.03.2011-03.04.2011. Dusseldorf: Springer Verlag, pp. 96-110. http://www.springerlink.com/content/lw5812w5k78744m8/; https://doi.org/10.1007/978-3-642-19811-3_8
Emergent phenomena occur due to the pattern of non-linear and distributed local interactions between the elements of a system over time. Surprisingly, agent based crowd models, in which the movement of each individual follows a limited set of simple rules, often re-produce quite closely the emergent behaviour of crowds that can be observed in reality. An example of such phenomena is the spontaneous self-organisation of drinking parties in the squares of cities in Spain, also known as "El Botellon" . We revisit this case study providing an elegant stochastic process algebraic model in Bio-PEPA amenable to several forms of analyses, among which simulation and fluid flow analysis. We show that a fluid flow approximation, i.e. a deterministic reading of the average behaviour of the system, can provide an alternative and efficient way to study the same emergent behaviour as that explored in  where simulation was used instead. Besides empirical evidence, also an analytical justification is provided for the good correspondence found between simulation results and the fluid flow approximation.
; Linear and multilinear algebra; matrix theory; Partial differential equations; Induction (Mathematics)