Modelling Non-linear Crowd Dynamics in Bio-PEPA

Citation

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

Abstract
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" [20]. 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 [20] 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.

Keywords
; Linear and multilinear algebra; matrix theory; Partial differential equations; Induction (Mathematics)