Continuum modelling of pedestrian flows: From microscopic principles to self-organised macroscopic phenomena

The dynamics of pedestrian flows can be captured in a continuum modelling framework. However, compared to vehicular flow, this is a much more challenging task. In particular the integration of flow propagation and path choice are known to be problematic. Furthermore, pedestrian flow is characterised by different self-organised phenomena, such as the formation of dynamic lanes and diagonal stripes, which have not yet been captured in a continuum modelling framework. This contribution puts forward a novel multi-class continuum model that captures some of the key features of pedestrian flows. It considers path choice behaviour on both the strategic (pre-trip) and tactical (en-route) level. To achieve this, we present a methodology to derive a continuum model from a microscopic walker model, in this case the social forces model. In doing so, we show that the interaction term present in the social forces model introduces a local path choice component in the equilibrium velocity. Having derived the model, we analyse its properties both by means of mathematical analyses and simulation studies. This reveals the general behaviour of the model, as well as the ability of the model to reproduce self-organised structures, and phase transitions. To the best of our knowledge, this is the first continuum model that is able to reproduce these self-organised structures.