Mesoscopic modelling of pedestrian movement using Carma and its tools

In this paper we assess the suitability of the Carma (Collective Adaptive esource-sharing Markovian Agents) modelling language for mesoscopic modelling of patially-distributed systems where the desired model lies between an individual-based (microscopic) spatial model and a population-based (macroscopic) spatial model. Our modelling approach is mesoscopic in nature because it does not model the movement of individuals as an agent-based simulation in two-dimensional space, nor does it make a continuous-space approximation of the density of a population of individuals using partial differential equations. The application which we consider is pedestrian movement along paths which are expressed as a directed graph. In the models presented, pedestrians move along path segments at rates which are determined by the presence of other pedestrians, and make their choice of the path segment to cross next at the intersections of paths. Information about the topology of the path network and the topography of the landscape can be expressed as separate functional and spatial aspects of the model by making use of Carma language constructs for representing space. We use simulation to study the impact on the system dynamics of changes to the topology of paths and show how Carma provides suitable modelling language constructs which make it straightforward to change the topology of the paths and other spatial aspects of the model without completely restructuring the Carma model. Our results indicate that it is difficult to predict the effect of changes to the network structure and that even small changes can have significant effects.