Simulation of pedestrian flows by optimal control and differential games

Gaining insights into pedestrian flow operations and assessment tools for pedestrian walking speeds and comfort is important in, for instance, planning and geometric design of infrastructural facilities, as well as for management of pedestrian flows under regular and safety-critical circumstances. Pedestrian flow operations are complex, and vehicular flow simulation modelling approaches are generally not applicable to pedestrian flow modelling. This article focusses on pedestrian walking behaviour theory and modelling. It is assumed that pedestrians are autonomous predictive controllers that minimize the subjective predicted cost of walking. Pedestrians predict the behaviour of other pedestrians based on their observations of the current state as well as predictions of the future state, given the assumed walking strategy of other pedestrians in their direct neighbourhood. As such, walking can be represented by a (non-co-operative or co-operative) differential game, where pedestrians may or may not be aware of the walking strategy of the other pedestrians.