Constructal theory of pedestrian dynamics

The standard benefit of modeling pedestrian streams is the ability to quantify and understand flow patterns, which can be helpful to avoid some potentially dangerous situations. Here we show that the most basic features of pedestrian dynamics can be put on a unifying theoretical basis, which is provided by the constructal law. This law states that every flow system evolves in time so that it develops the flow architecture that maximizes flow access under the constraints posed to the flow. In this Letter, we develop a model of pedestrian streams that accounts for the influence of pedestrian density. The constructal law is invoked in order to quantify both the so-called optimal level of service and system capacity for pedestrian streams.