Constructal design for pedestrian movement in living spaces: Evacuation configurations

Here we show that the configuration of an inhabited area controls the time required by all the pedestrians to vacate the space. From the minimization of the global evacuation time emerges the optimal configuration of the area. This is a fundamental principle for designing living spaces with efficient evacuation quality, and it is demonstrated here with several simple building blocks that can be used as components of more complex living structures: single walkway, corner, and T-shaped walkway. We show analytically and numerically that the ratio of the widths of the stem and branches of the T-shaped walkway has an optimal value that facilitates the evacuation of all the inhabitants. This result is fundamental, and is the crowd-dynamics equivalent of the Hess-Murray rule for the ratio of diameters in bifurcated ducts with fluid flow.