  Human dynamics and sociophysics suggest statistical models that may explain
and provide us with better insight into social phenomena. Here we tackle the
problem of determining the distribution of the population density of a social
space over time by modelling the dynamics of agents entering and exiting the
space as a birth-death process. We show that, for a simple agent-based model in
which the probabilities of entering and exiting the space depends on the number
of agents currently present in the space, the population density of the space
follows a gamma distribution. We also provide empirical evidence supporting the
validity of the model by applying it to a data set of occupancy traces of a
common space in an office building.
