  Capacity restrictions in stores, maintained by mechanisms like spacing
customer intake, became familiar features of retailing in the time of the
pandemic. Shopping rates in a crowded store under a social distance regime is
prone to considerable slowdown. Inspired by the random particle collision
concepts of statistical mechanics, we introduce a dynamical model of the
evolution of shopping rate as a function of a given customer intake rate. The
slowdown of each individual customer is incorporated as an additive term to a
baseline value shopping time, proportional to the number of other customers in
the store. We determine analytically and by simulation the trajectory of the
model as it approaches a Little's Law equilibrium, and identify the point
beyond which equilibrium cannot be achieved. By relating customer shopping rate
to the slowdown compared to the baseline, we can calculate the optimal intake
rate leading to maximum equilibrium spending. This turns out to be the maximum
rate compatible with equilibrium. The slowdown due to the largest possible
number of shoppers is more than compensated for by the increased volume of
shopping. This macroscopic model is validated by simulation experiments in
which avoidance interactions between pairs of shoppers are responsible for
shopping delays.
