  This paper addresses congested transport, which can be described, at
macroscopic scales, by a continuity equation with a pressure variable generated
from the hard-congestion constraint (maximum value of the density). The main
goal of the paper is to show that, in one spatial dimension, this continuum PDE
can be derived as the mean-field limit of a system of ordinary differential
equations that describes the motion of a large number of particles constrained
to stay at some finite distance from each others. To show that these two models
describe the same dynamics at different scale, we will rely on both the
Eulerian and Lagrangian points of view and use two different approximations for
the density and pressure variables in the continuum limit.
