  In this paper, we propose a macroscopic model that describes the influence of
a slow moving large vehicle on road traffic. The model consists of a scalar
conservation law with a non-local constraint on the flux. The constraint level
depends on the trajectory of the slower vehicle which is given by an ODE
depending on the downstream traffic density. After proving well-posedness, we
first build a finite volume scheme and prove its convergence, and then
investigate numerically this model by performing a series of tests. In
particular, the link with the limit local problem of [M. L. Delle Monache and
P. Goatin, J. Differ. Equ. 257 (2014), 4015--4029] is explored numerically.
