  We consider the problem to transport resources/mass while abiding by
constraints on the flow through constrictions along their path between
specified terminal distributions. Constrictions, conceptualized as toll
stations at specified points, limit the flow rate across. We quantify flow-rate
constraints via a bound on a sought probability density of the times that
mass-elements cross toll stations and cast the transportation scheduling in a
Kantorovich-type of formalism. Recent work by our team focused on the existence
of Monge maps for similarly constrained transport minimizing average kinetic
energy. The present formulation in this paper, besides being substantially more
general, is cast as a (generalized) multi-marginal transport problem - a
problem of considerable interest in modern-day machine learning literature and
motivated extensive computational analyses. An enabling feature of our
formalism is the representation of an average quadratic cost on the speed of
transport as a convex constraint that involves crossing times.
