the subway reduces
to a question of mass transport
along a directed graph
with around a hundred nodes, or stations.
of course the weights on the arcs
(representing the number of passengers traveling
between each two stations)
does not remain constant--
so we must introduce time,
i.e, a differential equation, but the problem remains,
the solution to the rush hour crunch does require fractional trains,
naturally, but that is not a problem for the theoretician.