Transportation systems consist not only of the physical and organizational ele-
ments that interact with each other to produce transportation opportunities, but also
of the demand that takes advantage of such opportunities to travel from one place
to another. This travel demand, in turn, is the result of interactions among the var-
ious economic and social activities located in a given area. Mathematical models
of transportation systems represent, for a real or hypothetical transportation sys-
tem, the demand flows, the functioning of the physical and organizational elements,
the interactions between them, and their effects on the external world. Mathematical
models and the methods involved in their application to real, large-scale systems are
thus fundamental tools for evaluating and/or designing actions affecting the phys-
ical elements (e.g., a new railway) and/or organizational components (e.g., a new
timetable) of transportation systems.