  We show that keeping a constant lower limit on the net-time headway is the
key mechanism behind the dynamics of pedestrian streams. There is a large
variety in flow and speed as functions of density for empirical data of
pedestrian streams, obtained from studies in different countries. The net-time
headway however, stays approximately constant over all these different data
sets. By using this fact, we demonstrate how the underlying dynamics of
pedestrian crowds, naturally follows from local interactions. This means that
there is no need to come up with an arbitrary fit function (with arbitrary fit
parameters) as has traditionally been done. Further, by using not only the
average density values, but the variance as well, we show how the recently
reported stop-and-go waves [Helbing et al., Physical Review E, 75, 046109]
emerge when local density variations take values exceeding a certain maximum
global (average) density, which makes pedestrians stop.
