  We study the dynamics of the totally asymmetric exclusion process with open
boundaries by phenomenological theories complemented by extensive Monte-Carlo
simulations. Upon combining domain wall theory with a kinetic approach known as
Boltzmann-Langevin theory we are able to give a complete qualitative picture of
the dynamics in the low and high density regime and at the corresponding phase
boundary. At the coexistence line between high and low density phases we
observe a time scale separation between local density fluctuations and
collective domain wall motion, which are well accounted for by the
Boltzmann-Langevin and domain wall theory, respectively. We present Monte-Carlo
data for the correlation functions and power spectra in the full parameter
range of the model.
