  We investigate both analytically and by numerical simulation the kinetics of
a microscopic model of hard rods adsorbing on a linear substrate, a model which
is relevant for compaction of granular materials. The computer simulations use
an event-driven algorithm which is particularly efficient at very long times.
For a small, but finite desorption rate, the system reaches an equilibrium
state very slowly, and the long-time kinetics display three successive regimes:
an algebraic one where the density varies as $1/t$, a logarithmic one where the
density varies as $1/\ln(t)$, followed by a terminal exponential approach. The
characteristic relaxation time of the final regime, though incorrectly
predicted by a mean field arguments, can be obtained with a systematic
gap-distribution approach. The density fluctuations at equilibrium are also
investigated, and the associated time-dependent correlation function exhibits a
power law regime followed by a final exponential decay. Finally, we show that
denser particle packings can be obtained by varying the desorption rate during
the process.
