  Granular media jam into a panoply of metastable states. The way in which
these states are achieved depends on the nature of local and global constraints
on grains; here we investigate this issue by means of a non-equilibrium
stochastic model of a hindered granular column near its jamming limit. Grains
feel the constraints of grains above and below them differently, depending on
their position. A rich phase diagram with four dynamical phases (ballistic,
activated, logarithmic and glassy) is revealed. The statistics of the jamming
time and of the metastable states reached as attractors of the zero-temperature
dynamics is investigated in each of these phases. Of particular interest is the
glassy phase, where intermittency and a strong deviation from Edwards' flatness
are manifest.
