  A model glass is considered with one type of fast ($\beta$-type) of
processes, and one type of slow processes ($\alpha$-type). On time-scales where
the fast ones are in equilibrium, the slow ones have a dynamics that resembles
the one of facilitated spin models. The main features are the occurrence of a
Kauzmann transition, a Vogel-Fulcher-Tammann-Hesse behaviour for the relaxation
time, an Adam-Gibbs relation between relaxation time and configurational
entropy, and an aging regime. The model is such that its statics is simple and
its (Monte-Carlo-type) dynamics is exactly solvable. The dynamics has been
studied both on the approach to the Kauzmann transition and below it. In
certain parameter regimes it is so slow that it sets out a quasi-equilibrium at
a time dependent effective temperature. Correlation and Response functions are
also computed, as well as the out of equilibrium Fluctuation-Dissipation
Relation, showing the uniqueness of the effective temperature, thus giving
support to the rephrasing of the problem within the framework of out of
equilibrium thermodynamics.
