  We study the evolution of a gluon system under conditions of density and
temperature similar to those explored in the early stage of ultra-relativistic
heavy-ion collisions. We first describe the implementation of Relativistic
Boltzmann-Nordheim (RBN) transport approach that includes in the collision
integral the quantum effects of Bose-Einstein Statistics. Then, we describe the
evolution of a spatially uniform gluon system in a box under elastic collisions
solving the RBN for various initial conditions. We discuss the critical
phase-space density that leads to the onset of a Bose-Einstein condensate (BEC)
and the time scale for this process to occur. In particular, thanks to the fact
that RBN allows to relax the small angle approximation, we study the effect at
both small and large screening mass $ m_{D} $. For small $ m_{D}\ll T $ we see
that our solution of RBN is in agreement with the recent extensive studies
within a Fokker-Planck scheme in small angle approximation. For the same total
cross section but with large $ m_{D}\simeq 2\, T $ (large angle scatterings),
we see a significant time speed-up of the onset of BEC respect to small
$m_{D}\ll T$. This further strengthen the possibility that at least a transient
BEC is formed in the early stage of ultra-relativistic heavy-ion collisions.
