We investigate aging in glassy systems based on a simple model, where a poi
nt in configuration space performs thermally activated jumps between the mi
nima of a random energy landscape. The model allows us to show explicitly a
subaging behavior and multiple scaling regimes for the correlation functio
n. Both the exponents characterizing the scaling of the different relaxatio
n times with the waiting time and those characterizing the asymptotic decay
of the scaling functions are obtained analytically by invoking a "partial
equilibrium" concept.