  The dielectric alpha relaxation is the dielectric manifestation of the glass
transition. In spite of this fact, the more commonly used models, the Arrhenius
model and the Williams--Landel--Ferry model, do not take into account the
structural state of the system to modelize this relaxation. In thermally
stimulated discharge current (TSDC) experiments, the sample is out of
equilibrium during most of the discharge ramp. Not surprisingly, the capability
of these models to represent the data points at temperatures well below the
glass transition temperature is very poor. To overcome this limitation, we have
used the Tool--Narayanaswamy-Moynihan (TNM) model, that takes into account the
structural state of the system, to modelize TSDC data. Although it is mostly
applied to calorimetric and volumetric experiments we show how it can be
employed on dielectric data. The numerical results support the applicability of
the model and suggest how the dielectric and the structural relaxation times
may be related. The TNM model turns out to be physically sound since the
modelization of dielectric data gives also a reasonable structural kinetics of
the system. The qualitative differences between the TNM model and the
equilibrium models for different TSDC experiments is discussed. Experimental
data coming from TSDC experiments where the thermal history of the sample is
changed do not provide additional evidence but nevertheless are compatible with
the parameter values that were obtained in the fits to the TNM model.
