  We study the asymptotic behavior of empirical processes generated by
measurable bounded functions of an infinite source Poisson transmission process
when the session length have infinite variance. In spite of the boundedness of
the function, the normalized fluctuations of such an empirical process converge
to a non-Gaussian stable process. This phenomenon can be viewed as caused by
the long-range dependence in the transmission process. Completing previous
results on the empirical mean of similar types of processes, our results on
non-linear bounded functions exhibit the influence of the limit transmission
rate distribution at high session lengths on the asymptotic behavior of the
empirical process. As an illustration, we apply the main result to estimation
of the distribution function of the steady state value of the transmission
process.
