# Some analytical aspects of regenerative simulation of fluid models

**Prof. Evsey V. Morozov, Ruslana S. Goricheva, Oleg V. Lukashenko (IAMR KarSC RAS, Petrozavodsk, Russia), Prof. Michele Pagano (University of Pisa, Pisa, Italy)**

Brownian input is an important particular case of the Gaussian processes, which are now well-recognized model to describe the traffic dynamics of a wide class of modern telecommunication networks. We discuss application of the regenerative theory and estimate the loss (blocking) probability in a queueing system with finite buffer which is fed by a Brownian input. The simulation technique is used because the explicit analytical result is not available for such type of systems. To validate the correctness of simulation we compare received numerical results with known values for infinite buffer systems which is hopefully exist for systems with Brownian input.

The loss rate process has typically very complicated dependence structure, and it makes evaluation of its parameters very hard problem in the framework of classical statistics. Hopefully, Brownian process has independent increments, and thus stationary performance of the considered model can be accurately estimated by means of well-developed regenerative simulation technique.

In particular, we develop confidence estimation of the stationary loss probability using classical regenerations which occur when the system (server and buffer) becomes empty. And different types of regeneration points are considered. Another important aspect is discretization. We explore the influence of discretization step to abstained results. Some numerical results are assumed to be included.