ИСТИНА

One of the most important tasks in analyzing the operation of a telecommunications system is to assess the quality of service of this system. For this, the probability of a system buffer overflow is often used. It is rarely possible to calculate it explicitly, so one or another estimate of this characteristic is used. In our report, we consider a system whose input load is the sum of some average load and the sum of independent fractional Brownian motion and stable Levy motion. The system has one service device with a service intensity of $C>0$. When $r = C- m >0$, there is a stationary mode. Let $Q$ be the maximum load in stationary mode. We are interested in the value $P(Q>b)$ for large $b$. Earlier, we obtained lower asymptotic estimates of this value. In our report, we propose some upper asymptotic estimates. Both upper and lower bounds have a power order. The proof method is based on Slepyan's theorem (1962) and some ideas from the work by K. Debicki, Z. Michna, T. Rolski (see \cite{DMR}). This research was carried out in accordance with the scientific program of the Moscow Center for Fundamental and Applied Mathematics and Faculty of Computational Mathematics and Cybernetics in Moscow University.