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 (1998). 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.