ИСТИНА

When analyzing the operation of a telecommunications system, it is important to be able to assess the quality of service of this system. One of the most popular characteristics of service quality is the probability of system buffer overflow. It is quite rare to find an exact explicit expression for this characteristic. One or another estimate is used more often. In our report, we investigate the system, where input load flow is the sum of some average load and the sum of independent fractional Brownian motion and stable Levi motion. The service is performed by a single server with a service intensity of $C>0$. Under the condition $r = C- m >0$, there is a stationary mode in the system. We are interested in the value of $P(Q>b)$ for large $b$, where $Q$ is the maximum value of the load in stationary mode. We obtain lower and upper asymptotic estimates for this value for large values of the buffer size. Both estimates decrease powerfully with increasing buffer volume. The method of proof is based on Slepyan's theorem (1962) and some ideas from the work of K. Debicki, Z. Mikhny, 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.