ИСТИНА

The problem of quality of service estimation is the most important one in telecommunication systems analysis. For many years these estimates were made on the basis of Poisson model or close to it Markov models. In the early nineties on the basis of measurements of traffic carried out at Bell laboratories it was discovered that traffic modern telecommunication systems has a completely new properties. Later it was confirmed in many other empirical studies. It has been discovered that such traffic has three important new properties: it is self-similar in a wide range of scales of measurements, has the property of long-term dependence and magnitude of the load, coming from separate sources, has a distribution with heavy tails. It has been shown that if you do not take into account these features, it leads to serious errors in the evaluation of service quality. In our report using the methodology proposed in the paper of Norros (1994) we propose some lower asymptotic estimate of the overflow probability of large buffer when the input is a stream consisting of two independent components: the fractional Brownian motion and stable Levy motion with the same Hurst parameters. In subsequent work we will consider the case when incoming stream consists of several independent components with different Hurst parameters.