Performance estimation in nonhomogeneous traffic models

The last few decades reveal a steady interest in traffic models based on self-similar processes. The Fractal Brownian motion (beta-traffic, low connection speed) and $\alpha$-stable Levy process ($\alpha$-traffic, high connection speed) are quite flexible and convenient tools for modeling the system load. Currently, the properties of «pure» processes including their influence on different performance measures in multiservice networks are well studied. But the compound traffic models based on both components are practically not analysed at all. Estimation of the QoS characteristics for such models is a new and a very nontrivial problem. In this paper we analyse the nonhomogenous traffic model based on sum of independent Fractional Brownian motion and symmetric $\alpha$-stable Levy process with different Hurst exponents $H_1$ and $H_2$. For such model we find asymptotical lower bound for the overflow probability when the size of buffer $b\to \infty$.