Computations of Scale Factors
Ming Li · 2022
The contributions in this Chapter are in six aspects. First, we propose the formulas to compute the small-scale factor r and large-scale one a of traffic in Theorems 11.1 and 11.2, respectively. Second, we put forward the asymptotic expressions of r for t → 0 and a for t → 0 and c for t → ∞ in Theorems 11.3 and 11.4, respectively. In the third aspect, we present the formulas of the minimum of r and a in Corollaries 11.1 and 11.2, as well as the minimum of the asymptotic values of r when t → 0 and a if t → ∞ in Corollaries 11.3 and 11.4, respectively. In the fourth, we bring forward the approximations of the fractal bound of traffic in Theorem 11.5 and Corollary 11.5, respectively. In the five, the applications of the present computations of two scale factors to traffic bound and traffic delay bound are explained with real traffic traces. Finally, we propose the formula for the maximum of a fractal delay bound in Corollary 11.6.