This paper derives equations. Assume the Internet operates as $M$/Pareto/$1$/$K$ queues, the flow blocking probability is $P_B = 1-\dfrac{\Gamma(K)}{m+\lambda\Gamma(K)}$, where $\lambda$ is the arrival rate, $m$ is the first busy period (i.e. mean of Pareto), $\Gamma(K)=\dfrac{m}{1-\rho}(P_0+P_1+...+P_{K-1})$ is the $k$-th busy period, and $P_j$ denotes the probability of having $j$ customers in the $M$/Pareto/$1$/$K$ queue.

The generating function for $P_j$ is obtained from the M/G/1 analysis:

with $B(s)$ is the Laplace transform of the Pareto pdf $b(t)=\alpha t^{-(\alpha+1)}$, where $t>1$, $% $, mean equals to $m=\alpha/(\alpha-1)$. However, using this method is computationally intensive and the paper proposed the following approximation:

## Bibliographic data

@inproceedings{
title = "Internet Flow Blocking Probability Calculation",
author = "Helen Y Tang and Steed J Huang and H.-M. Fred Chen",
booktitle = "Proc. Canadian Conference on Electrical and Computer Engineering",
volume = "2",
pages = "659--663",
month = "Mar 7-10",
year = "2000",
}