The alpha stable self-similar stochastic process has been proved an effective model for high variable data traffic. A deep insight into some special issues and considerations on use of the process to model aggregated VBR video traffic is made. Different methods to estimate stability parameter α and self-similar parameter H are compared. Processes to generate the linear fractional stable noise (LFSN) and the alpha stable random variables are provided. Model construction and the quantitative comparisons with fractional Brown motion (FBM) and real traffic are also examined. Open problems and future directions are also given with thoughtful discussions. The alpha stable self-similar stochastic process has been proved an effective model for high variable data traffic. A deep insight into some special issues and considerations on use of the process to model aggregated VBR video traffic is made. Processes to generate the linear fractional stable noise (LFSN) and the alpha stable random variables are provided. Model construction and the quantitative comparisons with fractional Brown motion (FBM) and real traffic are also examined. Open problems and future directions are also given with thoughtful discussions.