In this paper

we analyze the superposition of AR1 process.We discover that when the parameters of these AR1 processes satisfy some specified conditions

the superposition process has the property of self similarity.This can be a physical explanation of the self similar nature of the packet network

and partly answers the question why the short range dependent traffic sources can cause the fractal phenomena in modern network.We present the mathematical analysis and simulation result

and a fast algorithm to generate long run time series is also derived.