Research and Simulation of Network Self-Similar Traffic Flow Model Based on FARIMA with Three Core Functions

This study focuses on the research and simulation of network self-similar traffic flow models using FARIMA (Fractional AutoRegressive Integrated Moving Average) methodology. The model implementation consists of three core MATLAB functions: av.m computes statistical mean values through iterative averaging algorithms, far.m handles fractional differencing and moving average calculations using time-series decomposition techniques, and zsrs.m performs residual standardization through variance normalization procedures. These functions implement key components of the FARIMA framework for modeling long-range dependence in network traffic. The research includes comprehensive analysis of network self-similarity characteristics, time series modeling methodologies, and detailed explanations of FARIMA parameter estimation. The implementation demonstrates how fractional differencing parameters (d-values) capture long-memory properties in network traffic patterns. Through in-depth investigation of these elements, we have derived significant conclusions regarding traffic pattern predictability and buffer sizing requirements, providing valuable references for further exploration of self-similar traffic flow modeling in modern networking applications.