GOP ARIMA: Modeling the nonstationarity of VBR processes

In this work, we develop a stochastic model, GOP ARIMA (autoregressive integrated moving average for a group of pictures) for VBR processes with a regular GOP pattern. It explicitly incorporates the deterministic time-dependent behavior of frame-level VBR traffic. The GOP ARIMA model elaborately represents the inter- and intra-GOP sample autocorrelation structures and provides a physical explanation of observed stochastic characteristics of the empirical VBR process. We explain stochastic characteristics of the empirical VBR process, e.g., slowly decaying sample autocorrelations and strong correlations at the lags, based on the aspect of nonstationarity of the underlying process. The GOP ARIMA model generates synthetic traffic, which has the same multiplicative periodic sample autocorrelation structure as well as slowly decaying autocorrelations of the empirical VBR process. The simulation results show that the GOP ARIMA process very well captures the behavior of the empirical process in various respects: packet loss, packet delay, and frame corruption. Our work makes a contribution not only toward providing a theoretical explanation of the observed characteristics of the empirical VBR process but also toward the development of an efficient method for generating a more realistic synthetic sequence for various engineering purposes and for predicting future bandwidth requirements.