Testing VBR video traffic for stationarity

It has been previously reported that variable bit rate video traffic displays signs of long-range dependence (Beran et al. 1995, and Garrett 1993), which is defined within the framework of weak stationarity. The concept of weak stationarity is of fundamental practical interest, because it implies the existence and independence with time of mean and autocovariance. Since mean and variance might be used as parameters for policing the traffic stream on a broadband communication network, it is important to verify the underlying assumption of weak stationarity. The results presented in this paper strongly call into question this assumption. As a possible explanation, we offer shifting level processes which are asymptotically weakly stationary for infinite sample sizes.