Shifting level process exhibiting long-range dependence over finite time scale

Abstract

Variable bit rate (VBR) video traffic displays long-range dependence (LRD), i.e., VBR video exhibits a considerable amount of correlation even over long time spans. Traditional Markov model has Short-range dependence (SRD). Many VBR video traffic models with LRD have been proposed, e.g., fractional Brownian noise, fractional autoregressive integrated moving average processes, etc. But most of them are not tractable mathematically for analysis. In this paper, we address the shifting level (SL)process for the modeling of VBR video traffic. Shifting level process is stochastically determined by two distributions: distribution for heights and distribution for interrenewal time. The autocorrelation function of SL process is determined by the distribution of the interrenewal time.When the interrenewal time distribution for SL process has the distribution with power tail,SL process is LRD but mathematical analysis is difficult. So, to make the SL process to be tractable mathematically and to have slowly decaying autocorrelation up to a given large timescale, we model the interrenewal distribution of the SL process as a hyper-exponential distribution. We call the processes whose autocorrelations behave like LRD processes up to a given any large timescale Pseudo-LRD processes. Thus, by using SL proces whose interrenewal time has hyper-exponential distribution, we model mathematically tractable Pseudo-LRD process for VBR video traffic.