Shifting-level process as a LRD video traffic model and related queuing results Heejune Ahn * , Jae-kyoon Kim Visual Communications Laboratory, Department of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Taejon 305-701, South Korea Received 4 November 1998; received in revised form 28 July 1999; accepted 30 July 1999 Abstract Recently it has been reported that variable bit rate (VBR) video traffic exhibits long-range dependence (LRD). Various processes have been proposed for modeling traffic with LRD and analyzing its effects on network performance. However, in the previous models it is not possible to identify the effects of short- and long-term correlation of video traffic on queuing performance, and thus many seemingly contradictory arguments on the importance of LRD in VBR video traffic can be found in the literature. In this paper, we present a video traffic model based on the shifting-level (SL) process. We observe that the autocorrelation function (ACF) of an empirical video trace is accurately captured by a shifting-level process with compound correlation (SLCC): an exponential decay for small lags and a hyperbolic one for large lags. Especially, we present a parameter matching algorithm for video traffic. The continuous-time first-order discrete auto-regressive (C-DAR(1)) model, which is a short-range dependent (SRD) video traffic model, can be considered a kind of SLCC process with an exponential correlation term only. Thus, comparing the queuing performances of the C-DAR(1) model and the SLCC with that of a real video trace, it is possible to identify the effects of SRD and LRD in VBR video traffic on queuing performance. From simulation results, we find that LRD may have a significant effect on queuing behavior under heavy traffic loads and large buffer conditions.  2000 Elsevier Science B.V. All rights reserved. Keywords: VBR video traffic model; Shifting-level process; Compound correlation; Long-range dependence; Short-range dependence; Queuing behavior 1. Introduction Variable bit rate (VBR) video service is expected to be a major source of future packet-switching integrated service networks. Since the success of traffic control relies essen- tially on a sound understanding of input traffic, modeling of VBR video traffic has received intense interest. Among traf- fic characteristics, the first and second order statistics, i.e. rate-distribution (histogram) and the autocorrelation func- tion (ACF), which is equivalent to the power spectrum, are considered of first importance in estimation of network performance [1–3]. Recently, a number of empirical studies have demon- strated the existence of long-range dependence (LRD) or self-similarity in VBR video traffic [4]. Various processes have been proposed for modeling traffic with LRD and analyzing its effects on network performance [3, pp. 324– 348,4]. These include fractional Brownian motion [5,6], fractional ARIMA processes [7], chaotic maps [8], and semi-Markovian processes [9,10]. It has been reported that the LRD characteristic may impact significantly on queuing behavior. Especially, in their studies on data traffic, Erra- milli et al. [11] and Norros [6] argued that overall packet loss decreases very slowly with increasing buffer size. In other words, system performance may be overestimated if LRD in input traffic is overlooked. Nevertheless, conventional models for VBR video traffic are still based on Markovian processes. Markovian models are still being used and developed for performance estima- tion and traffic control. Further, advocates of Markovian modeling argue that Markovian models show accurate performance estimation in many situations in spite of a lack of LRD characteristics [1,12]. Therefore, it is natural to consider the following problem [13]: Under what condi- tions is LRD correlation of VBR video traffic crucial for queuing behavior? The ambiguity in the argument over the question whether LRD in VBR video traffic has significant effects on the network performance is due to the lack of a suitable traffic model that captures both SRD (in small lags) and LRD (in Computer Communications 23 (2000) 371–378 0140-3664/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S0140-3664(99)00169-3 www.elsevier.com/locate/comcom * Corresponding author. Tel.: +82-42-869-5418; fax: +82-42-869-8018. E-mail addresses: cityboy@viscom.kaist.ac.kr (H. Ahn), kimjk@ee.kaist.ac.kr (J.-K. Kim).