Fractal Traffic: Measurements, Modelling and Performance Evaluation zyxw Ronald G. Addie University of Southern Queenslland Toowoomba Queensland 4350, Australia Abstract zyxwvutsr Observations of both Ethernet traffic and variable bit rate (VBR) video traffic have demonstrated that these traffics exhibit “self-similarity” and/or infinit l e asymp- totic index of dispersion for counts (IDC). We report here on measurements of traffic an a commercialpublic broadband network where similar characteristics have been observed. zyxwvutsrqpo For the purpose of analysis and di- mensioning of the central links of an ATM network we analyse in this paper the performance zyxwvut of a single server queue fed by Gaussian trafic with infjlnite IDC. The analysis leads to an approximation fo,r the per- formance of a queue in which the arriving zyxwvut trafic is “fractal” Gaussian and consequently where there does not exist a dominant negative-exponential tail. The term ufractal” is used here in the sense thtzt the au- tocovariance of the traffic exhibits self-similarity, that is to say, where the autocovariance of an aggregate of the trafic is the same, or asymptotically the same for large time lags, as the original traffic. We are not con- cerned with proving or exploiting this self-similarity property as such, but only with performancle analysis techniques which are effective for such processes. In order to be able to test the performance analysis for- mulae, we show that trafic with the same arutocovari- awe as measured an a real network over a wide range of lags (sufficiently wide a range for the traffic to be equivalent from the point of view of queueing perfor- mance) can be generated as a mixture of two Gaussian AR(1) processes. In this way we demonstrate that the analytic performance formulae are accurate. 1 Introduction Future network developments are likely to be based heavily on Broadband ISDN (B-ISDN). Acc’ordingto Moshe Zukerman and Tim Neame Telecom Research Laboratories 770 Blackbum Rd., Clayton Victoria 3168, Australia standards developments, B-ISDN uses Asynchronous Transfer Mode (ATM) switching equipment. In ATM networks, zyxwv 513 octet cells are switched according to in- formation contained in their headers between ATM switches. VVhen cells arrive at a switch, they may be stored in a buffer awaiting transmission to their new destinations. If within a certain period of time the number of arriving cells, which may come from differ- ent and often bursty sources, is larger than the number of cells that can be served, the buffer may overflow and cells may be lost. For data services, such cell loss leads to retransmissions which delay messages, or may even cause network congestion collapse. In video services, cell loss reduces picture quality. Therefore, designers of ATM networks are faced with the challenge of how to provide required quality of service hut still maintain sufficient network utilization to operate an economi- cally viable network. In particular, there is a need for effective tools for dimensioning and connection admis- sion control. In fact, problems related to bursty traffic characterization and performance evaluation of statis- tical multiplexers have been considered amongst the most important teletraffic research challenges during the last 15 years See for example [lO], [14] [18],[20], [22],[25],[27],[29],[30],[31] and references therein. In [3]-[SI we have prolposed a new traffic model based on a stationary Glaussian process which can be used as a model of a superposition of a quite large variety of processes including the autoregressive model of [25]. It has the following, three important characteristics: (1) it is more general thain some of the other traffic mod- els, (2) it is amenable to queueing analysis, and (3) it is closed under superposition without the difficulty of computing performance measures increasing as the number of superposed processes increases. It is worth mentioning that the analysis of correlated Gaussian queues in [3#]-[8] extends beyond that of [13, zyx 281 (and references therein) which provide solution only under 0743-166W95 $04.00 zyxwvutsrqp 0 1995 IEEE 8b.l .I 977