D. Veitch. Novel Models of Broadband Traffic. In Proc. Globecom '93, pages 362--368, Houston, TX, December 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....LRD may be due to non stationarity in the data caused by the superposition of level shifts [9] or Dirac pulses [15] with short range dependent (SRD) stationary processes. Another approach has been to use stochastic models (such as fractional Brownian motion [26] zero rate renewal processes [35] and various other point processes [32] or deterministic models (such as chaotic maps [13] that exhibit the LRD observed in the experimental data. However, these models are analytically difficult to handle. Furthermore, they do not provide much insight into why they are meaningful on physical ....

D. Veitch. Novel Models of Broadband Traffic. In Proc. Globecom '93, pages 362--368, Houston, TX, December 1993.

....LRD may be due to nonstationarity in the data caused by the superposition of level shifts [9] or Dirac pulses [15] with short range dependent (SRD) stationary processes. Another approach has been to use stochastic models (such as fractional Brownian motion [27] zero rate renewal processes [36] and various other point processes [33] or deterministic models (such as chaotic maps [13] that exhibit the LRD observed in the experimental data. However, these models are analytically difficult to handle. Furthermore, they do not provide much insight into why they are meaningful on physical ....

D. Veitch. Novel Models of Broadband Traffic. In Proc. Globecom '93, pages 362--368, Houston, TX, December 1993.

....studies have been made for the design, control and performance of such networks, using traditional traffic models. It is likely that many of those results need major revision, particularly those pertaining to cell loss rates and congestion control, when self similar traffic models are considered [8]. In this paper, we will present a model, introduced by Likhanov, Tsybakov and Georganas[10] for the performance analysis of an ATM buffer, driven by (asymptotically) self similar input traffic. The resulting G D 1 queueing model will be mapped into a M G 1 model where the service time is Pareto ....

....the following features (formal proofs are given in [10] 1) An individual source behaves such that, at scarce random moments of time, it begins to generate bursts of a random number of cells with rate R. The burst length distribution has a heavy tail , decreasing as in a Pareto distribution[1, 8] with infinite variance. At the end of burst generation, the source becomes silent for a random time which is, as a rule, greater than the length of the cell generation interval; 2) The number of individual sources, M, is large, so that it can be considered as infinity, but l, the total intensity ....

D. Veitch, "Novel Models of Broadband Traffic", Proc. IEEE Globecom'93, Houston, Tx, Dec. 1993

....studies have been made for the design, control and performance of such networks, using traditional traffic models. It is likely that many of those results need major revision, particularly those pertaining to cell loss rates and congestion control, when self similar traffic models are considered [8]. Self similarity manifests itself in a variety of different ways: a spectral density that diverges in the origin, a non summable autocorrelation function (indicating long range dependence) an Index of Dispersion of Counts (IDC) that increases monotonically with the sample time T, etc. 1] A ....

D. Veitch, "Novel Models of Broadband Traffic", Proc. IEEE Globecom'93, Houston, Tx, Dec. 1993.

.... [28] fractional Gaussian noise [10] 28] fractional Brownian motion [25] 26] and Markovian models [32] In this work, we show that Fractal Point Processes (FPPs) provide novel tools for understanding, modeling and analyzing diverse types of self similar traffic behavior [35] 36] 37] [42]. In contrast to other approaches, the point process formulation concerns the dynamics of individual arrivals and how this gives rise to self similarity of packet counts in a mathematically rigorous manner. This formulation yields models exhibiting LRD, 1=f noise, and slowlydecaying variance, and ....

.... [22] 41] Likewise, we may call a stochastic point process fractal when a number of the relevant statistics exhibit scaling with related scaling exponents, indicating that the represented phenomenon contains clusters of points over all (or a relatively large set of) time or length scales [24] [42]. Since scaling leads mathematically to power law relations in the scaled quantities [22] a fractal process often has its statistics mathematically expressed by power law functions. We note that for a general point process, fractal scaling in one statistic does not necessarily imply fractal ....

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Veitch, D. Novel models of broadband traffic. In Proc. IEEE GLOBECOM, Houston, TX, 1993.

.... rates, burst length, and cellloss ratio have been extensively used (Paxson and Floyd [57] These values capture only first order statistics, and a need has been identified for descriptors that provide more information in order to describe highly correlated and bursty multimedia traffic (Veitch [59]) The natural approach is the use of traditional traffic flow models which are useful in modeling of nodes (Caceres et al. 51] Chen and Mandelbaum [52] Other concepts like packet trains (Jain [53] have also been proposed. Different kinds of stochastic models reported in the literature have ....

.... [55] These have been applied with techniques like weighted finite automata, vector quantization, selforganizing maps, and simulated annealing (Frost and Melamed [56] Other surveys in the area have been presented by Frost and Melamed [56] Paxson and Floyd [57] Sen et al. 58] and Veitch [59]. III. Conclusions As a result of this survey, we observed that the modeling techniques for multimedia traffic that are currently attracting the attention of the community are self similarity and TES modeling. This is due to the need to describe the complex nature of the non uniform traffic. In ....

D. Veitch, "Novel models of broadband traffic", in Proc. IEEE Globecom, pp. 1057-1061, 1993.

....generators of fractal structures. The concept of fractals can be introduced as a generalization of the familiar notion of dimension: just as a point, a line, a square and a cube can be said to have dimensions of 0, 1, 2, and 3 respectively, fractal objects have non integral dimensions. Mandelbrot [18] has demonstrated the significance of fractals in a wide range of mathematical and physical systems, and in particular, shows that fractal geometry provides a natural basis to describe irregular and bursty phenomena. There is no simple definition for fractals, and they are defined in terms of ....

....above a certain order may not exist. In particular, Meier Hellstern et al. observed that the best fit for the tail behavior of some data sets was obtained using interarrival densities with an infinite mean. The implications of this in queueing analysis are considered in [16] and by Veitch 92 [18]. Slowly Decaying Variances: In conventional traffic processes, the variance of the arithmetic mean of a traffic sample (consisting of the time series of packet counts) decays inversely as the sample size, asymptotically. Erramilli and Willinger 93 6 Modeling Packet Traffic with Chaotic Maps ....

D. Veitch, "Novel Models of Broadband Traffic," Proc. 7th Australian Teletraffic Research Seminar, Murray River, Australia, 1992.

....of self similarity by means of trace driven simulations; analysis of self similar traffic models; fast generation and simulation with self similar traffic. Early models of fractal traffic processes include Fractional Brownian Motion (FBM) Norros [34] zero rate renewal process models [11] [43] and deterministic chaotic maps [12] We will first summarize these approaches. The motivation for zero rate processes, based on renewal processes characterized by infinite mean inter arrival times, comes directly from Mandelbrot s early work on modeling bursty transmission errors [11] 43] In ....

....[11] 43] and deterministic chaotic maps [12] We will first summarize these approaches. The motivation for zero rate processes, based on renewal processes characterized by infinite mean inter arrival times, comes directly from Mandelbrot s early work on modeling bursty transmission errors [11] [43]. In these approaches, the burstiness of packet traffic is captured by the power law exponent that characterizes the decay of the inter arrival time distribution (which is related to the notion of a fractal dimension) While zero rate processes may be appropriate models for quality of service ....

D. Veitch, "Novel Models of Broadband Traffic," Proc. 7th Australian Teletraffic Research Seminar, Murray River, Australia, 1992.

....computer networks: the Fractal Renewal Process (FRP) Superposition of i.i.d. FRPs (Sup FRP) the FractalShot Noise Driven Poisson Process (FSNDP) and the Fractal Binomial Noise Driven Poisson point Process (FBNDP) Some of these models appear to exhibit greater variability than earlier models [8, 23, 24]. We have shown that these models fall into two classes, renewal based and DSPP based, depending on their construction, and how the heavy tailed property need not relate to the fractal nature of these models. Perhaps most importantly, the Hurst parameter H alone does not suffice in describing the ....

D. Veitch. Novel models of broadband traffic. In Proc. GLOBECOM '93, 1993.

....of the fluid model. This suggest an intuitive understanding of high Hurst parameter values as coming from the distribution of very long bursts (or activity periods etc. It has been indeed often observed that activity periods of a traffic source have heavy tailed distributions (see, e.g. [21]) In fact, this connection between long range dependence, activity periods with infinite variance and self similarity was established already by Mandelbrot who considered the convergence of aggregations of so called renewal reward processes with heavy tailed inter renewal distributions towards ....

D. Veitch. Novel models of broadband traffic. In Proc. 7th Australian Teletraffic Research Seminar, Murray River, Australia, 1992.

....dependent if and only if Z 1 0 Cov (R 0 ; R t ) dt = 1; which is equivalent to EB 2 = 1, i.e. B having infinite variance. It has been indeed often observed that activity periods of a traffic source are best modelled by heavy tailed distributions having infinite variance (see, e.g. [Vei92]) Consider next the cumulating traffic process A t = Z t 0 R s ds: It is straightforward to find that Var (A t ) b i 2EB 0 (t Gamma B 0 ) E(B 0 t) 2 j ; 4.1) where b = EB and B 0 has the residual lifetime distribution corresponding to that of B in the renewal theory ....

D. Veitch. Novel models of broadband traffic. In Proc. 7th Australian Teletraffic Research Seminar, Murray River, Australia, 1992.

.... testing real telecommunications systems, it is desirable to have traffic sources which are realistic, and hence display self similarity [18, 14] The Fractal Renewal Process (FRP) 12, 17] and variants, have been proposed as models for LongRange Dependent (LRD) or statistically self similar data [20, 18, 17, 8, 12, 23]. The FRP is a simple renewal point process with heavy tailed inter renewal times. The long range correlations in the process are directly introduced by the heavy tailed renewal times the only mechanism available because in a renewal process there can be no connections across renewal points. ....

Darryl Veitch. Novel models of broadband traffic. In IEEE GLOBECOM'93, Houston, Texas, 1993.

....of traffic with LRD may be on queueing performance. Intuition in the subject is highly tuned to short term, Markovian thinking which can be very misleading. Consider a renewal process where the interarrival time distribution has finite mean but infinite variance. It is not difficult to show [18] that such a process is long range dependent. The standard GI=M=m queueing analysis applies however, where new arrivals find a system containing an exponentially distributed amount of work. Thus LRD alone does not suffice to generate abnormal queueing behaviour. On the other hand, studies by ....

D.Veitch, Novel Models of Broadband Traffic, Proc. IEEE Globecom '93, Houston, Texas December (1993).

....in addition other aspects of the data to gain insight into the process of the arriving work itself. This is motivated by insights from analytical studies [27] 11] which show that the precise structure of arriving work is crucial, LRD in itself cannot determine performance. For example [11] 23] [36], the GI M 1 queue with interarrivals of infinite variance has a LRD arrival process but classical exponentially distributed queue tails. On the other hand Weibullian (stretched exponential) tails are found for the Fractional Brownian Storage Model of Norros [27] and for the superposition of a ....

D.Veitch, Novel Models of Broadband Traffic, Proc. IEEE Globecom '93, Houston, Texas, (December 1993).

....LRD may be on queueing performance. Intuition in the subject is highly tuned to short term, Markovian thinking which, as we now illustrate, can be very misleading. Consider a renewal process whose interarrival time distribution has mean 1= but infinite variance. It is not difficult to show (Veitch [20]) that such a process is long range dependent. The standard GI=M=1 queue analysis applies however, where new arrivals find a system containing an exponentially distributed amount of work. Thus LRD alone does not suffice to generate abnormal queueing behaviour (there is however a difference for ....

....new arrivals find a system containing an exponentially distributed amount of work. Thus LRD alone does not suffice to generate abnormal queueing behaviour (there is however a difference for high load, see Appendix 1) Now let the mean be infinite also, implying an arrival rate of zero (Veitch [20]) Despite the fact that such an arrival process cannot be stationary in the usual sense, GI=M=1 theory remains valid, yielding exponential queues at arrival instants even in this case. This illustrates that even the most fundamental of concepts such as the primordiality of the mean arrival rate ....

D. Veitch, Novel models of broadband traffic, Proc. IEEE Globecom '93, Houston, Texas, (December 1993)

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D. Veitch, "Novel models of broadband traffic", Proc. Globecom '93, Houston, TX, pp. 1057-1061, Dec. 1993

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D. Veitch, "Novel Models of Broadband Traffic", preprint, 1992.

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