N.G. Duffield, J.T. Lewis, N. O'Connell, R. Russell, and F. Toomey. Predicting Quality of Service for Traffic with Long--Range Fluctuations. In IEEE International Conference on Communications, Seattle, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....can be overly conservative or too optimistic [CLW94, Kni97] Furthermore, for traffic with long range dependence, equation (1.1) does not hold. In this case, the logarithm of the overflow probability does not decrease linearly with the buffer size, rather it decreases at a sub linear rate [DO96, DLO95] On the other hand, the many sources asymptotic [CW96, BD95] a similar result is proved in [SG95] for the case of on off fluid sources) assumes only the stationarity of the multiplexed traffic streams. The overflow probability using the many sources asymptotic can be approximated by ; 1.2) ....

N. G. Duffield, J. T. Lewis, and N. O'Connell. Predicting quality of service for traffic with long-range fluctuations. In Proc. of IEEE International Conference on Communications (ICC'95), pages 473--477, Seattle, WA, USA, September 1995.

....comment on usefulness of this procedure on page 16. There is good evidence that this bit rate process exhibits long range behavior [4] 27] This means that accurate characterization seems intractable by most conventional stochastic processes, such as various Markov processes. As discussed in [21], the apparent long range behavior could also be explained by lack of stationarity. In either case, the modeling is problematic. Provided that a model has been chosen, the user should then estimate the parameters for it and find a way to regulate the service rate t(t) so that R(t) strictly obeys ....

N. G. Duffield, et alii, "Predicting Quality of Service for Traffic with Long-Range Fluctuations, " in Proceedings of IEEE International Conference on Communications, Seattle, Washington, USA, June 18-22, 1995.

....considerable debate about how to model such processes. Different approaches have been taken that parallel those taken in other areas and described earlier. One approach has been to argue that the observed 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 have been drawn in the literature from experiments with long range dependent traffic. Indeed, mathematical analysis and simulation of queueing systems with LRD input shows that the queue occupancy exhibits an asymptotic behavior very much different from that observed with Markov sources [26] [9], 12] However, the literature on Markov modeling reports good performance prediction for finite buffer systems even when input traffic streams are correlated over many time scales [11] 17] 34] 18] We have shown that there exists a correlation horizon which separates relevant and ....

N. G. Duffield, J. T. Lewis, N. O'Connell, R. Russell, and F. Toomey. Predicting Quality of Service for Traffic with LongRange Dependence. In Proc. IEEE ICC'95, pages 473--477, Seattle, WA, September 1995.

....[7] and Grunenfelder et al. 8] Also, a different approach has been used to characterize traffic based on the notion of long term correlations. This approach is based on the theory of self similarity (see Leland et al. 9] Erramilli, Gordon and Willinger [10] and Duffield, Lewis and O Connel [11] and references therein) To compound the problem of choosing an appropriate model for ATM traffic, the ATM forum decided to standardize the following parameters: peak rate, sustainable rate, cell delay variation for the peak rate, and maximum burst length. Using the peak rate and the cell delay ....

N. G. Duffield, J. T. Lewis, and N. O'Connell. Predicting Quality of Service for Traffic with Long-Range Fluctuations. In Proceedings of the International Conference on Communications (ICC), 473--477, 1995. 20

....include: Traffic aggregation effects. The aggregate network traffic, even if from multiple independent sources, will still be self similar. Bursts will exist across many time scales and positive correlations in traffic will adversely affect the quality of service (QOS) provided to network users [7, 8]. The cell loss ratio (CLR) in a network with self similar traffic may be several orders of magnitude higher than that predicted by the traditional Markovian traffic models [3] Buffer ineffectiveness. Increasing the buffer sizes used in the network will have marginal impact on the cell loss ....

N. Duffield, J. Lewis, N. O'Connell, R. Russell and F. Toomey, "Predicting Quality of Service for Traffic with Long Range Dependence", Proceedings of ICC'95, Seattle, WA, pp. 473-477, September 1995.

....Carlo (MC) techniques. Such a situation leads to the development of fast simulation approaches, which can considerably reduce the computational effort. Some interesting results have been obtained also on the basis of large deviation theorems in the context of selfsimilar traffic. In particular in [2] the authors have derived some expressions relative to the steady state waiting time in a single server queue. An important result is for example that the steady state queueing distribution of a single server queue with deterministic service rate decays asymptotically in a Weibull fashion rather ....

....and with X k representing the number of cells arriving during the k th time slot. If we denote with Z k the amount of work that arrives in the time interval [0,k] and with S k the amount of work which can be processed in the same time interval, then we can define the workload process [10] 8] [2] as: W Z S k k k = k=0,1,2. 4) W= W k , k=0,1,2. is a stationary increment process so if we assume that at time zero the queue is empty then it is possible to demonstrate that the probability of a certain buffer usage at time k is given by: Pr( Pr( sup ) Q b W b k k k = 0 ....

N. G. Duffield, J. T. Lewis, N. O'Connell, R. Russell and F. Toomey. "Predicting the Quality of Service for Traffic with Long-Range Dependence". In Proc. IEEE ICC '95, pp. 473-477, Seattle, WA, 1995.

....considerable debate about how to model such processes. Different approaches have been taken that parallel those taken in other areas and described earlier. One approach has been to argue that the observed 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 have been drawn in the literature from experiments with long range dependent traffic. Indeed, mathematical analysis and simulation of queueing systems with LRD input shows that the queue occupancy exhibits an asymptotic behavior very much different from that observed with Markov sources [27, 9, 12]. However, the literature on Markov modeling reports good performance prediction for finite buffer systems even when input traffic streams are correlated over many time scales [11, 18, 35, 19] We have shown that there exists a correlation horizon which separates relevant and irrelevant ....

N. G. Duffield, J. T. Lewis, N. O'Connell, R. Russell, and F. Toomey. Predicting Quality of Service for Traffic with Long-Range Dependence. In Proc. IEEE ICC'95, pages 473--477, Seattle, WA, September 1995.

.... formula depends on the traffic being sufficiently Gaussian, which is more likely to be the case when traffic is aggregated from a large number of independent sources [17] Second, the derivation of the formula uses the Weibull distribution to approximate the tail of the queue length distribution [6, 17]. This approximation is logarithmically accurate for large buffers, so the buffer must be sufficiently large for the formula to apply. 2.2 Illustration of Norros Formula Figure 1 illustrates the effective bandwidth predicted by the Norros formula for a self similar traffic flow with mean bit rate ....

N. Duffield, J. Lewis, N. O'Connell, R. Russell and F. Toomey, "Predicting Quality of Service for Traffic with Long Range Dependence", Proceedings of ICC'95, Seattle, WA, pp. 473-477, September 1995.

....the buffer size in the network, as well as the marginal distribution (i.e. variability) of the bit rate of the traffic source [15, 16] Similar conclusions follow from our study of the Norros formula. Other researchers have also begun to address the issue of selfsimilarity in traffic management [17, 18, 19, 20, 21]. The remainder of this paper is organized as follows. Section 2 discusses the effective bandwidth problem, and presents the Norros formula and its parameters. Section 3 describes the simulation methodology used to test the formula. Section 4 presents the results of the simulation experiments, ....

.... depends on the traffic being sufficiently Gaussian, which is more likely to be the case when traffic is aggregated from a large number 1 of independent sources [10] Second, the derivation of the formula uses the Weibull distribution to approximate the tail of the queue length distribution [10, 18]. This approximation is logarithmically accurate for large buffers, so the buffer must be sufficiently large for the formula to apply. 3 SIMULATION METHODOLOGY We attempted to verify the Norros formula by comparing the effective bandwidth predicted by the formula to the effective bandwidth ....

N. Duffield, J. Lewis, N. O'Connell, R. Russell and F. Toomey, "Predicting Quality of Service for Traffic with Long Range Dependence", Proceedings of ICC'95, Seattle, WA, September 1995, pp. 473-477.

....the following: Traffic aggregation effects. The aggregate network traffic, even if from multiple independent sources, will still be self similar. Bursts will exist across many time scales and positive correlations in traffic will adversely affect the quality of service provided to network users [Duffield et al., 1995; Duffield, 1996] The cell loss ratio (CLR) in a network with self similar traffic may be several orders of magnitude higher than that predicted by the traditional Markovian traffic models used in most network planning studies [Chen et al., 1995] Buffer ineffectiveness. Increasing the buffer ....

N. Duffield, J. Lewis, N. O'Connell, R. Russell and F. Toomey, "Predicting Quality of Service for Traffic with Long Range Dependence", Proceedings of ICC'95, Seattle, WA, pp. 473-477, September 1995.

....engineering. This concern is based on two recent findings: i) VBR video traffic exhibits long range dependence (Hurst parameter larger than 0. 5) 2] ii) the buffer overflow probability (BOP) 1 of long range dependent (LRD) video traffic decays hyperbolically [14, 18] or in a Weibull fashion [5, 17]. A direct implication of (ii) is that the notion of effective bandwidth based on Markov models of which the BOP decays exponentially does not apply to LRD traffic (see Section 4 for detail) This has led many researchers and practitioners to believe that the LRD property of VBR video traffic will ....

....for LRD processes The first result on queueing analysis of self similar traffic seems to appear in Norros [17] in which the popular Weibull (lower) bound on the BOP has been established using fractional Brownian Motion. Also, using the techniques of large deviations theory, Duffield et al. [5] have shown that under mild conditions, the BOP of LRD traffic, whether exact or asymptotic, is again approximated by Weibull behavior as the buffer size goes to infinity. While the above results exhibit Weibull decays, Likhanov et al. [14] and Parulekar and Makowski [18] show that for the ....

[Article contains additional citation context not shown here]

N. G. Duffield, J. T. Lewis, and N. O'Connell. Predicting Quality of Service for traffic with long-range fluctuations. In Proc. ICC, Seattle, WA, 1995.

....traffic engineering of these networks. 3.2.3 Non Stationary Models The self similarity hypothesis to traffic modeling has also resulted in discussions and arguments that put into question a basic tenet of traffic modeling, namely the assumption of stationarity. In particular, Duffield et al. [3] put forward the argument based on one particular set of Ethernet LAN traffic measurements that the empirically observed large Hurst parameter for that data set in [11] may be due to non stationarity in the data, i.e. apparent shifts in the mean rate. While such alternate hypotheses are ....

N.G. Duffield, J.T. Lewis, N. O'Connell, R. Russell and F. Toomey, "Predicting Quality of Service for Traffic with Long-Range Fluctuations", Proc. ICC'95, Seattle, WA, pp. 473--477, 1995.

....have achieved visual smoothness. Unfortunately, even a set of 29 million data points is not sufficient to yield more than two or three such intervals, so an honest test cannot be made. Other questions have been raised concerning the possible non stationarity of the data. N. G. Duffield, et.al. [DUFF94] have examined the data in [LELA94] and have shown that at least some of the fluctuations can be attributed to changes in the packet arrival rates. But from our guesstimate arguments, it is clear that for all ff 1 the data will stabilize in principle if it is generated by a stationary process ....

Duffield N.G., J.T. Lewis, N. O'Connell, R. Russell, F. Toomey (1994): Predicting Quality of Service for Traffic with Long-Range Fluctuations. Technical Report DIAS-APG-94-31, Dublin Institute for Advanced Studies.

....This concern is based on two recent findings: i) VBR video traffic exhibits long range dependence (Hurst parameter larger than 0. 5) 2] ii) the buffer overflow probability (BOP) 1 associated with long range dependent (LRD) video traffic decays hyperbolically [14, 18] or in a Weibull fashion [7, 17]. A direct implication of (ii) is that the notion of effective bandwidth based on Markov models in which the buffer overflow probability (BOP) decays exponentially does not apply to LRD traffic (see Section 4 for detail) This has led many researchers and practitioners to assume that the LRD ....

....marginal distribution and no correlations contribute to multiplexer performance at the zero buffer size; and (ii) eventually the curves in Figs. 3 (c) and (d) will exhibit the same decaying characteristic when buffer size becomes larger and larger, for they all have the same Hurst parameter [7]. However, such a range of the buffer size is beyond the practical consideration; see Fig. 6. Total Buffer Size (msec) 0 2 4 6 8 10 v = 0.67 v = 1.0 v = 1.5 (a) Z v Total Buffer Size (msec) 0 2 4 6 8 10 Z with a = 0.7 Z with a = 0.9 Z with a = 0.975 Z with a = 0.99 (b) Z a Figure 4: Impact ....

N. G. Duffield, J. T. Lewis, and N. O'Connell. Predicting Quality of Service for traffic with long-range fluctuations. In Proc. ICC, Seattle, WA, 1995.

....across the segments seems to indicate that the dynamics of the process generating the traces varies with time. The results here are not conclusive because the exact nature of the correlation between estimates made in adjacent data segments is unknown. With respect to pOct it has been noted before [16] that, as shown in the upper plot in figure 9, there is 0 200 400 600 800 1000 1200 1400 1600 0 2 4 6 x 10 5 time (s) pOct Part I Part II Full trace : H = 0.80 Part I : H= 0.81 part II : H=0.79 0 5 10 15 20 25 30 log2(scale) log2(hatGamma) Figure 9: Elimination of level shift in pOct. The ....

....close to 0:80 are found for the whole trace and the portions to the left and right of the shift, showing that the LRD is not an artifact of the shift. a level shift (that is an apparent shift in the mean) at around the 16 19 minute mark of this half hour trace. As was shown in figure 4 from [16], variogram based H estimates [10] of the sub series to either side of this transition are lower and markedly different to that for the whole trace. This fact lends itself to the interpretation that the value obtained from the whole trace has been corrupted by a non stationarity in the mean, ....

N.G.Duffield, J.T.Lewis and N.O'Connell, Predicting Quality of Service for Traffic with LongRange Fluctuations, Proc. IEEE ICC'95, (1995) pp.473-478.

.... measurement studies on LAN, WAN, and variable bit rate video traffic in a variety of contexts prove to be fractal [2] 10] 13] 30] 34] 38] We employ only stationary FPP models in this paper, although fractal behavior may be observed from traces which appear to be non stationary [6]. 2.2 Second order statistical measures Important second order statistics for an FPP include the power spectral density (PSD) coincidence rate (CR) index of dispersion for counts (IDC) also called the Fano factor] and count based covariance function (COV) The CR measures the correlation ....

Duffield, N. G., Lewis, J. T., and O'Connell, N. Predicting Quality of Service for traffic with long-range fluctuations. In Proc. ICC, Seattle, WA, 1995.

....comment on usefulness of this procedure on page 16. There is good evidence that this bit rate process exhibits long range behavior [4] 27] This means that accurate characterization seems intractable by most conventional stochastic processes, such as various Markov processes. As discussed in [21], the apparent long range behavior could also be explained by lack of stationarity. In either case, the modeling is problematic. Provided that a model has been chosen, the user should then estimate the parameters for it and find a way to regulate the service rate #(t) so that R(t) strictly ....

N. G. Duffield, et alii, "Predicting Quality of Service for Traffic with Long--Range Fluctuations, " in Proceedings of IEEE International Conference on Communications, Seattle, Washington, USA, June 18--22, 1995.

.... Until the LRD of various VBR video traces [2, 9, 12] has been established, the majority of VBR video traffic models are based on short range dependent processes such as Markov modulated Poisson processes [10, 29] However, new theoretical queueing results with LRD input traffic reported in [6, 17, 20, 21] were more than sufficient to caution researchers and practitioners who depended on Markov based performance models. In addition, experimental queueing analysis reported in [8, 26] and the spectral analysis of queueing systems performed in [16] show convincing results that LRD has a dominant ....

N. G. Duffield, J. T. Lewis, and N. O'Connell. Predicting Quality of Service for traffic with long-range fluctuations. In Proc. ICC, Seattle, WA, 1995.

....engineering. This concern is based on two recent findings: i) VBR video traffic exhibits long range dependence (Hurst parameter larger than 0. 5) 2] ii) the buffer overflow probability (BOP) 1 of long range dependent (LRD) video traffic decays hyperbolically [13, 17] or in a Weibull fashion [5, 16]. A direct implication of (ii) is that the notion of effective bandwidth based on Markov models of which the BOP decays exponentially does not apply to LRD traffic (see Section 4 for detail) This has led many researchers and practitioners to believe that the LRD property of VBR video traffic will ....

....for LRD processes The first result on the queueing analysis of self similar traffic seems to appear in Norros [16] in which the popular Weibull (lower) bound on the BOP has been established using fractional Brownian Motion. Also, using the techniques of large deviations theory, Duffield et al. [5] have shown that under mild conditions, the BOP of LRD traffic, whether exact or asymptotic, is again approximated by Weibull behavior as buffer size goes to infinity. While the above results exhibit Weibull decays, Likhanov et al. [13] and Parulekar and Makowski [17] show that for the M=G=1 type ....

[Article contains additional citation context not shown here]

N. G. Duffield, J. T. Lewis, and N. O'Connell. Predicting quality of service for traffic with long-range fluctuations. In Proc. ICC '95, Seattle, 1995.

.... this application) In recent year there has been studies suggesting that the bit rate process exhibits long range behavior [3] 18] The implications have been considered recently [25] 26] 34] 74] The apparent behavior has also be explained as level shifts rather than as long range dependence [13][17] 22] In summary, one means of describing unregulated video sources is by fitting a stochastic model that captures the time scales of the program, and to calculate the equivalent capacity for the source. The use of a smoothing buffer can be captured by the calculation and will result in a ....

N. G. Duffield, et al., "Predicting Quality of Service for Traffic with Long--Range Fluctuations, " in Proceedings of IEEE International Conference on Communications, Seattle, Washington, USA, June 18--22, 1995. Gunnar Karlsson Video over ATM Networks 15

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N.G. Duffield, J.T. Lewis, N. O'Connell, R. Russell, and F. Toomey. Predicting Quality of Service for Traffic with Long--Range Fluctuations. In IEEE International Conference on Communications, Seattle, 1995.

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N.G. Duffield, J.T. Lewis, N. O'Connell, R. Russell, and F. Toomey. Predicting Quality of Service for Traffic with Long--Range Fluctuations. In IEEE International Conference on Communications, Seattle, 1995.

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N. Duffield, J. Lewis and N. O'Connell, Predicting quality of services for traffic with long-range fluctuations, in: Proc. of IEEE ICC'95, 1995.

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Duffield, N.G., Lewis, J.T., O'Connell, N., Russell, R. and Toomey, F. (1994). Predicting quality of service for traffic with long-range fluctuations.

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N. G. Duffield, J. T. Lewis, and N. O'Connell, Predicting quality of service of traffic with long-range fluctuations, Proc. IEEE ICC `95, pp. 473--477, 1995.

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