M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....sizes b, however, the single parameter H does not describe P [Q b] accurately. The LRD parameter H captures only the asymptotic decay with time scale of the variance of traffic. More recent work that refines (57) indicates that traffic characteristics at the CTS (39) impacts queuing more than H [13 16, 44, 45]. This implies that the variance of traffic at one particular time scale impacts P [Q b] more than H (see Section IV B) Here, we move beyond second order statistics (i.e. variance at multiple time scales) and demonstrate the impact of the entire marginal distribution of traffic at different ....

M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.

....sizes b, however, the single parameter H does not describe P [Q b] accurately. The LRD parameter H captures only the asymptotic decay with time scale of the variance of traffic. More recent work that refines (57) indicates that traffic characteristics at the CTS (39) impacts queuing more than H [13 16, 44, 45]. This implies that the variance of traffic at one particular time scale impacts P [Q b] more than H (see Section IV B) Here, we move beyond second order statistics (i.e. variance at multiple time scales) and demonstrate the impact of the entire marginal distribution of traffic at different ....

M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.

....for fGn with H 1=2 is much slower than the exponential decay predicted by SRD classical models [2] which correspond to the case H = 1=2. In spite of this result, there is still an ongoing discussion on the effect of LRD on queuing, with researchers arguing both for and against its importance [14 17, 41, 42]. In this section, we present an approach to queuing analysis which is particularly adapted to multiscale representations of signals and processes. More precisely, exploiting the inherent binary tree structure of the Haar scaling coefficients of both traffic models, the WIG and the MWM, we derive ....

M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.

....mass over negative values for the WIG model. d) Variance time plots of the real data trace (LBL TCP 3) and synthetic WIG and MWM data traces. spite of this result, there is still an ongoing discussion on the effect of LRD on queuing, with researchers arguing both for and against its importance [14 17, 38, 39]. The impact of multiscale marginals on queuing has been demonstrated experimentally in [28] To better understand how marginals affect queuing, we develop a novel queuing analysis which is particularly adapted to multiscale representations of signals and processes. More precisely, exploiting the ....

M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.

....see, for instance, 5,14,19] In particular, a number of papers have studied analytical models of queues driven by long range dependent arrivals, with the goal of deriving insights about the performance of communication networks that need to handle such traffic. Examples of such papers include [1,2,12,13,15 18,20,21]. A feature of most of these works is the observation that the tail behavior of queues with long range dependent inputs decays much slower than exponentially, either as a Weibull law or according to a power law, depending on the # Research supported in part by NSF grant NCR 94 22513. J.C. ....

....t R) It is straightforward to verify # #. This computation is left to the reader. Following Cox [9] equation (1) says, by definition, that (A(t) t R) is long range dependent. The arrival model described above is very similar to the ones considered in several earlier papers, e.g. [1,2,12,13, 15,16,18,20], and the practical relevance of considering arrival models of this type has been argued in [13,24] 3. Some preliminaries It is convenient to gather in one place some notation that will be used in the subsequent discussion. Recall that p k = P (# = k)andq k = P (# # k) l=k p l . We ....

M. Parulekar and A.M. Makowski, Tail probabilities for a multiplexer with self-similar traffic, in: Proceedings of the IEEE INFOCOM (1996) pp. 1452--1459.

....is an active c flIFIP 1996. Published by Chapman Hall research area since network dimensioning for Internet services has became a very important issue. However, performance metrics are obtained at the cell or packet level : buffer overflow probability and delay estimates under selfsimilar input [4, 7, 9, 10]. Buffer overflow probability and delay at the packet or cell level may not be an adequate QOS metric for service provisioning. Little literature exists on QOS metrics that relate Internet user satisfaction and network parameters such as end to end delay and bandwidth. David Clark addresses this ....

M. Parulekar and A. Makowski. Tail probabilities of a multiplexer with self-similar traffic. In IEEE INFOCOM '96, volume 3, pages 1452-- 1459, 1996.

....been shown in both data streams [14, 16] and VBR video streams [10] This fact tells us that traditional Markovian models cannot be extended into the broadband domain, as they are not able to accurately reflect the behaviour of LRD traffic streams. In response, many new models have been proposed [5, 12, 13, 18, 20] for LRD traffic. In this paper we examine the ability of the M Pareto process to meet our needs as a model for broadband traffic streams. In Section 2 we explain our technique for evaluating a traffic model, and define the queueing framework used throughout this paper. In Section 3 we give a ....

....bursts. The M Pareto model is just such a process, generating an arrival process based on overlapping bursts. The M Pareto model described below is closely related to that given in [15] and is one of a family of such processes which form a sub group of the more general M=G=1 models explored in [13, 18]. M Pareto traffic is composed of a number of overlapping bursts. Bursts arrive according to a Poisson process with rate . The duration of each burst is random, and chosen from a Pareto distribution. The complementary distribution function for a Pareto distributed random variable is given by Pr ....

M. Parulekar and A. M. Makowski. Tail Probabilities for a Multiplexer with Self-Similar Traffic. In Proceedings of Infocom '96, 1996.

....and the Hurst parameter as important traffic characteristics. However, consistent success in traffic modeling was not achieved even when these three parameters were fitted, suggesting that, although these factors are important, they do not tell the full story. There is now a growing body of work [8, 9] showing that these three parameters are insufficient to characterize a realistic traffic streams. In this paper, we demonstrate that modeling an LRD traffic stream by fitting only the mean, variance and Hurst parameter leads to accurate traffic modeling only in fortunate cases, and that an ....

M. Parulekar and A. M. Makowski. Tail Probabilities for a Multiplexer with Self-Similar Traffic. In Proceedings of Infocom '96, 1996.

....model involving long bursts. The M Pareto model is such a process, generating an arrival process based on overlapping bursts. The M Pareto model described below is closely related to that given in [8] and is one of a family of such processes which form a sub group of the M=G=1 models explored in [11]. M Pareto traffic is composed of overlapping bursts. The duration of each burst is a random variable chosen from a Pareto distribution. Using the Pareto distribution here allows the significant long bursts which characterise LRD traffic to appear in the model traffic. The complementary ....

M. Parulekar and A. M. Makowski. Tail Probabilities for a Multiplexer with Self-Similar Traffic. Proceedings of Infocom '96, 1996.

....allows accurate representation of such traffic (see [3 8] and references therein. Most attempts to achieve this goal have focussed on models using various measures for, and combinations of, the mean, variance and long term variability of a measured traffic trace. However, it has been shown in [7,9] that identical values for all three of these parameters can produce widely varying queueing performance results. In recent testing [9,10] we showed that the M Pareto model [5,11] produces different queueing performance results for identical values of the mean, variance and Hurst parameter. The ....

....source, is characterized by significant long bursts (see [16] and references therein) It is therefore appealing to model LRD traffic with a model which involves long bursts. The M Pareto model is one of a family of such processes which form a sub group of the more general M=G=1 models explored in [7,17]. For more details of the statistics of the M Pareto model, see [11] and references cited therein. An M Pareto process is basically a process composed of a number of overlapping bursts. Bursts arrive according to a Poisson process with rate , and have a Pareto distributed duration. The parameter ....

M. Parulekar and A. M. Makowski. Tail Probabilities for a Multiplexer with Self-Similar Traffic. In Proceedings of Infocom '96, 1996.

....As a more structural traffic model, a superposition of a large number of ON OFF type sources whose activity periods are heavy tailed, has received considerable attention. Such models are approximated by fluid models with M G 1 inputs, sometimes referred to as infinite source Poisson models. cf. [13, 14, 16, 15, 18, 33, 34, 35, 28, 19, 5]. The M G 1 input model described in [17] is of this type. Using a distributional limit theorem, Konstantopoulos and Lin ( 17] explain the suitability of an totally skewed stable L evy motion as a macroscopic traffic model for a high speed network switch. The limit process is self similar, but ....

M. Parulekar and A. M. Makowski. Tail probabilities for a multiplexer with a self-similar traffic. Proceedings of the 15th Annual IEEE INFOCOM, pages 1452--1459, 1996.

....mass over negative values for the WIG model. d) Variance time plots of the real data trace (LBL TCP 3) and synthetic WIG and MWM data traces. spite of this result, there is still an ongoing discussion on the effect of LRD on queuing, with researchers arguing both for and against its importance [14 17, 38, 39]. The impact of multiscale marginals on queuing has been demonstrated experimentally in [28] To better understand how marginals affect queuing, we develop a novel queuing analysis which is particularly adapted to multiscale representations of signals and processes. More precisely, exploiting the ....

M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.

....be easily captured by Poisson based models has motivated queueing theorists to propose and analyze new queueing models that capture these dependencies. One such model that has received attention is a buffer with server having rate c fed by an M=G=1 input process where G is heavy tailed (e.g. [1, 12, 19, 27]) This is of interest because of its versatility, i.e. the dependencies over different time scales can be controlled by varying the tail behavior of G. In this paper we consider the model introduced by Parulekar and Makowski [27] A discrete time single server queue (called the multiplexer) ....

....an M=G=1 input process where G is heavy tailed (e.g. 1, 12, 19, 27] This is of interest because of its versatility, i.e. the dependencies over different time scales can be controlled by varying the tail behavior of G. In this paper we consider the model introduced by Parulekar and Makowski [27]. A discrete time single server queue (called the multiplexer) with infinite waiting room and with service capacity c is fed by an integer valued process fb t ; t 2 INg. The r.v. b t is defined as the number of busy servers at time t 2 IN in an M G 1 queue with arrival intensity 0 and i.i.d. ....

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M. Parulekar, A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. of the IEEE Infocom'96 Conf., San Francisco, CA, Mar. 26-28, 1996, 1452-1459.

.... are available in [13] 22] 26] Proposed models include Fractional Brownian Motion [25] and its discrete time analog, Fractional Gaussian Noise [1] on off sources with subexponential activity periods [15] and references therein) and traffic model with subexponential session duration [28]. Under these new models the buffer distribution displays much heavier tails than the exponential tails typically associated with short range dependent Markovian models. Thus, from these analyses emerges theoretical support for the recommendation that in networks carrying long range dependent ....

.... input traffic is simply the number of busy servers in the infinite server system fed by a discretetime Poisson process with rate # (customers per timeslot) and with generic service time S (expressed in timeslots) A more detailed treatment input processes can be found in [20] 27] [28], 29] 30] This process is a versatile class of input traffic since both short range and long range dependent traffic can be generated by properly selecting the service distribution. A. ModelingM traffic sources Consider a system of infinitely many servers, and suppose B t customers arrive ....

M. Parulekar and A.M. Makowski, "Tail probabilities for a multiplexer with self--similar traffic," in Proceedings of IEEE INFOCOM '96, San Francisco (CA), April 1996, pp. 1452--1459.

....of displaying many forms of correlations including LRD. Our interest here is in the use of M=G=1 processes as a traffic model for video. In this section, we summarize some of the important properties of M=G=1 processes, as they relate to our modeling effort. Further details can be found in [18, 17]. Consider a discrete time M=G=1 queueing system in which customers arrive in i.i.d. Poisson batches of mean . Let n 1 be the size of the (n 1)th batch, i.e. the number of arrivals during time slot [n; n 1) The arrival process can be thought of as a discrete time version of a Poisson ....

M. Parulekar and A. M. Makowski. Tail probabilities for a multiplexer with self-similar traffic. In Proceedings of IEEE INFOCOM '96, pages 1452--1459, 1996.

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M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.

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M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.

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M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.

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M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.

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M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.

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M. Parukelar, A. M. Makowski, Tail probabilities for a multiplexer with self-similar traffic, Fifteenth Annual Joint Conference of the IEEE Computer Societies (INFOCOM96), Vol. 3, 1452 - 1459 (1996)

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M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.

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M. Parulekar and A. Makowski, "Tail probabilities of a multiplexer with self-similar traffic," in IEEE INFOCOM '96, vol. 3, pp. 1452--1459, 1996.

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M. Parulekar and A. Makowski, #Tail probabilities of a multiplexer with self-similar tra#c," in IEEE INFOCOM '96,vol. 3, pp. 1452#1459, 1996.

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M. Paulekar and A. M. Makowski, "Tail probabilities for a multiplexer with self-similar traffic," Proc. IEEE INFOCOM, pp. 1452--1459, 1996.

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