G. L. Choudhury, D. M. Lucantoni, and W. Whitt, "Squeezing the most out of ATM," IEEE Trans. Commun., vol. 44, pp. 203--217, Feb. 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....asymptotic decay rate of the tail distribution of the queue length at a local node, i.e. x 1 log P r(q x) 1) where q is the stationary queue length and is the decay rate. Equation (1) suggests the approximation for P r(q x) by e . As in Choudhury, Lucantoni and Whitt [10], one might wonder whether the approximation is good or not. In fact, Choudhury et al. 10] showed that the approximation can be very far from its true value if the node has a large number of homogeneous sources. To provide further support for the theory of e ective bandwidth, in this paper we ....

....x 1 log P r(q x) 1) where q is the stationary queue length and is the decay rate. Equation (1) suggests the approximation for P r(q x) by e . As in Choudhury, Lucantoni and Whitt [10] one might wonder whether the approximation is good or not. In fact, Choudhury et al. [10] showed that the approximation can be very far from its true value if the node has a large number of homogeneous sources. To provide further support for the theory of e ective bandwidth, in this paper we re ne the calculus proposed in Chang [5] Chang, Heidelberger, Juneja and Shahabuddin [8] ....

G. L. Choudhury, D. M. Lucantoni, and W. Whitt, \Squeezing the most out of ATM," preprint, 1993.

....concludes with the statement [9] This is clearly an issue of practical importance, and there is considerable scope for further work. However, until recently, there has been little study of the effect of multiplexing; most of the work has been theoretical studies of queueing behavior [9] 18] [19], 20] 21] 22] Also, through the experiences of network operators, it has been appreciated that the statistical variability of packet counts and byte counts, relative to the mean, decreases with the NAC; this is sometimes referred to as increased smoothness of the traffic. Recently, the ....

G. L. Choudury, D.M. Lucantoni, and W. Whitt, "Squeezing the Most Out of ATM," IEEE Transactions on Communications,vol. 44, no. 2, pp. 203--217, 1996.

....on Internet backbone links, the correlations [of longrange dependent traffic] while present, have little actual effect because the variance of the packet arrival process is quite small. In addition, there were theoretical discussions of the implications of increased multiplexing on queueing [13] [14], 15] 16] 17] But the problem with such theoretical study is that results depend on the assumptions about the individual traffic sources being superposed, and different plausible assumptions lead to different results. Without empirical study, it was not possible to resolve the uncertainty ....

G. L. Choudury, D.M. Lucantoni, and W. Whitt, "Squeezing the Most Out of ATM," IEEE Transactions on Communications,vol. 44, no. 2, pp. 203--217, 1996.

....so as to gain from statistical multiplexing of different VBR sources. The problem here is that a large amount of buffer ing may be needed in the sw itches to exploit statistical multiplexing. If only limited buffering is available, losses will lead to quality degradation. However, recent results [28, 29] show that, in many cases, the effective bandwidth techniques are unable to capture the effect of statistical multiplexing, and hence allocating network resources based on these models would be conservative. Both Choudhury et al. 28] and Shroff et al. 29] verified the limitations of the ....

....will lead to quality degradation. However, recent results [28, 29] show that, in many cases, the effective bandwidth techniques are unable to capture the effect of statistical multiplexing, and hence allocating network resources based on these models would be conservative. Both Choudhury et al. [28] and Shroff et al. 29] verified the limitations of the effective bandwidth techniques. Based on these results, new schemes have been proposed [30 33] to calculate the bandwidth used for admission control that improve network util ization s ignificantly without the need for a large amount of ....

G. L. Choudhury, D. M. Lucantoni, and W. Whitt, "Squeezing the Most out of ATM," IEEE Trans. Commun., vol. 44, no. 2, Feb. 1996, pp. 203--17.

....so as to gain from statistical multiplexing of different VBR sources. The problem here is that a large amount of buffering may be needed in the switches to exploit statistical multiplexing. If only limited buffering is available, losses will lead to quality degradation. However, recent results [14, 66] show that, in many cases, the effective bandwidth techniques are unable to capture the effect of statistical mul tiplexing, and hence allocating network resources based on these models would be conservative. Both Choudhury et al. 14] and Shroff et al. 66] verified the limitations of the ....

....will lead to quality degradation. However, recent results [14, 66] show that, in many cases, the effective bandwidth techniques are unable to capture the effect of statistical mul tiplexing, and hence allocating network resources based on these models would be conservative. Both Choudhury et al. [14] and Shroff et al. 66] verified the limitations of the effective bandwidth techniques. Based on these results, new schemes have been proposed [6, 11, 12, 43] to calculate the bandwidth used for admission control that improve network utilization significantly without the need for large amount of ....

G. L. Choudhur D. M. Lucantoni, and W. Whitt, "Squeezing the most out of ATM," IEEE Transactions on Communications, vol. 44, no. 2, 203-217, February 1996.

....telecommunications literature in the context of PH G 1 queues. A general treatment of which, with its special cases, can be found in Neuts [30] For recent work on applications of the MAP in traffic modeling and control in ATM networks, we refer the reader to works by Choudry, Lucantoni and Whitt [14] and Whitt [38] In this paper, we examine a queueing system for which the incoming arrival process is modeled by a MAP which is simple but general enough to cover many teletraffic models used for ATM source characterization. We assume that the service times are deterministic due to cell based ....

....phase type distribution H for which the first r moments are arbitrarily close to those of G. The k stage Erlang distribution is a special case of the phase type distribution that is commonly used in the ATM literature in references by Saito, Kawarasaki and Yamada [33] Choudry, Lucantoni and Whitt [14] and Skelly, Schwartz and Dixit [34] to approximate the deterministic service time distribution. In the case of a k stage Erlang distribution approximation, the rational approximant, B a (s) becomes k s k k : 23) There are two main disadvantages of this kind of approximations: ....

G. L. Choudhury, D. M. Lucantoni, and W. Whitt. Squeezing the most out of ATM. to appear in IEEE Trans. Commun., 1995.

.... than just the logarithmic asymptote considered in [6] 7] 8] 11] 12] Knowledge of the prefactor usually allows one to more accurately assess actual statistical multiplexing gains, and design admission control policies that are neither too conservative nor too aggressive (see, for example, [14], 15] Furthermore, we model the packet arrival processes as point processes rather than fluid processes. This seems to better capture the behaviour of real packet traffic under multiplexing, especially on the time scales relevant for overflows from O(1) buffers (see Section V for further ....

....underlying on off process and a finite conditional mean arrival rate #. Packets arrive as a Poisson point process with rate # during an on period, while no packets arrive during an off period. The ExponExpoff Class 3 sources have exponentially distributed on and off periods. This model was used in [14] to study the queueing behaviour of superposed ATM traffic. Class 4 are ParetoonExpoff sources, which have an exponential off period distribution and on periods that are Pareto with tail parameter . B. Verification of Assumption 3 for Traffic Models We now verify Assumption 3 for the five ....

Gagan L. Choudhury, David M. Lucantoni, and Ward Whitt, "Squeezing the Most out of ATM," IEEE transactions on communications, vol. 44, no. 2, 1996.

....investigation. I. Introduction T HE loss probability is an important QoS (Quality of Service) measure in communication networks. While the overflow probability, or the tail of the queue length distribution, in an infinite bu#er system has been extensively studied [1] 2] 3] 4] 5] [6], 7] there have been relatively few studies on the loss probability in finite bu#er systems [8] 9] 10] 11] In this paper, we propose a simple method to estimate the loss probability PL (x) in a finite bu#er system from the tail of the queue length distribution (or tail probability) P Q ....

G. L. Choudhury, D. M. Lucantoni, and W. Whitt, "Squeezing the Most Out of ATM," IEEE Transactions on Communications, vol. 44, pp. 203--217, Feb. 1996.

....concludes with the statement [9] This is clearly an issue of practical importance, and there is considerable scope for further work. However, until recently, there has been little study of the effect of multiplexing; most of the work has been theoretical studies of queueing behavior [9] 18] [19], 20] 21] 22] Also, through the experiences of network operators, it has been appreciated that the statistical variability of packet counts and byte counts, relative to the mean, decreases with the NAC; this is sometimes referred to as increased smoothness of the traffic. Recently, the ....

G. L. Choudury, D.M. Lucantoni, and W. Whitt, "Squeezing the Most Out of ATM," IEEE Transactions on Communications,vol. 44, no. 2, pp. 203--217, 1996.

....I. INTRODUCTION For the purpose of network dimensioning and connection admission control (CAC) it is important to have a simple method for estimating the network resources required under given traffic conditions. Effective bandwidths are a widely used method for achieving this goal [1], 2] 3] 4] The effective bandwidth is a single number which is assigned to each traffic stream, based on the properties of the traffic, the buffering in the network and the allowable overflow probability. This value represents the amount of network bandwidth required to satisfy the ....

....one, Equation (2) should be written as Pr Q x x e z x (4) to highlight the possibility of x 1 or x 1. Furthermore, x is not necessarily independent of . This possibility will be further elaborated when we consider Gaussian arrival processes in Section VI. As [1] shows, where x 1 is not a valid assumption, effective bandwidths calculated in this fashion can be extremely inaccurate. If the traffic stream is long range dependent (LRD) the rate of decay of the queue length distribution may be much slower than exponential [7] 8] so Equation (2) is ....

G. L. Choudhury, D. M. Lucantoni, and W. Whitt, "Squeezing the most out of ATM," IEEE Transactions on Communications, vol. 44, no. 2, pp. 203--217, Feb. 1996.

....Ishizaki and Takine Bounds for the tail distribution 3 arguments (see, e.g. 1,7,21] and references therein) With these results, wecan efficiently find the asymptotic decayratej. Compared with the asymptotic decay rate, the asymptotic decay constant ff is much harder to obtain in general [5]. For example, even though the asymptotic decay constant can be found through the exact analysis, its computation is very time consuming when we consider a superposition of Markovian sources having multiple time scale correlations. In addition, when periodic sources are superposed, the asymptotic ....

.... reasons, some straightforward approximations to the asymptotic decay constant ff (e.g. ff =1,or ae (traffic intensity) have been proposed so far (see, for example, 21] It is known, however, that the asymptotic decay constantcan vary by several orders of magnitude depending on source models [5]. Thus such a straightforward approximation to the asymptotic decay constant can lead to a large overestimate or underestimate of the tail distribution. The unique feature of this work is to consider the initial phase combinations of periodic sources explicitly and derive upper and lower bounds of ....

G. L. Choudhury, D. M. Lucantoni and W. Whitt, Squeezing the most out of ATM, IEEE Trans. Commun. 44 (1996) 203--217.

.... therein) On the other hand, Sohraby has proposed an approximation T S n of the tail distribution Tn [15] T S n ae(z ) n : 53) It is known, however, that the coefficient of (z ) n can be much smaller than the aboves, especially when the numberofmultiplexed sources is large [4]. Therefore the above approximations overestimate the tail distribution when the number of sources is large. Now we show some numerical examples. In Figs. 1 2, we assume that the numberofGBMS sisequal to 20, all sources are homogeneous, i.e. R (k) 10, B (k) 50:0, ae (k) 0:035 for ....

G.L.Choudhury, D.M.Lucantoni and W.Whitt, "Squeezing the most out of ATM," IEEE Trans. Commun.,Vol.44, pp.203--217, 1996.

.... been assumed to be one in most studies of call admission control (CAC) based on the effective bandwidths technique (see, e.g. 4, 7, 20, 21, 34, 35] and references therein) It is known, however, that the asymptotic decay constant can vary by several orders of magnitude depending on source models [5]. Contrary to the previous works, we discuss an approximate formula of the loss probability taking the asymptotic decay constant into account. In Section 6, we apply the results obtained in Section 5 to a queue where the arrival process is a superposition of generalized binary Markov sources ....

....as P loss (1=z ) N # (30) where N denotes the buffer size. Note here that the asymptotic decay constant is assumed to be equal to one in this framework. It is, however, known that the asymptotic decay constant can vary byseveral orders of magnitude depending on source models [5]. Thus such a straightforward approximation to the asymptotic decay constant can lead to considerable overestimation or underestimation of the tail distribution. If a CACoverestimates the tail distribution, it cannot use network resource effectively. On the other hand, if a CAC underestimates the ....

G. L. Choudhury,D.M.Lucantoni and W. Whitt, "Squeezing the most out of ATM," IEEE Trans. Commun.,Vol.44, pp.203--217, 1996.

....a Markov chain is useful for the network performance studies, because it is analytically and computationally tractable for addressing admission control issues. Fluid flow models for determining loss and delay statistics based on dominant eigenvalues have been discussed in several previous papers [35,36]. Two layer encoding has statistically smoother variations in its enhancement layer relative to one layer VBR video. This feature allows a tighter characterization of UPC parameters. Two layer encoding also results in a significant per source bandwidth savings compared to one layer video, ....

G. Choudhury, D.M. Lucantoni, and W. Whitt, "Squeezing the most out of ATM," IEEE Trans. Comm., vol. 44, p203-217, 1996.

....equivalent bandwidths is less than the channel capacity. A calls equivalent bandwidth is assigned according to the formula: 2) where Based on simulation experiments using this model, it always meets its desired loss rate bounds. In fact, it has been criticized for allocating too much bandwidth [Cho94] since it ignores statistical multiplexing. In any case it is a useful benchmark. 1.4 An Access Controller Taxonomy To understand the relationship between these controllers we develop a simple taxonomy for classifying access controllers. e loss rate upper bound = m i mean transmission rate of ....

Choudhury, G.L., Lucantoni, D.M., Whitt, W., "Squeezing the Most Out of ATM," to be presented at the 14th International Teletraffic Congress in France, to be held June 6-10, 1994.

....researchers have shown that aggregation of even a fairly small number of traffic streams is usually sufficient for the Gaussian characterization of the input process. Further, Gaussian processes are closed under superposition. Therefore, unlike the case of Markovian queueing models (e.g. see [19], 20] for difficulties with Markovian queueing models) analyzing a queue with a large number of Gaussian sources is no more difficult than analyzing a queue with a single Gaussian source. Gaussian processes are completely specified by their first two moments. This makes Gaussian traffic ....

G. L. Choudhury, D. M. Lucantoni, and W. Whitt, "Squeezing the Most Out of ATM," IEEE Transactions on Communications, vol. 44, pp. 203-- 217, Feb. 1996.

....for sufficiently large N and small d, or vice versa, good approximations are obtained. These types of effects are born out by simulation [11] and indicate in part why some performance studies using effective bandwidths give excellent results while others give rather bad performance estimates [2, 10]. For simplicity we have only discussed the case of multiplexing N homogeneous streams. For heterogeneous mixes of traffic, we can consider i.i.d. sources which are each a mix of the appropriate number of heterogeneous streams, see [12] and the asymptotics follow immediately. Thus, qualitatively, ....

G. Choudhury, D. Lucantoni, and W. Whitt, "Squeezing the most out of ATM." Preprint, 1993.

No context found.

Choudhury, G. L., Lucantoni, D. M., and Whitt, W., "Squeezing the most out of ATM," IEEE Trans. on Comm., vol. 44, pp. 203-17, 1996.

....concepts. In Section 5 we discuss the application of the scaling to calculate asymptotic parameters of probability distributions. In Section 6 we apply the new scaling algorithm to compute small tail probabilities in the statistical multiplexing model considered by Choudhury, Lucantoni and Whitt [10], i.e. the BMAP G 1 queue. In Section 7 we describe the variant of the main scaling algorithm for generating functions. In Section 8 we present the scaling algorithm for multidimensional transforms, which may be Laplace transforms in some dimensions and generating functions in others. We apply ....

....here, however, is that the scaling enables us to accurately compute very small tail probabilities. 6. A Multiplexing Example We now consider the MMPP D 1 queueing model used to study the e#ectiveness of e#ective bandwidths to describe bu#er overflow probabilities with statistical multiplexing in [10]. In that model there are N independent sources sending fixed length cells to a bu#er, which is drained by an output channel at a fixed rate whenever cells are present. The cell service time distribution is thus deterministic and its value is set at 1 (by choosing the unit of time) As in [10] ....

[Article contains additional citation context not shown here]

G. L. Choudhury, D. M. Lucantoni and W. Whitt, "Squeezing the most out of ATM," IEEE Trans. Commun. 44, 203--217 (1996).

....remarks. Since this paper was written, we have made significant extensions of the results here in Choudhury and Whitt [9] and Glynn and Whitt [13] 14] We have also developed numerical algorithms and evaluated the approximations based on the asymptotics. In Choudhury, Lucantoni and Whitt [8] we show that the quality of the cruder asymptotic approximations in (6) based on the decay rates h and s alone can deteriorate dramatically when the number of sources gets large. 2. The Model and the Determining Equations The model is specified by n m nonnegative mean one random variables U i , ....

G. L. Choudhury, D. M. Lucantoni and W. Whitt, "Squeezing the most out of ATM," submitted, 1993.

....we can even approximate the asymptotic constant by 1 and get good approximations for the higher percentiles; see Example 6.2 below. However, we have found that the asymptotic constant can be very far from 1 when the arrival process is the superposition of a large number of independent sources [12]. In such circumstances, we evidently need more than the asymptotic decay rate to find good approximations for tail probabilities. 2. The Batch Markovian Arrival Process In this section we review the basic properties of the BMAP. For more details, see Lucantoni [25,26] The BMAP can be defined ....

....required decreases, and (3) the traffic intensity decreases. Focusing on the number of streams, we see from Tables 10 and 11 that for any given r and any given required percentile, the quality of the asymptotic exponential approximation degrades as we increase the number of streams from 1 to 2. In [12] we investigate this issue further. There we show that the percentile where the asymptotic exponential approximation is judged good typically increases as the number of streams increases. This phenomenon occurs because the asymptotic constants a and b in (37) and (38) themselves are exponential in ....

Choudhury, G. L., D. M. Lucantoni and W. Whitt. Squeezing the most out of ATM. submitted, 1993.

.... environments, we exploit numerical transform inversion algorithms for solving the piecewise stationary M t G t 1 queue in Choudhury, Lucantoni and Whitt [8] and the MAP G 1 queue in Lucantoni [29] Lucantoni, Choudhury and Whitt [30] Choudhury and Whitt [10] and Choudhury, Lucantoni and Whitt [9]. We also gain insight by looking at how the limiting fluid process depends on the queueing model. It turns out that the behavior of the environment process is critical, whereas the behavior of the queueing processes within environment states is not critical. This is easy to understand from the ....

....fluid process directly, although it is not di#cult to do so. Instead, we consider scaled MMPP G 1 models and observe when convergence is taking place. Here we only consider the steady state workload distribution, which we compute using the algorithm in Choudhury, Lucantoni and Whitt [9], a part of the Q 2 tool described in Choudhury and Whitt [10] We could also compute transient distributions using Lucantoni, Choudhury and Whitt [30] For the special case of exponential service times, the QBD process algorithm of Latouche and Ramaswami [27] is an attractive alternative, but ....

Choudhury, G. L., Lucantoni and Whitt, W. (1995) Squeezing the most out of ATM. IEEE. Trans. Commun. 44, 203--217.

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G. L. Choudhury, D. M. Lucantoni, and W. Whitt, "Squeezing the most out of ATM," IEEE Trans. Commun., vol. 44, pp. 203--217, Feb. 1996.

No context found.

G. L. Choudhury, D. M. Lucantoni, W. Whitt, "Squeezing the most out of ATM," IEEE Transactions on Communications, vol. 44, no. 2, pp. 203--217, Feb. 1996.

No context found.

G. L. Choudhury, D. M. Lucantoni, and W. Whitt, "Squeezing the most out of ATM," preprint, 1993.

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