C. Courcoubetis and R. Weber, "Buffer overflow asymptotics for a switch handling many traffic sources," J. Appl. Prob., vol. 33, no. 3, pp. 886--903, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....be very inaccurate. This is usually the case when many sources (N ) are multiplexed# under this assumption it was shown in [9] that ff e ;flN forsomeconstant fl. A more formal analysis of the multiplexing of a large number of sources and an improvement of the EB approximation is given in [14,15]. Complementing the work done in [9] in [19]wehaveshown that EB approximation maybevery inaccurate in the presence of multiple time scale arrivals. Similar observations of inaccuracy of the EB approximation in the presence of multiple time scales (in the context of nearly decomposable ....

C. Courcobetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. Manuscript, December 1994.

....bits may be in flight between queues. The framework we adopt in this paper is simpler than that analysed by these authors in that we directly model only rates and not queue lengths, but more complex in that we model a network with an arbitrary number of bottleneck resources. Theoretical work [11], 12] on queues serving the superposition of a large number of streams indicates circumstances when the busy period preceding a buffer overflow may be relatively short, and several authors have argued the advantages of preventing queue build up through the bounding of rates (see, for example, ....

Courcoubetis C and Weber RR (1996). Buffer overflow asymptotics for a switch handling many traffic sources. Journal Applied Probability , 33, 886903.

....reported by several authors, the first known to us being A. Dembo and O. Zeitouni (talk at National Meeting of the Operations Research Society of America, Boston, April 1994) Large deviation papers supporting (1.6) and (1. 7) have been written by Botvich and Duffield [9] Courcoubetis and Weber [21], Simonian [40] and Tse, Gallager and Tsitsiklis [44] To state their result, let W n be the steady state waiting time with n sources. Paralleling (1.4) their result is n 1 logP(W n nx) I(x) as n , 1.8) for an appropriate function I(x) yielding the approximation P(W n x) ....

....Statistical Analysis, Theory and Applications, ed. P. A. W. Lewis, Wiley, New York, 1972. 20] C. Courcoubetis, G. Kesidis, A. Ridder, J. Walrand and R. R. Weber. Admission control and routing in ATM networks using inferences from measured buffer occupancy. IEEE Trans. Commun. to appear. [21] C. Courcoubetis and R. R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources, University of Cambridge, 1994. 22] A. Dembo and O. Zeitouni. presentation at the national meeting of the Operations Research Society of America, Boston, April 1994. 23] A. I. Elwalid and ....

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C. Courcoubetis and R. R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources, University of Cambridge, 1994.

....that a large class of distributions yields an open set D. This class includes the distributions with rational Laplace transforms (e.g. phase type distributions) Large deviation results for queues like (2. 17) have also been obtained lately by Abate et al. 1] Chang [10] Courcoubetis and Weber [15], de Veciana et al. 19] Duffield and O Connell [21] Elwalid and al. 25] Kesidis et al. 35] Parulekar and Makowski [53] Simonian and Guibert [59] among others. Remark 2.1 When the Markov chain (Y n ) is stationary, the stability condition E [U 0 ] 0 follows from Loynes [49] In the ....

C. Courcoubetis and R. Weber, "Buffer Overflow Asymptotics for a Switch Handling Many Traffic Sources". Submitted to J. Appl. Prob.

....approximation. However, as discussed in [25] the EB approximation may often be highly inaccurate. This is usually the situation when many sources (N) are multiplexed; in this case it was shown that ff e Gammafl N for some constant fl. More formal investigation of this effect was conducted in [43, 105, 35]. In [25] it was also shown that the single exponential approximation may be poor; the authors suggest a procedure for approximating the queue length distribution with three exponentials. In this chapter we complement the work done in [25] by investigating the impact of multiple time scales on the ....

C. Courcobetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. Manuscript, December 1994.

.... that the approximation can be refined as P (X B) ffe GammaffiB ; where ff can be computed either numerically [11] or by capturing the gains of bufferless statistical multiplexing using the Chernoff bound [17] or appropriate large deviations scaling to account for a large number of sources [8, 14]. Such a refinement is considered to be reasonably accurate for most practical applications. Further, for most well behaved service time distributions, if ff is exactly calculated, P (X B) ffe GammaffiB [2] where f(x) g(x) denotes lim x 1 f(x) g(x) 1: Assuming a preemptive resume model, ....

C. Courcoubetis and R.R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. Journal of Applied Probability, September 1996.

....traffic overload, without the need for source traffic characterization, is provided by the Virtual Queue mechanism: a resource marks packets or not depending on the state of a fictitious queue, of lower capacity than the real queue. In Section III D we use the many sources asymptotic [27] [28], 29] to provide important insights into the relevant packet level timescales, and thus into the robustness of such mechanisms. Finally, in Section IV, we conclude. II. Connection level network models We now explore more fully how an end system or user might decide whether or not to enter the ....

....types, at the cost of a more elaborate notation. Suppose a connection generates a workload for the resource of X[0; t] in time [0; t] assume X has stationary increments, and that the workloads generated by different connections are independent. Then the many sources asymptotic regime [27] [28], 29] shows that for large systems log P (c; b; n) sup t inf s fstnff(s; t) Gamma s (b ct)g : 26) where ff (s; t) 1 st log E h e sX[0;t] i 0 s; t 1 (27) is the effective bandwidth of an individual source. Let (s ; t ) be an extremal pair for Equation (26) then t is the ....

C. Courcoubetis and R. Weber, "Buffer overflow asymptotics for a switch handling many traffic sources," Journal of Applied Probability, vol. 33, pp. 886--903, 1996.

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C. Courcoubetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. J. Appl. Prob., 33:886--903, 1996.

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C. Courcoubetis, R. Weber, Buffer overflow asymptotics for a switch handling many traffic sources, J. Appl. Prob. 33 (1996) 886--903.

.... the source, i.e. the characteristics of the multiplexed traffic, their QoS requirements, and the link resources (capacity and buffer) Specifically the time parameter t (measured in, e.g. milliseconds) corresponds to the most probable duration of the busy period of the buffer prior to overflow [16] (i.e. the time to fill the buffer) The space parameter s (measured in, e.g. kbits corresponds to the degree of multiplexing and depends, among others, on the size of the peak rate of the multiplexed sources relative to the link capacity. Effective bandwidths are increasing in s [15] In ....

....B = Nb. The following holds for Q(N c; N b; Nn) lim N 1 log Q(N c; N b; Nn) 4 s(b ct) st n j j (s; t) 5 I ; 2) where I is called the asymptotic rate function. The last equation is referred to as the many sources asymptotic and has been proved for discrete time in [16], for continuous time in [17] and for a more special case in [18] Due to equation (2) the buffer overflow probability (BOP) can be written as P(overflow) NI o(N) which leads to the following approximation when N is large: log P(overflow) s(B Ct) st R (s; t) R ; 3) where R ....

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C. Courcoubetis and R. Weber, "Buffer overflow asymptotics for a switch handling many traffic sources," Journal of Applied Probability, vol. 33, pp. 886--903, 1996.

....as network dimensioning, call acceptance control, and charging for network services. Closely related is the ability to identify and measure quantities such as the relevant space and time scales (see below) This is important for accurate and efficient traffic modeling. The many sources asymptotic [CW96, BD95, SG95], based on the theory of large deviations, is an approach for estimating the overflow probability and identifying the relevant time scales at a buffered ATM output link which multiplexes a large number of sources. In addition, the effective bandwidth formula based on this asymptotic appears to be ....

....of Computer Science, University of Crete, Heraklion, Greece Assume that there are J different source types. Let P[overflow] denote the buffer overflow probability, and X j [0; t] the load produced by a source of type j in interval t. If X j [0; t] has stationary increments, the following holds [CW96]: lim N 1 N log P[overflow] sup inf [st ae j ff j (s; t) Gamma s(b ct) 2) where ff j (s; t) is the effective bandwidth of a source of type j and is given by (1) The many sources (or large N) asymptotic leads to the following approximation for the overflow probability ....

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C. Courcoubetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. Journal of Applied Probability, 33, 1996.

.... the source, i.e. the characteristics of the multiplexed traffic, their QoS requirements, and the link resources (capacity and buffer) Specifically the time parameter t (measured in, e.g. milliseconds) corresponds to the most probable duration of the busy period of the buffer prior to overflow [4] (i.e. the time to fill the buffer) The space parameter s (measured in, e.g. kb ) corresponds to the degree of multiplexing and depends, among others, on the size of the peak rate of the multiplexed sources relative to the link capacity. Effective bandwidths are increasing in s [7] In ....

....c; N b; Nn) lim N 1 log Q(N c; N b; Nn) Gamma inf 4 s(ct b) Gamma st n j ff j (s; t) 5 = GammaI ; 2) where I is called the asymptotic rate function. The last equation is referred to as the many sources asymptotic (or infsup formula) and has been proved for discrete time in [4], for continuous time in [2] and for a special case in [12] Due to equation (2) the overflow probability can be written as P(overflow) e GammaN I o(N) which leads to the following approximation when N is large: log P(overflow) Gamma inf = GammaF R ; 3) where ff R (s; t) is the ....

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C. Courcoubetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. Journal of Applied Probability, 1996.

....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) where N is the number of sources and I is the ....

....many sources asymptotic can be obtained using the Bahadur Rao theorem which adds to equation (1.2) a prefactor term of the form A= N , where A depends only on the characteristics of the multiplexed sources and is independent of the number of sources N . The work in [LM97] extended the proof in [CW96] to obtain the improvement, while [HW94, MdV96] introduced the improvement earlier as a heuristic and applied it for on off Markov fluid sources. A similar improvement has also been used for the large buffer asymptotic [EHL 95] and shown to give good results for video teleconference traffic ....

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C. Courcoubetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. Journal of Applied Probability, 33:886-903, 1996.

....a link with capacity C = 622 Mbps and total buffer B = 30 cells. The bufferless on off fluid approximation gives a CLP less than , when in fact the actual CLP is 10 . To analyze the above model, we apply the continuous time version of the large asymptotic techniques which were developed in [CW96]. Our approach simultaneously captures the effects at the cell scale and burst scale, and accurately computes the cell loss probability. This contrasts with other work which has addressed either the cell scale or the burst scale alone. Using a simple heuristic, we are able to investigate the ....

....mean dev. Empirical mean dev. Bursts CELL SCALE REGIME FLUID REGIME Figure 2: Cell loss regimes. The value of b depends on the network and source parameters. The rest of the paper is structured as follows. In Section 2, we review the discrete time many sources asymptotic developed in [CW96], and show that it can be generalized to a continuoustime form which is able to capture the cell scale effects. In Section 3, we apply this asymptotic to constant bit rate (CBR) traffic (i.e. T off = 0) and compare the CLP estimated using our approach with that estimated using other ....

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C. Courcoubetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. Journal of Applied Probability, 33, 1996.

....of usage based charging is itself a debatable issue, and in this paper we argue that effective charging schemes that require only two simple measurements (time and volume) can be created. Our approach is based on the notion of effective bandwidth as a proxy for resource usage [8] Both theory [5,8,3] and experimentation [4] has shown that a connections resource usage depends on its context, i.e. the link resources and the composition and characteristics of the other trafiic it is multiplexed with. In the effective bandwidth definition we consider, this dependence is only through a pair of ....

.... where s, t are system defined parameters that depend on the characteristics of the multiplexed traffic and the link resources (capacity and buffer) Specifically, the time parameter t (measured in, e.g. msec) corresponds to the most probable duration of the buffer busy period prior to overflow [5,21]. The space parameter s (measured in, e.g. kb 1) corresponds to the degree of multiplexing and depends, among others, on the size of the peak rate of the multiplexed sources relative to the link capacity. In particular, for links with capacity much larger than the peak rate of the multiplexed ....

[Article contains additional citation context not shown here]

C. Courcoubetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. J. Appl. Prob., 33:886-903, 1996.

....of usage based charging is itself a debatable issue, and in this paper we argue that effective charging schemes that require only two simple measurements (time and volume) can be created. Our approach is based on the notion of effective bandwidth as a proxy for resource usage [9] Both theory [6,9,3] and experimentation [5] has shown that a connection s resource usage depends on its context, i.e. the link resources and the composition and characteristics of the other traific it is multiplexed with. In the effective bandwidth definition we consider, this dependence is only through a pair of ....

.... where s, t are system defined parameters that depend on the characteristics of the multiplexed traffic and the link resources (capacity and buffer) Specifically, the time parameter t (measured in, e.g. msec) corresponds to the most probable duration of the buffer busy period prior to overflow [6,22]. The space parameter s (measured in, e.g. kb 1) corresponds to the degree of multiplexing and depends, among others, on the size of the peak rate of the multiplexed sources relative to the link capacity. In particular, for links with capacity much larger than the peak rate of the multiplexed ....

[Article contains additional citation context not shown here]

C. Courcoubetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. J. Appl. Prob., 33:886-903, 1996.

....of usage based charging is itself a debatable issue, and in this paper we argue that effective charging schemes that require only two simple measurements (time and volume) can be created. Our approach is based on the notion of effective bandwidth as a proxy for resource usage [9] Both theory [6,9,3] and experimentation [5] has shown that a connection s resource usage depends on its context, i.e. the link resources and the composition and characteristics of the other traffic it is multiplexed with. In the effective bandwidth definition we consider, this dependence is only through a pair of ....

.... where s; t are system defined parameters that depend on the characteristics of the multiplexed traffic and the link resources (capacity and buffer) Specifically, the time parameter t (measured in, e.g. msec) corresponds to the most probable duration of the buffer busy period prior to overflow [6,22]. The space parameter s (measured in, e.g. kb Gamma1 ) corresponds to the degree of multiplexing and depends, among others, on the size of the peak rate of the multiplexed sources relative to the link capacity. In particular, for links with capacity much larger than the peak rate of the ....

[Article contains additional citation context not shown here]

C. Courcoubetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. J. Appl. Prob., 33:886--903, 1996.

....C = 622 Mbps and total buffer B = 30 cells. The bufferless on off fluid approximation gives a CLP less than 10 Gamma8 , when in fact the actual CLP is 10 Gamma6 . To analyze the above model, we apply the continuous time version of the large asymptotic techniques which were developed in [CW96]. Our approach simultaneously captures the effects at the cell scale and burst scale, and accurately computes the cell loss probability. This contrasts with other work which has addressed either the cell scale or the burst scale alone. Using a simple heuristic, we are able to investigate the ....

....mean dev. Empirical mean dev. Bursts CELL SCALE REGIME FLUID REGIME Figure 2: Cell loss regimes. The value of b 0 depends on the network and source parameters. The rest of the paper is structured as follows. In Section 2, we review the discrete time many sources asymptotic developed in [CW96], and show that it can be generalized to a continuoustime form which is able to capture the cell scale effects. In Section 3, we apply this asymptotic to constant bit rate (CBR) traffic (i.e. T off = 0) and compare the CLP estimated using our approach with that estimated using other ....

[Article contains additional citation context not shown here]

C. Courcoubetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. Journal of Applied Probability, 33, 1996.

No context found.

C. Courcoubetis and R. Weber, "Buffer overflow asymptotics for a switch handling many traffic sources," J. Appl. Prob., vol. 33, no. 3, pp. 886--903, 1996.

No context found.

Courcoubetis, C. and Weber, R. 1996. Buffer overflow asymptotics for a switch handling many traffic sources. Journal of Applied Probability 33.

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C. Courcoubetis and R. Weber (1994). Buffer overflow asymptotics for a switch handling many traffic sources. To appear in Journal of Applied Probability.

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C. Courcoubetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. J. Appl. Prob. vol. 33, pp. 886--903, 1996.

No context found.

Courcoubetis, C. and Weber, R. (1996). Buffer overflow asymptotics for a switch handling many traffic sources. J. Appl. Prob., 33.

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Courcoubetis, C. and Weber, R. R. (1996). Buffer overflow asymptotics for a switch handling many traffic sources. J. Appl. Prob., 33:886--903.

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C. Courcoubetis and R. Weber, "Buffer overflow asymptotics for a switch handling many traffic sources," J. Appl. Prob. 33, pp. 886--903, 1996.

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