B. Bensaou, J. Guibert, J. Roberts and A. Simonian, Performance of an ATM multiplexer queue in the fluid approximation using the Benes approach, Annals of Operations Research 49 (1994) 137--160.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....sources was assumed to be random (e.g. a Poisson process) Lately, the model of periodic arrival sources was generalized to contain multiple arrivals rather than single arrival within one period. And the queues with such type of sources (termed generalized periodic sources) were considered in [2] [4], 6] 10] 11] 14] 17] 19] and [20] In these references, 10] is the first one who gave the exact closed form solution of the queue length distribution for the queue with homogeneous Worst Case Traffic (WCT) sources (i.e. the multiple arrivals in one period arrive back to back, or say, ....

.... is the first one who gave the exact closed form solution of the queue length distribution for the queue with homogeneous Worst Case Traffic (WCT) sources (i.e. the multiple arrivals in one period arrive back to back, or say, consecutively) Bounds and approximations were also given in references [4], 10] 14] 19] and [20] for either the discrete time or continuous time queues with homogeneous WCT sources or periodic on off sources. Other variants of the generalized periodic sources such as the batch periodic source may be found in [3] Applications of the generalized periodic source ....

B. Bensaou, J. Guibert, J. W. Roberts and A. Simonian, "Performance of An ATM Multiplexer Queue in the Fluid Approximation using the Benes Approach," Ann. Oper. Res., 49:137-160, 1994.

....routing) Many approaches for evaluating the CLR at the so called burst scale congestion for multiplexers loaded with a superposition of on off sources have been proposed in the literature. The first approach approximates the actual arrival process by fluid flow (FF) see Anick et al. 1982) and Bensaou et al. 1994)) In this approximation, the fluctuation of cell arrival rates can accurately be represented by assuming that the information arrives in a continuous flow rather than in discrete cells. The CLR is accurately approximated by the overflow probability which is obtained by solving an adequate ....

....equations through the Gauss Seidel algorithm. These approaches are efficient in predicting the CLR in an ATM multiplexer. However, when the system size becomes large, computation complexity increases in the FF approximation and memory problems arise in the MMDP approximation. It is also shown in Bensaou et al. 1994) that the CLR depends on many unknown and unpredictable traffic parameters (e.g. burst length distribution, To avoid these problems, the goal is to derive a model independent algorithm to predict the CLR in large sized systems by relying only on information from some small sized systems. In ....

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Bensaou, B., Guibert, J., Roberts, J. W., and Simonian, A. (1994). Performance of an ATM multiplexer queue in the fluid approximation using the Benes approach. Annals of Operations Research, 48.

.... C, in a logarithmic scale, the approximation of G( is a linearly decreasing function whose slope is determined by z 0 (C) and the intercept on the ordinate axis (for x = 0) is governed by the constant A(C) The calculation of z 0 (C) has been widely addressed in the literature (e.g. 1] 5] [6]) In this paper, we focus mainly on the determination of a new tight approximation of the intercept A(C) and the application of the new approximations to determine the required bandwidth. The remainder of the paper is organized as follows. In the next section, we present briefly the previous ....

B. Bensaou, J. Guibert, J. W. Roberts, and A. Simonian, "Performance of an ATM multiplexer queue in the fluid approximation using the Benes approach," Annals of Operations Research, vol. 49, pp. 137--160, 1994.

....heterogeneous traffic sources case, as shown in [4] z 0 (C) can be obtained as the largest negative solution of a non linear equation, which can be solved numerically. The determination of the constant A(C) proves, however, much more difficult. Many approximations of A(C) have been proposed [1] [7], 8] 9] The tighter the approximation of A(C) to the intercept of the exact cell loss probability, the better is the approximation of G(x) and thus of the required bandwidth. In this paper, we address the determination of a new tight approximation of the intercept 3 A(C) This approximation ....

....approximation has two major drawbacks: the first one is that to calculate the coefficient a 0 it is necessary to calculate all the stable eigenvalues z i . The second one, by far more severe, is that approximation (4) always underestimates the exact result. Moreover, it has been shown in [7] that under certain traffic conditions, the difference between the exact result and the approximation is very large even when the buffer size is (unrealistically) very large. In [9] an upper bound to (4) was derived by simply replacing the factor a 0 hOE 0 ; 1i by 1, leading to G(x) e z 0 x ....

B. Bensaou, J. Guibert, J. W. Roberts, and A. Simonian, "Performance of an ATM multiplexer queue in the fluid approximation using the Benes approach," Annals of Operations Research, vol. 49, pp. 137--160, 1994.

....process can generate Weibullian tail behaviour, which implies buffer sizes which grow much faster with load than in the classical case. In this paper we analyze a fluid or storage (see [15] queueing system with LRD input. Fluid systems have been used before (Brichet et al. 2] Bensaou et al. [1] and Guibert [11] to model bursty traffic in ATM networks over time scales where the granularity of the ATM cells, and the quasi deterministic nature of their arrivals, no longer dominate. We consider On Off sources, that is sources with mutually independent, alternating silence periods with no ....

....This fact is intimately associated with the Weibullian form of the queue (at high load) found for that case. Another, very different choice of normalization is to leave the peak rate and the capacity fixed, but to increase the mean length of the off periods as sources are added. As discussed in [1] (see also [4] in the limit of a large number of sources, this leads to an aggregate source model where new bursts arrive according a Poisson process. Physically the picture is of large set of high rate sources, each of which emit a single burst of highly variable volume. This is a reasonable ....

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B.Bensaou, J.Guibert, J.W.Roberts and A.Simonian, Performance of an ATM multiplexer queue in the fluid approximation using the Benes approach, Annals of Operations Research 49 (1994) 137-160.

....case has a power law tail with infinite mean Thus the non classical choice of service times without second moment causes dramatically different queueing behaviour. In this paper, we analyze a fluid or storage queueing system with LRD input. Fluid systems have been used before (e.g. Bensaou et al. [2], Guibert [7] to model bursty traffic fed into ATM multiplexer queues, when considering time scales where the granularity of the ATM cells no longer dominates. The input sources are assumed to be of On Off type, that is, with mutually independent, alternating silence periods (no work arriving) ....

....and or activity periods, the input process becomes long range dependent and the queueing problem is fundamentally non Markovian. Despite this, a useful lower bound L to Q is not difficult to define (Guibert and Simonian [8] and, by applying the Benes method for the fluid queue (Bensaou et al. [2]) we can also estimate an upper bound U in the heavy traffic limit as the number of sources grows to infinity. We find that the tails of the limiting distributions are not exponential but Weibullian, namely L(x) O 1 x 1 GammaH expf GammaRx 2(1 GammaH) g ; U(x) O i ....

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B. Bensaou, J. Guibert, J. W. Roberts, A. Simonian, Performance of an ATM multiplexer queue in the fluid approximation using the Benes approach, Annals of Operations Research, 49 (1994), pp.137-160

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B. Bensaou, J. Guibert, J. Roberts and A. Simonian, Performance of an ATM multiplexer queue in the fluid approximation using the Benes approach, Annals of Operations Research 49 (1994) 137--160.

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B.Bensaou, J.Guibert, J.W.Roberts, A.Simonian, Performance of an ATM multiplexer queue in the fluid approximation using the Benes approach, Annals of Operations Research, 49 (1994), pp.137-160.

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