A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video conferencing," IEEE J. Select. Areas Commun., vol. 13, pp. 1004--1016, Aug. 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....scaled asymptotic rate function R w.r.t. B. Indeed, for the superposition of ON OFF Markov fluids when B is small it was shown in [26] that R C 1 C 2 B, where C 2 0. Also, for large B, it is shown in [16] that R converges to a linear function in B; similar indications can be found in [24]. On the other hand, concavity is not always the case, as for the sub bursty Markovian sources considered in [17] Since we could not hope for a general result validating (13) and or (12) we had to resort to experimentation. Thus, we have done extensive experiments to validate (12) and (13) for ....

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing," IEEE Journal on Selected Areas in Communications, vol. 13, no. 6, 1995.

....statistics, a property which is not achieved by any other known method. Second, a very broad and realistic class of AFC s can be matched, including, for example, Markovian models such as the Markov modulated Poisson process of Skelly et al. 17] the TES based models [22] or the DAR models [24]. Note that all of these examples taken from the literature can only match exponentially decreasing ACF s. Third, an SRP model can match subexponential ACF s, and as such, it is a uniquely efficient and simple model capturing longrange dependence. Note that the arrival model (see [16] also ....

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing," IEEE J. Select. Areas Commun., vol. 13, no. 6, 1995.

....In particular, the M=G=1 input traffic will be LRD when G is Pareto, with a shape parameter in the interval (1; 2) 5] 2. 2 Discrete Autoregressive of Order One Process The DAR(1) process is a popular Markovian (hence, SRD) model that has been used to characterize video teleconferencing traffic [8]. This process can exhibit any arbitrary marginal distribution. Its autocorrelation structure is similar to that of the common AR(1) process. To generate a DAR(1) process, we start with two mutually independent random sequences fV n : n = 1; 2; g and fY n : n = 1; 2; g. The sample space ....

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing. IEEE Journal on Selected Areas in Communications, 13(6):1004--1016, August 1995.

....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 ....

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for atm multiplexers with applications to video teleconferencing. IEEE Journal on SelectedAreas in Communications, 13(6):1004--1016, August 1995.

....investigate the application of the same modeling methodology, based on multi fractal scaling, to model traffic features of VBR video traffic below a frame level. Although there has been considerable research on video traffic (for a representative, but far from exhaustive list see [10] 11] 3] [12]) much of the prior literature (see [11] 3] is concerned with modeling fluctuations in video traffic at and above the frame level. However, as has been argued [10] performance can be very often determined by fluctuations at the cell level. One would thus expect characterizations at the slice ....

....This is done by calculating the maximum per millisecond rate in the traffic trace, aggregating the traffic over intervals of 512 ms, and assigning all the traffic in each 512 ms interval to the beginning of the interval at this maximum rate. This was suggested as a very conservative estimate in [12]. As can be seen from the figure, this approximation, while duly serving as an upper bound for the average queue length, is a gross overestimate. Thus while high frequency features are important in determining performance at low utilizations, it is worth trying to find better approximations than ....

[Article contains additional citation context not shown here]

A. Elwalid, D. Heyman, T. V. Lakshman and D. Mitra, "Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing", IEEE J. Selected Areas in Comm., Vol. 13, No. 6, pp 1004-16, Aug 1995.

....thorough investigation of this problem was done in [AMS82] Many other results for multiplexing Markovian OnOff processes followed. These led to the Equivalent Bandwidth theory for Markovian, or, in general, exponentially bounded arrival processes; extensive references can be found for example in [EHL95, GLW94, DUC95]. Recently statistical analysis has increasingly shown that the traffic streams in modern broad band networks exhibit long tailed (subexponential) characteristics. For the case of Ethernet traffic such results were examined in [LTW93] These statistical results have stimulated research in ....

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing," IEEE Journal on Selected Areas in Communications, vol. 13, pp. 1004--1016, August 1995.

....the on off markovian model can serve as a conservative estimate of the queue length, and hence, of the delay violation probability. The queue length tail probabilities for the 2 state markovian model have been studied well in the literature, and large deviations estimates have been developed [5]: PfQ qg Le Gammaffiq (7) where L is the loss in bufferless multiplexing as estimated from Chernoff s theorem [6] log L k j logf1 Gamma w j w j e s h j g Gamma s C (8) wherein w j = j = j j ) and s is the solution of: k j w j h j e 1 Gamma w j w j e = ....

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for atm multiplexors with applications to video teleconferencing. IEEE Journal on Selected Areas in Communications, 13(6):1004--1016, August 1995.

....of the independent random variables. An approxi mate convolution algorithm is described in [28] However, convolution often leads to numerical problems. We there fore apply the Large Deviation (LD) approximation, which is known to be accurate and also computationally very effi cient [43] [13], 15] 40] to the expectation in the numer ator. Towards this end, let . s) denote the logarithm of the moment generating of We define Note that u (s) lnE[eSV ] v : by the independence of the U s. The large deviation (LD) approximation gives the following approximation ....

A. Elwalid, D. Heyman, T. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for ATM multiplexers with application to video teleconferencing. IEEE Journal on Selected Areas in Communications, 13(6):1004 1016, August 1995.

....distributions of the independent random variables. An approximate convolution algorithm is described in [7] However, convolution often leads to numerical prob lems. We therefore apply the Large Deviation (LD) approximation, which is known to be accurate and also computationally very efficient [13, 4, 5, 11], to the expectation in the numerator. Towards this end, let u (s) denote the logarithm of the moment generating of us(s) lnE[e US] We define U : U. Note that by the independence of the U s. The large deviation (LD) approximation gives the following approximation for O [13] 1 e ....

A. Elwalid, D. Heyman, T. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for ATM multiplexers with application to video teleconferencing. IEEE Journal on Selected Areas in Communications, 13(6):1004 1016, August 1995.

....examples to show the great potential of our measurement based traffic modeling technique to the real traffic engineering world. Other than using the superposition of two state Markov chains, a few studies are available for measurement based traffic modeling to match with collective and In [2], a multistate Markov chain is constructed to model an MPEG video, but its correlation function still contains a single real exponential as a two state Markov chain. In [5] Jagerman and Melamed proposed a measurement based modeling technique called transform expand sample (TES) A TES process ....

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing," IEEE J. Select. Areas Commun., vol. 13, pp. 1004--1016, 1995.

....function for . We define # by the independence of the s. The large deviation (LD) approximation gives the following approximation for [1] ## ### # where# is the unique solution to # The LD approximation is known to be very accurate [1] 4] [18], 9] 19] and is also computationally very efficient. We use the LD approximation for the numerical studies in this paper. In summary, 15) is a simple expression for the worst case loss probability ; this simple expression involves the independent Bernoulli random variables , whose ....

A. Elwalid, D. Heyman, T. Lakshman, D. Mitra, and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with application to video teleconferencing," IEEE Journal on Selected Areas in Communications, vol. 13, no. 6, pp. 1004--1016, Aug. 1995.

....In particular, the M jGj1 input traffic will be LRD when G is Pareto, with a shape parameter in the interval (1; 2) 4] B. Discrete Autoregressive of Order One Process The DAR(1) process is a popular Markovian (hence, SRD) model that has been used to characterize video teleconferencing traffic [6]. This process can exhibit any arbitrary marginal distribution. Its autocorrelation structure is similar to that of the common AR(1) process. To generate a DAR(1) process, we start with two mutually independent random sequences fVn : n = 1; 2; g and fYn : n = 1; 2; g. The sample space ....

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing. IEEE Journal on Selected Areas in Communications, 13(6):1004--1016, August 1995.

....process at the time scale where overflows occur. In large systems, modeling should be performed using only the first and second order characteristics of the input process (diffusion approximation) This shows that our method agrees with the established ones for the cases of heavy multiplexing (see [9, 5, 6]) 3.4 The Case of B = 0 We consider bufferless links where we substitute real traffic using Gaussian sources. The overflow probability of the link depends only on steady state characteristics of the input process. The time parameter of bufferless systems is always (independently of the input ....

....the concavity of the scaled asymptotic rate function FR w.r.t. B. Indeed, for the superposition of ON OFF Markov fluids and small B it was shown in [13] that FR C 1 C 2 p B. Also, for large B, it is shown in [4] that FR converges to a linear function in B; similar indications can be found in [5]. On the other hand, concavity is not always the case, as for the sub bursty Markovian sources considered in [2] Since we could not hope for a general result validating (17) and (22) we had to resort to experimentation. Thus, we have done extensive experiments to validate (17) and (22) for ....

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing. IEEE Journal on Selected Areas in Communications, 13(6), 1995.

....DAR(1) multiserver queue, Teleconference traffic, multiserver ATM multiplexer, matrix analytic method, Markov regenerative theory, performance analysis 1. Introduction Discrete autoregressive process of order 1 (DAR(1) is known to be a good model for the VBR coded teleconference traffic [1] and it is mathematically tractable for queueing model [2, 3] Moreover, it is described by a few parameters and it is easy to match the probability distribution and the decay rate of the autocorrelation function of DAR(1) with those of the measured real traffics. Kamoun and Ali[4] modeled an ATM ....

A. Elwalid, D. Heyman, T.V. Laksman, D. Mitra and A. Weiss, Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing, IEEE Journal of Selected Areas in Communications, Vol. 13, No. 6, pp. 1004--1016, 1995.

.... succinctly in terms of a small number of parameters such as the first two moments of the per frame bit rate and the coefficient of an assumed exponential autocorrelation function [17] These parameters can be used in Markovian models to evaluate the performance of a network multiplexer (e.g. [6]) However, such statistical parameters cannot be efficiently policed. For less stereotyped video sequences, even these parameters are inadequate since the distribution of output rate can vary substantially for different minutes long segments of the same sequence [15] 10] Indeed, long video ....

A. Elwalid, D. Heyman, T. V. Lakshman, and A. Weiss, and D. Mitra, "Fundamental bounds and approximations for ATM multiplexers with application to video teleconferencing," IEEE J. Select. Areas Commun., vol. 13, pp. 1004--1016, Aug. 1995.

....that can be enforced without overly throttling the compres sion rate. Modeling We first look at modeling as a means to describe a bit rate function to the network. There are several attempts to model the variable rate coded video bit stream R (t) in the literature, such as references [16] 22] [23] [25] 34] 42] 59] 65] 67] 70] 85] 90] 94] 96] Most of these studies combine the modeling with some queuing analysis to determine multiplexing performance. See comment on usefulness of this procedure on page 16. There is good evidence that this bit rate process exhibits long range ....

A. Elwalid, et alii, "Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing," IEEE Journal on Selected Areas in Communications, Vol. 13, No. 6, August 1995, pp. 1004-1016.

....Services architecture (or IntServ) and the Differentiated Services architecture (or DiffServ) 1. 3 Integrated Services architecture The Integrated Services (IntServ) architecture was developed within the IETF in the mid nineties [15, 118, 115] and has its roots in earlier research results [5, 79, 27, 28, 38]. The basic premise in IntServ is that applications have hard network performance requirements, and they cannot operate effectively unless these requirements are met. For instance, an IP telephony application may require a maximum end to end delay of 200msec for each packet, while a video ....

A. Enwalid, D.Heyman, T.V.Lakshman, D.Mitra, and A.Weiss, "Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing," IEEE Journal on Selected Areas in Communications, vol. 13, no. 6, pp. 1004--1016, August 1995.

....when the actual source behaviour is close to the worst case behaviour assumed in the above calculation. For other upper bounds on the cell loss probability see Rasmussen et al. 21] Castelli, Cavallero, and Tonietti [2] Doshi [6] and the closely related work by Elwalid, Mitra, and Wentworth [10]. 2.4 Comparative Performance Analysis of the lossoriented CAC Schemes In this section, we provide a numerical comparison among the following CAC schemes: a) the method proposed by Guerin, Ahmadi, and Naghshineh [14] for calculating the effective bandwidth (hereafter referred to as the Part Two ....

....the network switches. The Part Two ATM Traffic Management and Control 131 scheduling mechanism determines to a large extent the packet queueing delay at each switch. A lot of work has been done in the area of calculating packet delays for various scheduling disciplines such as First In First Out [10, 11], Static Priority [10, 11] Weighted Fair Queueing [20] and Earliest Deadline First [19] When comparing scheduling disciplines it is necessary to evaluate the following aspects: Admission schedulability region: how many connections from each class can be admitted without violating their ....

[Article contains additional citation context not shown here]

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss. Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing. IEEE Journal on Selected Areas in Communications, 13:1004-1016, 1995.

....of the independent random variables. An approximate convolution algorithm is described in [28] However, convolution often leads to numerical problems. We therefore apply the Large Deviation (LD) approximation, which is known to be accurate and also computationally very e cient [43] [13], 15] 40] to the expectation in the numerator. Towards this end, let U i (s) denote the logarithm of the moment generating of U i : U i (s) ln E[e sU i ] We de ne U : X i2I(n)fjg U i : Note that U (s) X i2I(n)fjg U i (s) 7 by the ....

A. Elwalid, D. Heyman, T. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for ATM multiplexers with application to video teleconferencing. IEEE Journal on Selected Areas in Communications, 13(6):1004-1016, August 1995.

....will compare the performance our MVA loss approximation with simulations and also with other schemes in the literature. We call the LikhanovMazumdar technique described earlier L M, or LM: Gaussian when further approximated by a Gaussian process, the Cherno# dominated eigenvalue technique in [38] Cherno# DE, the average peak rate method in [39] Ave Peak, the analytical technique developed in [24] Hybrid, and the famous e#ective bandwidth scheme Effective BW [40] We now consider the practically important case of multiplexed voice sources. The input MMF process, which has widely ....

A. Elwalid, D. Heyman, T.V. Lakshman, D. Mitra, and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing," IEEE Journal on Selected Areas in Communications, vol. 13, no. 6, pp. 1004-- 1016, Aug. 1995.

.... 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 irrelevant correlation with respect to the performance measure of interest. Intuitively, the CH depends on the correlation structure of the input traffic, and on the system under study, namely ....

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss. Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing. IEEE J. Sel. Areas in Communication, 13(6):1004--1016, August 1995.

....to the traces used for the JSQ experiments (see Section 3. 3) We then statistically multiplex the smoothed traces on a bufferless 45 Mbps link and calculate P time loss using the Large Deviation (LD) approximation described in [28] and [37] The LD approximation is known to be very accurate [1, 15, 6, 7, 28]. We do this for two versions of optimal smoothing: no initiation delay and a 10 frame initiation delay [31] 37] 5] We chose Optimal Smoothing for our comparison, as optimal smoothing minimizes the peak rate and variability of the smoothed traffic for a given client buffer. The results are ....

A. Elwalid, D. Heyman, T. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for ATM multiplexers with application to video teleconferencing. IEEE Journal on Selected Areas in Communications, 13(6):1004--1016, August 1995.

....the link capacity. In the effective bandwidth approach, this probability is assumed to be close to one (and is taken as one in the calculations) Rege [16] compares various approaches for effective bandwidth and proposes some modifications to enhance the accuracy of the scheme. Elwalid et al. [17] proposed a method in which they combined Chernoff bounds and effective bandwidth approximation to overcome the shortcomings of the effective bandwidth. This method provides better accuracy than effective bandwidth for the case mentioned above of a bufferless multiplexer that can achieve ....

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss. Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing. IEEE JSAC, 13:1004--1016, 1995.

....### ### # # # # # # (7) Consider a queue of infinite buffer size supplied by a data source of constant data rate # (see Figure 2) The queue length #### # ### # ##### # could be non zero. Therefore, the delay #### experienced by a packet could be non zero. The theory of effective bandwidth [2, 3] can be easily adapted to this case, that is, the probability of #### ever exceeding a delay bound #### satisfies ###### # #### # ####### ### #### ## ### ####### (8) where ## ### ##### ### #### are functions of source rate #. # ### # ####### # ## is the probability that the buffer is ....

A. Elwalid, et al., "Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing, " IEEE JSAC, pp. 1004--1016, Aug. 1995.

....flow queuing model Large deviations theory provides techniques for estimating properties of rare events such as their frequency and the manner in which they occur. Recently, large deviations theory gained popularity as a valid methodology for analysis of ATM networks [4,7,19] Elwalid et al. [3] proposed the Chernoff dominant eigenvalue approximation to model the buffering behavior of some queuing systems in the asymptotic case. The queue length distribution of a queuing system fed by a large number of Markov modulated sources is approximated by G(b) # Ae zb , 1) where G(b) is the ....

.... of service for the BTS BSC link is defined in terms of both the delay of an arbitrary packet and the packet loss probability: The delay should be less than d = 4 msec for 99.99 of the packets, i.e. a 10 4 delay budget of 4 msec must be kept, and the packet loss should be below some # #[10 6 , 10 3 ]. In the results, the link capacity C is given as a multiple of DS0 channels (64 Kbps) and is denoted by n 64, where n is an integer #1. Using the discrete time model, figures 6 and 7 show the probability for a packet to experience a delay of more than d = 4 msec and the packet loss ....

A. Elwalid, D. Heyman, T.V. Lakshman, D. Mitra and A. Weiss, Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing, IEEE Journal on Selected Areas in Communications 13 (1995) 1004--1016.

....(MRP) The MRP was shown to better capture the burstiness in the low activity video data, although it was still inadequate in matching the tail probabilities at large buffer sizes. Further, the DAR model has been found to be more favorable for modeling multiplexed VBR teleconferencing traffic [8]. Relatively fewer analyses exist for full motion video. Garrett and Willinger [9] propose a self similar process to model long range dependence features found in the analysis of the Star Wars movie sequence. This model is very parsimonious in the number of parameters, but does not lend itself ....

A. Elwalid, D. Heyman, T.V. Lakshman, D. Mitra and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing," IEEE J. Select. Areas Commun. , vol. 13, p1004-1016, August 1995.

....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, the picture for mixes of heterogeneous sources is quite similar to the i.i.d. case. For completeness we note a related work [9] where a slightly different approach to approximation was taken. 2.3 Gaussian processes and frequency domain characteristics Gaussian traffic models for the net input into a queuing system often arise as heavy traffic approximations or aggregation limits. Herein we take the point of view that ....

....[17] permitting a rough evaluation of the essential time scales, e.g. scene changes, frame correlations, or picture blocks. Such time scales however depend on the type of compression and nature of the media, thus teleconferencing applications have different scales than say MPEG coded video [9]. 3.2 Interval based approximations for bandwidth requirements Once an estimate for t is available, we may consider using interval based traffic descriptors and bandwidth allocation schemes such as [7, 16, 17, 18] There are at least two simple options: 1) to approximate A(0; t ] by a ....

A. Elwalid, D. Heyman, T. Lakshman, D. Mitra, and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing, " IEEE J. Selec. Areas Commun., vol. 13, no. 6, pp. 1004--16, Aug. 1995.

....S(t) are used to obtain an estimate of Gamma ln p(ae k ; T ae k Gamma H Gamma Lmax ) which is used for finding the next iterate of ae using the RM algorithm. The actual LB parameters are updated only periodically after renegotiation. We use an affine approximation for ln p(ae; B) see [16] and [17] Writing jS (ae) as the negative of the asymptotic slope of the ln p(ae; B) vs. B curve (the subscript S denotes that fact that the source S(t) feeds the buffer) we approximate ln p(ae; B) ln P (S ae) Gamma jS (ae)B where the random variable S is the marginal of the source rate ....

Anwar Elwalid, Daniel Heyman, T. V. Lakshman, Debasis Mitra, and Alan Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing," IEEE Journal on Selected Areas in Communications, vol. 13, no. 6, pp. 1004--1016, August 1995.

.... et al. showed that there is an effective bandwidth for both the Markovian and the more general (non Markovian) models [35] Elwalid et al. proposed using the upper and lower bounds for the effective bandwidth; statistical multiplexing gains among different connections are achieved in this method [36]. For CAC that uses effective bandwidth, uses RSM, and is measurement based, Tedijanto and Gun proposed a method in which the violation probability of a leaky bucket type UPC device is calculated, and bandwidth renegotiation between users and networks is encouraged when the violation probability ....

A. I. Elwalid et al., Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing, IEEE J. Select. Areas Commun., vol. 13, no. 6, pp. 1004--1016, Aug. 1995.

....#. Therefore, the EB approximation does not account for statistical multiplexing gain and could be quite 0 7803 4386 7 98 10.00 (c) 1998 IEEE 0 7803 4386 7 98 10.00 (c) 1998 IEEE conservative [14, 25] This has resulted in renewed interest in the accurate estimation of the asymptotic constant C [2, 16, 17]. In this paper, we develop a single exponential asymptotic upper bound for the tail probability P( Q x ) based on the Extreme Value Theory for Gaussian processes [4] Since the asymptotic decay rate of this bound is the same as that of the tail probability, this implies that we find an upper ....

A. Elwalid, D. Heyman, T. Lakshman, D. Mitra, and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing," IEEE Journal on Selected Areas in Communications, vol. 13, pp. 1004--1016, Aug. 1995.

....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 non stationary case one may use a coupling argument due to Borovkov and Foss ....

A. I. Elwalid, D. Heyman, T. V. Laksjman, D. Mitra, A. Weiss, "Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing", IEEE J. on Selected Areas Commun., 13, 6, pp. 1004--1016, 1995.

....on an exponential approximation to the tail of the distribution of the buffer content in steady state. This approximation holds when the buffer sizes are very large, and the tail probabilities are small. Several researchers have attempted to redress these shortcomings. For example, Elwalid et al. [11] and [12] modify the effective bandwidth methodology and develop the Chernoff Dominant Eigenvalue (CDE) approximation for single class traffic. To avoid approximations, other approaches have been developed. They include deriving upper and lower bounds for the tail of buffer content process in ....

A.I. Elwalid, D. Heyman, T.V. Lakshman, D. Mitra, and A. Weiss (1995). Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing. IEEE Journal on Selected areas in Communications, 13(6), 1004--1016.

....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 ....

....a thorough investigation of this problem was done in [3] Many other results for multiplexing Markovian On Off sources followed. These led to the Equivalent Bandwidth theory for Markovian (or in general exponentially bounded) arrival processes; extensive references can be found for example in [43, 50, 41]. Recently statistical analysis has increasingly shown that the traffic streams in modern broad band networks exhibit long tailed (subexponential) characteristics. For the case of Internet traffic, such results were examined in [107] These statistical results have stimulated research in queueing ....

[Article contains additional citation context not shown here]

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for atm multiplexers with applications to video teleconferencing. IEEE Journal on Selected Areas in Communications, 13(6):1004--1016, August 1995.

....policies reported by Elwalid and Mitra [9] We do not provide numerical comparison since they use Chernoff bounds in their calculations, whereas we do not. In the remaining section we describe three possible extensions to the work reported here. 1. Chernoff Bounds. Chernoff bounds (see [10] and [9] can be used to further fine tune the effective bandwidth analysis. This is relatively straightforward. 2. Multiple Priorities. The analysis can be very easily extended to N 2 priorities. Exactly the same analysis holds for the first two priorities. The effective bandwidth of the ....

A.I. Elwalid, D. Heyman, T.V. Lakshman, D. Mitra, and A. Weiss. Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing. IEEE Journal on Selected areas in Communications, 13(6), 1004--1016, 1995.

....a call admission control scheme with a simple, novel traffic model for VBR service that can effectively realize the potential statistical multiplexing gains and is capable of supporting multiple QoS service levels. The call admission control scheme is based on the well known Chernoff bound method [5, 8, 9, 23]. Our contribution lies in the traffic model used in the scheme. We propose a parsimonious bounding model approach that uses only a few generic parameters to characterize the marginal distribution of video streams. Specifically, we introduce a new five parameter traffic model to capture the ....

....of smoothed video streams have important consequences for traffic modeling. For example, the traffic modeling techniques presented in [7, 12, 24] that characterize the heavytailed marginal distributions are not applicable to the smoothed video traces. Neither is the DAR(1) traffic model in [5] which assumes that the marginal distribution can be approximated by a negative geometrical distribution. Clearly, different techniques are needed for modeling smoothed video traces. In Section 4, we present a simple technique for characterizing the marginal distribution that is applicable for ....

[Article contains additional citation context not shown here]

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing. IEEE Journal of Selected Areas in Communications, 13(6):1004-- 1016, August 1995.

....On Off models, Anick, Mitra, Sondhi [2] analyzed the impact of the burstiness on queueing performance. Subsequent studies explored more general Markov models with finite state space. These led to the Equivalent Bandwidth theory for Markovian arrival processes, see for instance Elwalid et al. [6] and Glynn Whitt [7] Statistical analysis has provided increasing evidence that the traffic streams in modern broadband networks exhibit long tailed (subexponential) characteristics. For the case of Ethernet traffic, such findings were reported by Willinger et al. 15] These statistical ....

Elwalid, A., Heyman, D., Lakshman, T.V., Mitra, D., Weiss, A. (1995). Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing. IEEE Journal on Selected Areas in Communications 13, 1004-1016.

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A. Elwalid, D. Heyman, T. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for ATM multiplexers with applications to videoconferencing. IEEE Journal on Selected Areas in Communications, 13: 1004 -- 1016, 1995.

.... use shared buffers and first in first out scheduling, the number of calls that can be carried can be quite accurately determined (provided that source models are accurate and have the properties necessary for analytical tractability) One method, called the Chernoff dominant Eigenvalue method [49] applies to sources modeled by time reversible Markov chains. Many other schemes (most of which are based on different methods for calculating an effective bandwidth associated with the source and its QoS requirements) can also be used to determine the number of calls that can be carried [73, ....

....have to be accounted for, possibly by making the admission control more conservative. Another factor to consider is that the admission control calculations typically only consider the mean stationary loss probability. It may be necessary to consider the distribution of losses as well. In [49], the multiplexing gain is found to be in the range of 3 to 4 whereas the peak to mean ratio for this traffic is 5. Here the multiplexing gain is calculated by comparing the number of calls carried to the number that would be carried if peak rate allocation were used (and not by comparing it to ....

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss, "Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing", IEEE Journal on Selected Areas in Communications: Special Issue on Fundamental Advances in Networking, pp. 1004-1016, August 1995.

....models. In both access models, we study largedeviations asymptotics for the scaling introduced by Weiss [31] i.e. the regime in which the number of users grows large and resources (buffer and bandwidth) scale proportionally. We derive exponential approximations , comparable to those in [3] 4] [9] for the ordinary FIFO discipline. Exponential approximations of the first feedback model, i.e. without the threshold, were obtained earlier by Ramanan and Weiss [23] for exponential file sizes and think times. Our major contribution is that these results are explicit and the computations are ....

....approximations for large buffers. Let # the equation lim t## t 1 log IEe = c#. Define, for i =0, 1, a i : lim log IE i e A(t) c# t. In Duffield [8] it is proven that, for x ##, J(x) # x r a 1 a 0 o(x) Following the Chernoff Dominant Eigenvalue method of [9], we propose an even simpler approximation: IP x I(0) 13) Here # = r (r c) # c, and I(0) is given in Lemma IV.1. In [9] it is shown that this approximation is conservative for all x (in fact it is the best possible linear estimate that is conservative for all x) Notice that ....

[Article contains additional citation context not shown here]

A. Elwalid, D. Heyman, T. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for ATM multiplexers with applications to videoconferencing. IEEE Journal on Selected Areas in Communications, 13: 1004 -- 1016, 1995.

....= # T 0 # K # i=2 r i (t) ## (#r(t) #r # (t) #r # i Q (r i (0) r i (t) # dt . 8.58) 8.3 Large bu#er asymptotics: open model The large bu#er asymptotics for I(B) are easier to calculate than the small bu#er asymptotics. We feel that, for applications, they are less useful. In [EHL] it was shown that lim B## I(B) B = inf #x:x 1 C # (#x, 0) x 1 C . 8.59) By (7.7) #(#x, 0) h (##, x 1 #, 0) K # j=2 h (# 1j x 1 , # j1 x j , 0) 8.60) # h (##, x 1 #, 0) 8.61) since h is positive, with equality if and only if # j1 x j = # 1j x 1 . Therefore lim B## I(B) B ....

....1 , z 1 ) dt = # # C # C # 1 log C # # # 1 # C # B # . 8.76) That is, we obtain the following result: as B ##, I(B) I(0) # # C # C # 1 log C # # # 1 # C # B # o(1) 8.77) Note that the additive terms are all positive since # C. In [EHL] we showed that I(B) I(0) # # 1 # C # B (8.78) for B 0, and showed that there is a constant u such that I(B) I(0) u # # 1 # C # B (8.79) for all B 0. We believe that the smallest u which satisfies this inequality is u = #C # C # 1 log C # # , but haven t ....

[Article contains additional citation context not shown here]

Anwar Elwalid, Daniel Heyman, T.V. Lakshman, Debasis Mitra, and Alan Weiss, "Fundamental bounds and approximations for ATM Multiplexers with application to video teleconferencing," IEEE J. Selected Areas in Comm. 13 pp. 1004--1016, 1995.

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A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video conferencing," IEEE J. Select. Areas Commun., vol. 13, pp. 1004--1016, Aug. 1995.

No context found.

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing. IEEE J. Select. Areas Com., 13(6):10041016, August 1995.

No context found.

Anwar Elwalid, Daniel Heyman, T. V. Lakshman, Debasis Mitra, and Alan Weiss, "Fundamental bounds and approximations for atm multiplexers with applications to video teleconferencing," IEEE Journal on Selected Areas in Communications, vol. 13, no. 6, pp. 1004--1016, August 1995.

No context found.

A. Elwalid, D. Heyman, T.V. Lakshman, and D. Mitra. Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing. IEEE Journal on Selected Areas in Communications, 13(6), August 1995.

No context found.

A. Elwalid, D. Heyman, T.V. Lakshman, and D. Mitra. Fundamental Bounds and Approximations for atm Multiplexers with Applications to Video Teleconferencing. IEEE Journal on Selected Areas in Communications, 13(6), August 1995.

No context found.

ELWALID,A.,HEYMAN,D.,LAKSHMAN, T.V., MITRA,D.AND WEISS, A. (1995). Fundamental bounds and approximations for atm multiplexers with applications to video teleconferencing. IEEE Journal on Selected Areas in Communications 13, 1004--1016.

No context found.

A. Elwalid, D. Heyman, T. V. Lakshman, and D. Mitra, \Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing, " IEEE J. Select. Areas. Commun., vol. 13, pp. 1004-1016, Aug. 1995.

No context found.

ELWALID,A.,HEYMAN,D.,LAKSHMAN,T.V.,MITRA,D.AND WEISS, A. (1995). Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing. IEEE J. Sel. Areas Commun. 13, 1004--1016.

No context found.

A. Elwalid, D. Heyman, T. V. Lakshman, D. Mitra, and A. Weiss. Fundamental bounds and approximations for ATM multiplexers with application to video teleconferencing. IEEE J. Select. Areas Commun., 13(6):1004--1016, August 1995.

No context found.

A. Elwalid, D. Heyman, T.V. Lakshman, D. Mitra and A. Weiss, "Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing," IEEE J. Select. Areas Commun., vol. 13, p1004-1016, August 1995.

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