S. Q. Li and H. D. Sheng, "Queue response to input correlation functions: Discrete spectral analysis," IEEE/ACM Trans. Networking, vol. 1, pp. 522--533, Oct. 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to inaccurately estimation of loss and delay of packets. Gihr and Tran Gia [3] have stated that the autocorrelation function is able to visualize process dependencies better than the Index of Dispersion of Counts (IDC) Grunenfelder et al. 4] 5] 6] Helvik et al. 8] 9] Li et al. 11] [12], 13] and Ramamurthy and Sengupta [18] 19] have used the autocorrelation function for the description of more complex and realistic input traffi scenarios. In [5] the autocorrelation function of a video codec source was fitted into an Autoregressive Moving Average Model (ARMA) using the power ....

S. Li, C. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis", Infocom 1992, pp. 382-394.

....systems [10] Here a knowledge of Z[F] is used in Haywards approximation, an extension of Erlangs blocking formula to estimate the additional servers needed for Z[F] 1. The utility of the peakedness characterization for analysis of delay systems has been suggested in [11] Previous studies [12,13] have considered equivalent second order statistics such as index of dispersion for counts or intervals, spectral functions and correlation functions to characterize arrival processes and their impact on queueing behavior. 4. Summary Measurements of on line service traffic have been analyzed. ....

S. Li and C. Hwang, "Queue response to input correlation functions: Discrete spectral analysis," IEEE/ACM Trans. on Networking, 1, pp. 522-533, (1993).

....time (in sub periods) time (in slots) n m T= m Figure 1: The relevant time scales associated with the GPM source. variations in the input process on many different time scales. When T s = 1, for instance, the proposed source model reduces to the periodic Markov chain model considered in [14], where the first and second moments of the queue length process are determined for an infinite capacity queue in discrete time. 2.2 The Sub Period Level Autocorrelation Function In this section, the cell arrival autocorrelation function for a GPM source will be considered. In order to simplify ....

S.Q. Li and C.L. Hwang. Queue response to input correlation functions: Discrete spectral analysis. In IEEE INFOCOM'92, Florence, Italy, 1992.

....the source spends in each state can be made greater than or equal to 1, the proposed traffic model is capable of capturing variations in the input process on many different time scales. When T s = 1, for instance, the proposed source model reduces to the periodic Markov chain model considered in [5], where the first and second moments of the queue length process are determined for an infinite capacity queue in discrete time. The input rate autocorrelation function for source k, n) where the lag n is indexed at sub period boundaries, is defined as R (n) E m fl m n . It is ....

S.Q. Li, C.L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis", IEEE INFOCOM

....the traffic characteristics is essential for networks to reserve an appropriate amount of resource and guarantee QoS, a description (or model) of the traffic is needed. One can model the traffic by a stochastic process, such as Gaussian process, or Markov Modulated Poisson Process, see e.g. [22, 35], and then analytically evaluate the performance of the system. However, stochastic traffic descriptors are difficult to enforce and or verify. Moreover, the predicted performance is then sensitive to modeling errors and vulnerable to mis behaving users. By contrast, traffic could be modeled ....

....given the information about the current link capacity, buffer sizes, number of connections, and traffic characteristics. One approach to estimating performance is to generate statistical models for traffic and then analytically evaluate the steady state performance of the queue, see, e.g. [22, 35]. Unfortunately, the enforcement of such source models and the sensitivity of predicted performance to modeling errors are two concerns. Even if traffic can be adequately modeled, the problem of actually estimating the performance of statistically multiplexed traffic streams is generally ....

S.Q. Li and C.L. Hwang. Queue response to input correlation functions: Discrete spectral analysis. IEEE/ACM Trans. Networking, 1(5):522--533, 1993.

....assume an artificial model of cell level traffic. Instead they use an instantaneous rate from aggregate connections (Fig. 12) The instantaneous rate is a kind of modeling of the burstlevel time scale. Low frequency components of traffic fluctuation have significant impact on queuing performance [49, 50]. The instantaneous rate captures such low frequency components in traffic fluctuation. Low frequency components are kept intact even as the traffic goes through the network [40] Thus we can take the same measurement method for all the nodes in a network. Note that because SC95 assumes that the ....

S. Q. Li and C. L. Hwang, Queue response to input correlation functions: discrete spectral analysis, IEEE/ACM Trans. Networking, vol. 1, no. 5, pp. 522--533, Oct. 1993.

....desirable for an analytical approach of queueing performance evaluation in an ATM network. On the other hand, a detailed ATM traffic statistical structure is currently unknown. Only extensive measurements on ATM networks in the next years will provide sufficient information. It has been shown [1] [2] that merely a reduced set of parameters of the incoming traffic decisively influences the performance of a queueing system. Small to medium size Markov chains (MC) models should consequently suffice when we are interested on specific QoS parameters like losses and delays. Measurements done on ....

S. Li, C.-L. Hwang, "Queue Response to Input Correlations Functions: Discrete Spectral Analysis", IEEE INFOCOM'92, Florence, May 1992.

....models. This is equivalent to approximating a correlation function decaying as a power law by a sum of exponentials; although always possible, the number of parameters required in this approach will tend to infinity as the sample size increases. Such approaches are pursued, for example in [22] and [27, 28], and can be used successfully for solving certain queueing performance problems numerically. However, in this paper we argue strongly in favor of modeling LRD based on the principle of parsimony, also known as Occam s Razor (see for exam1 ple [21] The paper s second major contribution ....

.... original trace (A) fully shuffled trace (C) externally shuffled trace with block size m = 10 (E) and internally shuffled trace with block size m = 10 (F) Our experimental results are also qualitatively consistent with the results obtained from the frequency domain based approach considered in [27, 28] where it is noted that low frequencies in the power spectra dominate queueing behavior; recall that the LRD manifests itself as a sharp divergence in the low frequency region of the power spectrum. 4 Parsimonious Traffic Modeling One can conclude from the previous section that conventional ....

S.Q. Li and C.L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis ", IEEE/ACM Trans. on Networking 1, pp. 522533, 1993.

....yielded the following expression for the complementary cummulative distribution of the system contents. Pr[u k 1 m] # # l=0 Pr[p k p k 1 . p k l m l u k l =0]Pr[u k l =0] Intricate questions are what the link is between this general result and the general observation made in e.g. [46, 66] concerning the impact of the psd of the tra#c at low 49 1.0E 2 1.0E 1 1.0E 0 1.0E 4 1.0E 5 1.0E 6 1.0E 7 Figure 30: log Pr[u n]versuslogn, simulations for GI G # tra#c of type B. 1.0E 3 1.0E 2 1.0E 1 1.0E 0 1.0E 3 1.0E 4 1.0E 5 Figure 31: log Pr[u n]versuslogn, simulations for GI G # tra#c ....

S. Li and C. Hwang. Queue Response to Input Correlation Functions: Discrete Spectral Analysis. In Proceedings of INFOCOM '92. IEEE, May 1992.

....monomedia traffic stream belonging to one particular multimedia source, here referred to as Tagged Source (TS) it is more efficient to model the aggregate of the remaining N 1 multimedia sources as a whole, that is, as a unique source, here referred to as A TS source. For this purpose, as in [42 43] it has been demonstrated 12 that the performance of a multiplexer is affected by only the first and second order statistics of the arrival process, we model the above A TS source by means of an SBBP process, n , matching the emission pdf and the autocorrelation function of the N 1 ....

S. Q. Li and C. L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis", IEEE/ACM Trans. Networking, Vol. 1, No. 5, Oct. 1993 (received the IEEE Infocom'92 Conference Paper Award).

....for the complementary cummulative distribution of the system contents. P r[u k 1 m] 1 X l=0 P r[p k p k Gamma1 : p k Gammal m lju k Gammal = 0]P r[u k Gammal = 0] Intricate questions are what the link is between this general result and the general observation made in e.g. [46, 66] concerning the impact of the psd of the traffic at low 49 1.0E 2 1.0E 1 1.0E 0 1.0E 4 1.0E 5 1.0E 6 1.0E 7 Figure 30: log Pr[u n] versus log n, simulations for GI G 1 traffic of type B. 1.0E 3 1.0E 2 1.0E 1 1.0E 0 1.0E 3 1.0E 4 1.0E 5 Figure 31: log Pr[u n] versus log n, ....

S. Li and C. Hwang. Queue Response to Input Correlation Functions: Discrete Spectral Analysis. In Proceedings of INFOCOM '92. IEEE, May 1992.

....the lack of such periodic components. A peak at frequency 0 (DC component) implies an asymmetric constant average level of the signal. The relevance of the frequency domain approach to random traffic offered to queueing systems has been recently highlighted by the work of S.Q. Li and coworkers [13, 14, 20, 21]. This work has demonstrated the importance of secondorder characterizations of input traffic on queueing, loss and output traffic statistics; more specifically, it suggests that the low frequencies of the spectrum dominate these performance measures. An application of the frequency domain ....

Li, S.Q. and Hwang, C.L., "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. Networking, Vol. 1, No. 5, 522--533, 1993.

....delays in a finite server group of exponential servers, based only on the traffic parameters ( A ; z A;exp ) 3. 8 FREQUENCY DOMAIN APPROACH TO TRAFFIC The Frequency Domain Approach (FDA) focuses on second order statistics of offered traffic and their effect on queue response to that traffic [61, 62, 86]; it has been motivated by the need to characterize multimedia traffic in high speed networks. FDA is distinguished by the fact that it directly utilizes the frequency domain (the traffic spectral functions) and advocates their use as a unified traffic measurement for analyzing and controlling ....

....as a unified traffic measurement for analyzing and controlling queueing systems with heterogeneous offered traffic. Analogously to periodic input functions in signal processing, elements of constant, sinusoidal, rectangular pulse, triangle pulse, and their superpositions are used in Li and Hwang [61] to represent various second order traffic statistics, and to observe their effect on queueing performance. The main finding is that only the low frequencies in the traffic spectrum 41 have a significant effect on queueing statistics. However, this approach has limited applications, since it does ....

Li, S.Q. and Hwang, C.L., "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. on Networking 1:5 (1993), 522--533.

....networks. Our identification approach for the circulant modulated Poisson process (CMPP) consists of two steps: the identification of the first order parameters and the determination of the circulant stochastic matrix which matches the second order statistics of the data. 1 Introduction Li et al. [6] have indicated that mathematical models can be used to perform several tasks in control mechanisms of ATM networks. The models they propose are measurement based and include the time correlation of traffic. Whereas the approach of Li et al. 6, 7, 8] is mainly based on the frequency domain, this ....

....statistics of the data. 1 Introduction Li et al. 6] have indicated that mathematical models can be used to perform several tasks in control mechanisms of ATM networks. The models they propose are measurement based and include the time correlation of traffic. Whereas the approach of Li et al. [6, 7, 8] is mainly based on the frequency domain, this paper is concerned with measurement based parameter estimation in the time domain: the models match the cumulative distribution function and the autocorrelation function of the measured data as described in [11] This paper is concerned with the ....

S.Q. Li and C.L. Hwang. Queue response to input correlation functions: discrete spectral analysis. IEEE/ACM Transactions on Networking, 1(5):522--533, 1993.

....a cumulative distribution function identical to that of the MMPP. Upper bound on the CMPP model order: Suppose that each number is represented in fixed point format with a digits after the point. It is then possible to write each ( M ) i as a rational number with denominator 10 a which implies ffi = 10 a . In the worst case, the greatest common divisor of all numerators is equal to 1. For this case, the order of the CMPP must be chosen to be equal to 10 a to model the same distribution function as the MMPP we started from. The risk to end up with a very high model order is avoided in the ....

Li S.Q. and Hwang C.L. (1993a) Queue response to input correlation functions: discrete spectral analysis. IEEE/ACM Transactions on Networking 1(5), 522-533.

....its time complexity and accuracy with the method of Li and Hwang [8] I. INTRODUCTION The circulant modulated Poisson process (CMPP) is a restricted version of the Markov modulated Poisson process (MMPP) which is known to be a good model for the arrival processes in telecommunication networks [6, 7, 11]. Applications of these models for ATM networks are found in [6, 4, 10] A real traffic stream a(t) arriving at a queueing system is generally described by a train of impulses corresponding to message arrivals. In this paper, we consider the stochastic process a k (k = 1; 2; where a k is ....

....I. INTRODUCTION The circulant modulated Poisson process (CMPP) is a restricted version of the Markov modulated Poisson process (MMPP) which is known to be a good model for the arrival processes in telecommunication networks [6, 7, 11] Applications of these models for ATM networks are found in [6, 4, 10]. A real traffic stream a(t) arriving at a queueing system is generally described by a train of impulses corresponding to message arrivals. In this paper, we consider the stochastic process a k (k = 1; 2; where a k is the number of cells that arrive during the time interval (k Gamma 1; ....

S.Q. Li and C.L. Hwang. "Queue Response to Input Correlation Functions: Discrete Spectral Analysis", IEEE/ACM Transactions on Networking, vol. 1, 1993, pp. 522-533.

....to inaccurately estimation of loss and delay of packets. Gihr and Tran Gia [3] have stated that the autocorrelation function is able to visualize process dependencies better than the Index of Dispersion of Counts (IDC) Grunenfelder et al. 4] 5] 6] Helvik et al. 8] 9] Li et al. 11] [12], 13] and Ramamurthy and Sengupta [18] 19] have used the autocorrelation function for the description of more complex and realistic input traffic scenarios. In [5] the autocorrelation function of a video codec source was fitted into an Autoregressive Moving Average Model (ARMA) using the power ....

S. Li, C. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis", Infocom 1992, pp. 382-394.

....of the circulant transition matrix is based on an unconstrained optimisation algorithm in which the circulant matrix structure is exploited. We compare our results to those of Yi and De Moor [4] Keywords: traffic modelling, circulant modulated Poisson process, ATM Summary Li et al. [1] have indicated that mathematical models can be used to perform several tasks in control mechanisms of ATM networks. The models they propose are measurement based and include the time correlation of traffic. Whereas the approach of Li et al. 1, 2, 3] is mainly Work supported by the Flemish ....

....modulated Poisson process, ATM Summary Li et al. 1] have indicated that mathematical models can be used to perform several tasks in control mechanisms of ATM networks. The models they propose are measurement based and include the time correlation of traffic. Whereas the approach of Li et al. [1, 2, 3] is mainly Work supported by the Flemish Government (BOF (GOA MIPS) AWI (Bil. Int. Coll. FWO (projects, grants, res. comm. ICCoS) IWT (IWT VCST (CVT) ITA (ISIS) EUREKA (Sinopsys) the Belgian Federal Government (IUAP IV 02, IUAP IMechS) the European Commission (HCM (Simonet) TMR ....

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S.Q. Li and C.L. Hwang. Queue Response to Input Correlation Functions: Discrete Spectral Analysis. IEEE/ACM Transactions on Networking, vol. 1, no. 5, Oct. 1993, pp. 522-533.

....that is to be presented at the IEEE Infocom 96 Conference in San Franscisco in March 1996. QoS) guarantees for VBR video is non trivial in packet switched networks. For instance, correlated traffic with heavy tail distribution dramatically increases the queue length statistics at a multiplexer [1, 12, 13, 14]. Supporting VBR video traffic at a deterministic fixed service, not close to the peak, usually results in large buffers, large delay, and large delay jitter. Although the larger the correlation, the larger the queue length statistics at a multiplexer. The opposite is true for the errors of ....

S. Q. Li and C. L. Hwang., "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. on Networking, Vol. 1, No. 5, Oct. 1993, pp. 522-533.

....range of network design and engineering problems. Traditional Markovian (or more general, short range dependent) input streams to queues are known to impact queueing performance (see for example, 6, 104, 113, 133, 134, 207, 240, 263, 264, 271, 351, 384, 400] and a range of techniques (e.g. [101, 163, 251, 265, 317, 405]) are by now available to quantify these impacts and their implications for network management and control. For example, considerable attention has been paid in the recent past to the problem of call admission control in high speed networks based on the notion of effective bandwidth, e.g. 49, ....

S. Q. Li and C. L. Hwang. Queue response to input correlation functions: Discrete spectral analysis. IEEE/ACM Transactions on Networking, 1:522--533, 1993.

....with the Poisson parameters. P describes the transition probabilities between the 4 states. The Poisson parameter i of the Poisson process characterises the number of emitted cells when the Markov chain is in that state i. In addition to the first paragraph of this section, it is shown in [4] that the low frequencies of the arrival pattern affect the queueing analysis the most, which is in fact easy to comprehend. Because the identification of the MMPP is only necessary to speed up the CAC, only the Modelling ATM traffic 4 information that influences this queueing analysis needs to ....

C. L. Hwang and S. Q. Li. Queue response to input correlation functions : discrete spectral analysis. IEEE/ACM Transactions on Networking, 1(5):522--533, October 1993.

.... of buffer size and CLR) Once the bandwidth is properly chosen, and all the video models have the corresponding same marginal distribution of frame size, then the difference in buffer behavior will be again caused by the difference in their higher order statistics, mainly the autocorrelations [13]. Therefore, we expect that our conclusions are unlikely to be significantly affected by other marginal distributions, though future work might be needed to support this. 6.2 Multiple time scale based traffic analysis There is a significant amount of interest in capturing the time scale at which ....

....affected by other marginal distributions, though future work might be needed to support this. 6. 2 Multiple time scale based traffic analysis There is a significant amount of interest in capturing the time scale at which key statistics of traffic to network performance are to be evaluated [11, 12, 13, 16]. Our conclusions clearly indicate that traffic behavior after certain time scale (i.e. CTS) is not relevant to network performance such as CLR. As discussed in [16] the CTS is closely related with the cutoff frequency c introduced in [11, 12, 13] Note that a practical buffer size is about one ....

[Article contains additional citation context not shown here]

S. Q. Li and C. L. Hwang. Queue response to input correlation functions: Discrete spectral analysis. IEEE/ACM Trans. Net., 1:522--533, 1993.

....of a slowly decaying auto correlation structure [4, 5, 6, 16] Providing efficient transport and Quality of Service (QoS) guarantees for VBR video is nontrivial in packet switched networks. For instance, correlated traffic dramatically increases the queue length statistics at a multiplexor [1, 11, 12, 13]. Supporting VBR video traffic at a deterministic fixed service, not close to the peak, usually results in large buffers, large delay, and large delay jitter. Because bandwidth in ATM networks can be allocated on demand, dynamic bandwidth allocation and re negotiation during the connection ....

S. Q. Li and C. L. Hwang., "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. on Networking, Vol. 1, No. 5, Oct. 1993, pp. 522533.

....are given in [27] Our results indicate that rapid high frequency variations in the connection arrival process can largely be ignored and that it is the low frequency variations that have the greatest impact on the performance of a loss system. This is consistent with the results presented in [20, 21], which show that input power in the low frequency band has the dominant impact on performance in a system with queueing, whereas high frequency power can largely be neglected. We note that the cutoff frequency above which the high frequencies can be ignored was found to decrease with increases in ....

S. Li and C. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Transactions on Networking, Vol. 1, No. 5, pp. 522-533, Oct. 1993.

....arrival process, and that is the focus of this paper. Since the processes we consider are assumed to be stationary, the autocorrelation function has the same information as the power spectrum. Use of the spectrum of an arrival processes to help predict queue performance was extensively explored in [1, 2, 3]. A conclusion in these papers is that the queueing performance is dominated by the input power spectrum in the low frequency band, and that in contrast with input bispectrum, trispectrum and steady state distribution, the input power spectrum is most essential to queueing analysis. Certainly, ....

....single, deterministic server (i.e. Delta=D=1 type server) Three different types of random processes are explored. Two state Markov modulated Poisson processes and periodic sequence modulated Poisson processes are considered in Sections 2 and 3. These types of processes were both considered in [1] and are both special cases of the discrete version of the circulant modulated Poisson processes investigated in [2] We find that for these processes the response of a queue can vary substantially as the parameters of the source model vary, with the mean and autocorrelation function fixed. ....

[Article contains additional citation context not shown here]

S.Q. Li and C.L. Hwang, "Queue response to input correlation functions: discrete spectral analysis," IEEE/ACM Trans. Networking, vol. 1, no. 5, pp. 522-533, Oct. 1993.

....clearly indicate that traffic behavior after certain time scale (i.e. CTS) is not relevant to network performance such as cell loss probability. Thus, it is of particular interest to capture the time scale at which key traffic characteristics affect the network performance as discussed in [16, 13]. We believe that the notion of CTS is intuitive and provides quantitatively much more accurate description of the impact of different time scale behavior on queueing performance. Further work is currently under way on finding the CTS of various types of traffic sources including MPEG coded video, ....

S. Q. Li and C. L. Hwang. Queue response to input correlation functions: Discrete spectral analysis. IEEE/ACM Trans. Net., 1:522--533, 1993.

....(n 2) Ts time (in sub periods) time (in slots) n m T= m Figure 1: The relevant time scales associated with the GPM source. variations in the input process on many different time scales. When T s = 1, for instance, the proposed source model reduces to the periodic Markov chain model considered in [14], where the first and second moments of the queue length process are determined for an infinite capacity queue in discrete time. 2.2 The Sub Period Level Autocorrelation Function In this section, the cell arrival autocorrelation function for a GPM source will be considered. In order to simplify ....

S.Q. Li and C.L. Hwang. Queue response to input correlation functions: Discrete spectral analysis. In IEEE INFOCOM'92, Florence, Italy, 1992.

....step . 39 7.2.2 Operations preceding the optimisation . 40 7.3 Comparison between MMPP and CMPP identification . 40 8 Conclusions 42 1 Introduction Mathematical models have had a rather passive role in communication networks. Li et al. [15] have indicated that mathematical models can be used to perform several tasks in control mechanisms of ATM networks. The models they propose are measurement based and exploit the time correlation of traffic. Whereas the approach of Li et al. is mainly based on the frequency domain [15, 16, 17] ....

....Li et al. 15] have indicated that mathematical models can be used to perform several tasks in control mechanisms of ATM networks. The models they propose are measurement based and exploit the time correlation of traffic. Whereas the approach of Li et al. is mainly based on the frequency domain [15, 16, 17], this paper is concerned with measurement based parameter estimation in the time domain: the models match the cumulative distribution function and the autocorrelation function of the measured data as described in [28] An important innovation described in this paper is the fast characterisation ....

S.Q. Li and C.L. Hwang. Queue Response to Input Correlation Functions: Discrete Spectral Analysis. IEEE/ACM Transactions on Networking, vol. 1, no. 5, October 1993, pp. 522-533.

....proposed for the identification of such a mathematical model. 2 Mathematical background 2.1 Model choice The main purpose of the mathematical model is to increase the speed of the queueing analysis. Therefore the model only needs to capture the properties important for the queueing analysis. In [2, 3] it is illustrated that the most important features of the traffic are the first and second order statistic moments (probability distribution function and autocorrelation) Moreover the lower frequencies of the arrival pattern affect the queueing analysis the most, which is in fact easy to ....

S.Q. Li and C.L. Hwang. Queue response to input correlation functions : discrete spectral analysis. IEEE/ACM Transactions on Networking, 1(5):522--533, Oct. 1993.

....of multiplexer performance approximations. A similar approach was taken in [12] which approximates a general second moment autocorrelation function by that of a two state Markov Modulated Poisson Process and determines queue performance based on the MMPP characterization. In [13] 21] 22] [23], second order traffic statistics are used to calculate queue performance metrics by considering the power spectrums of the individual input streams. For example, in [23] the impact of each individual component of a stream s power spectrum on queue performance was analyzed. Specifically, a ....

....Markov Modulated Poisson Process and determines queue performance based on the MMPP characterization. In [13] 21] 22] 23] second order traffic statistics are used to calculate queue performance metrics by considering the power spectrums of the individual input streams. For example, in [23], the impact of each individual component of a stream s power spectrum on queue performance was analyzed. Specifically, a stream s power spectrum is mapped to a Markov Chain transition matrix, from which the queue performance is obtained and related back to the properties of the original power ....

[Article contains additional citation context not shown here]

S. Li and C. Hwang. Queue response to input correlation functions: Discrete spectral analysis. IEEE/ACM Transactions on Networking, 1(5):552--533, October 1993.

....see for instance [6, 9, 15, 32] However, providing guarantees on maximum delay and delay jitter performance in the presence of long range dependence in traffic is non trivial. It has been shown that correlated input traffic dramatically increases the queue length statistics at a multiplexor [16, 17, 19], and new experimental results based on shuffled (randomized) Ethernet traffic data indicate that the impact of long range dependence is significantly larger than that of short range dependence [5] However, precise estimates of queue length tail distributions are needed, and these appear ....

....plays a crucial role, regardless of the tail distribution. In particular, if the low frequency components have a large energy in the power spectrum of the process, the range of variation of the resulting process can be large, and this can overshadow the effect of the high frequency components [16, 17]. Queue lengths for real VBR video traffic may turn out to be larger than our simulation numbers show because the fractionally differenced ARIMA process generates innovations that are Gaussian, and the distribution of real VBR video has a larger tail in its distribution [26] Therefore, it appears ....

[Article contains additional citation context not shown here]

S. Q. Li and C. L. Hwang., "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. on Networking, Vol. 1, No. 5, Oct. 1993, pp. 522533.

.... with Ethernet traces [17] establish a number of points related to packet traffic modeling: i) while packet traffic has short term correlations in addition to the longrange dependent structure, delay and queue length performance is dominated by long range correlations (see also Li and Hwang [29]) ii) second order descriptions are sufficient when the traffic consists of aggregates of a large number of independent sources (iii) the FBM model reproduces the queueing behavior observed with actual Ethernet traces. Krishnan [23] derives a new class of performance results for the FBM model, ....

S.Q. Li and C.L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis ", IEEE/ACM Trans. on Networking 1, pp. 678-692, 1992.

....needs further investigation. A more computationally efficient method based on Fast Fourier Transform has been proposed [39] to model Fractional Gaussian Noise traffic in the frequency domain. Another method based on Markov models has been proposed to model the frequency components of video traffic[28]. Both methods suggest that interesting properties of either Ethernet or video traffic could be investigated in the frequency domain. Therefore, the questions remain open (1) how to develop a model which is capable of modeling heterogeneous network traffic, and (2) how to develop a model which is ....

S.Qi Li and C-L Hwang. Queue response to input correlation functions: Discrete spectral analysis. IEEE/ACM Transactions on Networking, 1:317--329, 1993.

....from the time between consecutive cells or packets ( s) to consecutive frames (ms) to higher level properties of video such as scenes (s) to entire movies or video calls. Different modeling perspectives have been taken in examining this complex time dependency structure. Li and Hwang, in [3], argue from the frequency domain point of view, that the low frequency band of the autocorrelation s Fourier transform (long term correlation) has the most significant impact on queueing. Lazar et al. 4] developed video models for the slice and frame time scales, and showed that in the case of ....

....effect on the asymptotic queueing behavior is the subexponential (long range) dependency and that in the strict stability scenario the dominant effect is due to the fast time scale buildups puts in the broader context some conflicting results from the literature. Indeed, a number of authors [3], 15] 16] contend that long range dependence of one form or another has a dominant impact on the queue, while others claim that it JELENKOVI C, LAZAR AND SEMRET: EFFECT OF TIME SCALES AND SUBEXPONENTIALITY IN MPEG ON QUEUEING 3 does not [17] 18] 4] Our framework allows one to ....

[Article contains additional citation context not shown here]

S. Qi Li and C.-L. Hwang, "Queue response to input correlation functions: Discrete spectral analysis," IEEE/ACM Trans. Networking, vol. 1, no. 5, pp. 317--329, 1993.

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S. Q. Li and C. L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. Networking, Vol. 1, No. 5, Oct. 1993, pp. 522(received the IEEE Infocom'92 Conference Paper Award).

....for the general construction of a(t) and s(t) In consequence, two state Markov chains are frequently used to construct different processes with limited statistic properties. Our work in the past several years focused on the development of fast algorithms for both modeling and queueing analysis [1, 2, 3, 4, 5, 6, 7, 8]. SMAQ tool (Statistical Match And Queueing tool) naturally grew out of this development for the integration of traffic service modeling and queueing analysis. A fundamental distinction of our work from others is that SMAQ tool is measurement based. In our view, both a(t) and s(t) can be composed ....

S. Q. Li and C. L. Hwang,"Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. Networking, Vol. 1, No. 5, Oct. 1993, pp. 522 (received the IEEE Infocom'92 Conference Paper Award).

....power spectral function P ( and its steady state statistics by input rate distribution function f(x) For the following two reasons we consider only funtions P ( and f(x) of the input process. First, the queueing performance is found to be much less dependent on higher order input statistics [1, 2]. Second, in signal processing area, only P ( and f(x) are likely to be measured in practice [4] In other words, instead of considering the queue response to the original random input process, here we measure only the queue response to second order and steady state input statistics. In queueing ....

....l C 2 l 2 l 2 with C 2 l = 1 fl 2 X i X j i fl i fl j g li h lj ; 2) where ffi ( is the Dirac delta function. The DC term 2 fl 2 ffi ( in (2) refers to the average input rate fl. The white noise term fl in (2) is attributed to the Poisson local dynamics of MMPP [1, 2]. Denote by i the steady state probability of MC in state i. For = 0 ; 1 ; N Gamma1 ] the solution of is derived from Q = 0 and e = 1, where e is a unit column vector. We get fl = P N Gamma1 i=0 fl i i . The input rate distribution of MMPP is a discrete function ....

S. Q. Li and C. L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. Networking, Vol. 1, No. 5, Oct. 1993, pp. 522-533 (received the IEEE Infocom'92 Conference Paper Award).

....4 Input Process Construction The N state MMPP input process is constructed such that Q is diagonalizable with distinct eigenvalues [0; 1 ; N Gamma1 ] Denote the right column and the left row eigenvector of the l th eigenvalue by g l and h l , respectively. Then as demonstrated in [11, 12], each eigenvalue contributes a complex exponential term to the input rate autocorrelation R i ( fl(t)fl(t ) fl 2 N Gamma1 X l=1 l e l j j (19) with l = P k P j k fl k fl j g lk h lj and mean input rate fl. Correspondingly, each eigenvalue contributes a bell shaped ....

S.Q. Li and C.L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. Networking, Vol. 1, No. 5, Oct. 1993, pp. 522--533 (received the IEEE Infocom'92 Conference Paper Award).

No context found.

S.Q. Li and C.L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," Proc. of IEEE Infocom'92, pp. 382-394 (which received the Conference Paper Award of Infocom'92).

.... Response to Input Correlation Functions: Continuous Spectral Analysis San qi Li Chia Lin Hwang Department of Electrical and Computer Engineering University of Texas at Austin Austin, Texas 78712 August 4, 1995 Abstract This paper, together with [1] and [2] opens a new window for the study of queueing performance in a richer, heterogeneous input environment. It offers a unique way to understand the effect of second and higher order input statistics on queues, and develops new concepts of traffic measurement, network control and resource ....

....approximations for the performance of an average queue. The autocorrelation function is used to describe the strong time autocorrelation revealed in voice and video traffic, and hence to derive the queue steady state solutions (refer to [5, 6, 7] for more references in related work) Recently in [1], we analyzed queue response to individual frequency components of the input power spectrum. In particular, we used the classic elements of DC, sinusoidal, rectangular, triangular and their superpositions, to build various input processes. The work in [1] explored a new concept of spectral ....

[Article contains additional citation context not shown here]

S.Q. Li and C.L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE Infocom'92, May 1992, pp. 382- 394 (received Conference Paper Award of Infocom'92; also accepted by IEEE/ACM Transactions on Networking).

....functions in traffic measurement are rate distribution f(x) histogram) and power spectrum P ( equivalently, autocorrelation function) The former describes steady state statistics; the latter captures second order statistics. The queueing performance is largely dependent on f(x) and P ( [6, 7]. Recently, Hajek and He observed that the the queueing behavior cannot be predicted solely based on the mean and P ( of the arrival process [8] They also stressed the importance of f(x) in determining queueing behavior. In our measurement architecture, traffic is further decomposed into three ....

....traffic, but none of them were able to quantitatively develop guidelines for transport of generic traffic subject to a maximum queueing delay. modulated Poisson process (CMPP) to match a wide range of P ( and f(x) in different frequrency regions. In relation to author s previous works [6, 7, 10, 15, 16, 17, 19], this paper focuses on the timescale decomposition in traffic measurement for link bandwidth allocation design. The paper is organized as follows. Section 2 provides the sample path deterministic analysis for the solution of ( L ; H ) along with the discussion of their significant implications ....

S. Q. Li and C. L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. Networking, Vol. 1, No. 5, Oct. 1993, pp. 522-533 (received the IEEE Infocom'92 Conference Paper Award).

....For all the system phenomena observed in this paper, affected by the individual effect of binary source dynamics, a unique observation is obtained with the power spectrum in frequency domain. That is, the larger the input powers in low frequencies, the longer the queue and the higher the loss rate [20] [21] Note that most correlated traffic queueing analyses so far have emphasized performance studies of a single separate link. There is a strong need to extend our effort to modeling of a network wide traffic integrations. The analytical bottleneck for such extension is how to characterize the ....

....b l ( to P ( Graphically, each such component will represents a bell shape curve located at the central frequency Imf l g with its half power bandwidth equal to Gamma2Ref l g. Note that the input power spectrum is always additive for the superposition of independent sources. Refer to [20][21] for detail analysis of input power spectrum. The work in [20] indicates that the queueing performance is essentially dominated by the power spectrum in low frequency band. In principle, the lower the frequency, the more the inputs are autocorrelated, and so the longer the queue. Now it is of ....

[Article contains additional citation context not shown here]

S.Q. Li and C.L. Hwang, "Queue response to input correlation functions: discrete spectral analysis," IEEE Infocom'92, May 1992, pp. 382-394 (this paper received the Conference Paper Award of Infocom'92).

....signal processing techniques are available to measure traffic statistics. In particular, second order statistics can be measured by many sophisticated software packages or in hardware chips. The concept of spectral representation of multimedia traffic in queueing analysis was first introduced in [5, 6, 7]. In [7] we used a special class of Markov chain, called a circulant, to construct input processes. One significant advantage of using circulant is to identify the impact of power spectrum, bispectrum, trispectrum and distribution of the input process on the characteristics of queue and loss rate. ....

....link capacity ae Gamma1 increases by the reduction of 1 which essentially shifts the bell to the low frequency band. Therefore, as 1 reduces, more input power is moved from the high frequency band to the low frequency band, which inherently causes the queueing performance to deteriorate [5]. The impact of the low central frequency 1 is especially strong when bandwidth B 1 is also small. As B 1 becomes smaller, more input power is concentrated in the neighborhood of the lower 1 . For each given 1 , the link capacity reaches its maximum around B 1 = 2 1 , because the input ....

S. Q. Li and C. L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. Networking., Vol. 1, No. 5, Oct. 1993, pp. 522533 (also received the Infocom'92 Conference Paper Award).

....theories, Markov chains have been commonly used to capture input traffic correlation properties. So far, no sophisticated statistical matching techniques are available for construction of Markov chain input models. Traffic spectral representation was first introduced to queueing analysis in [1, 2]. Many current signal processing theories and techniques for spectral representation of random processes can be used in network traffic measurement. Consider a Markov modulated Poisson process (MMPP) defined by transition rate matrix Q and input rate vector fl . Essentially, the eigenstructure ....

....for identifying ( of real exponential signals, i.e. R(n) P p l=1 l e l n in discrete time domain. It is well known that R[n] may be generated by the recursive difference equation R[n] Gamma P p l=1 a[k]R[n Gamma k] for n p with appropriate initial conditions fR[0] R[1]; R[p Gamma 1]g. The coefficients a[k] are related to the poles z l = e l by 1 P p k=1 a[k]z Gammak = Q p l=1 (1 Gamma z l =z) The poles are determined by solving linear equations for a[k] and then rooting the polynomial. The Prony method performs well in absence of noise. be ....

[Article contains additional citation context not shown here]

S. Q. Li and C. L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. Networking, Vol. 1, No. 5, Oct. 1993, pp. 522-533 (received the IEEE Infocom'92 Conference Paper Award).

....of Poisson input and exponential service time. In this paper we study the cross correlation between input and output processes. Consider a single server queueing system with a stationary random input process. Traditional queueing analyses focus on the steady state queueing performance. Recently in [1, 2, 3], a frequency domain approach was introduced for the evaluation of steady state performance in response to the input process s spectral properties. It was found that the input traffic characteristics in a certain low frequency band have dominant influence on the system steady state performance. ....

S. Q. Li and C. L. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. Networking, Vol. 1, No. 5, Oct. 1993, pp. 522-533 (also received the IEEE Infocom'92 Conference Paper Award).

No context found.

S. Q. Li and H. D. Sheng, "Queue response to input correlation functions: Discrete spectral analysis," IEEE/ACM Trans. Networking, vol. 1, pp. 522--533, Oct. 1993.

No context found.

San-qi Li, Chaia-Lin Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis", INFOCOM'92, vol.3, pp.0382.

No context found.

San-qi Li, Chaia-Lin Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis", INFOCOM'92,vol.3, pp.0382.

No context found.

S.Q. Li and C.L. Hwang. "Queue Response to Input Correlation Functions: Discrete Spectral Analysis", IEEE/ACM Transactions on Networking, vol. 1, 1993, pp. 522-533.

No context found.

S.-Q. Li and C.-L. Hwang. Queue response to input correlation functions: Discrete spectral analysis. IEEE/ACM Transactions on Networking, pages 522--533, Oct. 1993.

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