C. L. Hwang, and S. Q. Li, "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-MAtch Queueing (SMAQ) Tool," Accepted by IEEE Infocom'95 for publication.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to its twolevel structure, it is able to capture both the inter GOP and the intra GOP correlation. In order to obtain a model fitting the inter GOP correlation, the first and second order statistics of the I frame process are captured. For this purpose, the wellknown inverse eigenvalue problem [9] is solved in the discretetime domain. The model of the MPEG video is used to evaluate the loss probability in an ATM multiplexer loaded by an MPEG video source and an aggregate of external traffic. The accuracy of the model is evaluated by comparing the analytically obtained loss probability with ....

....intra GoP correlation, in this SBBP the pdfs for the B and P frames will depend on the I frame belonging to the same GoP. 3.2. 1 I frame model Determination of Yh ( from its pdf and its autocovariance function is the so called inverse eigenvalue problem, solved in the continuous time domain in [9]; now we present a summary of our solution in the discrete time domain. The inverse eigenvalue problem will be solved in two steps: first we approximate the measured autocovariance function with the sum of a predefined number, J, of exponential terms; then without approximation, we derive the ....

Chia-Lin Hwang and S. Q. Li, "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-Match Queueing (SMAQ) Tool", IEEE/ACM Transactions on Networking, vol. 5, no. 1, Feb. 1997.

.... type (i.e. each row is the previous row, shifted by one element) and within each state i the channel has a packet service rate of fi (channels currently subject to errors have a lower service rate) 24] As input data they use the service rate process Rc(t) tc, obtained from measurements [25]. They use the fact that the power spectral density function R(t) of the MMP generated by Q and (fro, fN ) can be explictly represented by the eigenvalues of Q. These values are chosen such that R(t) matches the measured power spectral density function of Rc(t) tc as closely as possible. Then ....

San qi Li and Chia-Lin Hwang. On the convergence of traffic measurement and queue- ing analysis: A statistical-match queueing (smaq) tool. IEEE/ACM Transactions on Networking, 5:95-110, February 1997.

....link. Next we consider the case where only the second order characteristics are important in determining performance, and, in particular, the key traffic properties are captured by a marginal distribution and the covariance of the rate process. This approach recently developed by Li et al. [13, 14, 17] has shown to be a remarkably good modeling tool. To further study these ideas, in 2.3 we consider Gaussian processes, where the second order characteristics completely determine L t (q) above. For such processes we show that t can be related to a so called cutoff frequency w c [17] through a ....

C.-L. Hwang and S.-Q. Li, "On the convergence of traffic measurement and queueing analysis: A statistical-match queueing (SMAQ) tool," in Proc. IEEE INFOCOM, 1995.

....of both the intramedia time relationships of each component monomedia source and the intermedia time relationships among the activities of the different component monomedia sources. Although the correlation function of the multimedia source can be calculated by the matrix Q W ( given in (4) [17], in this section we will calculate it as the sum of the auto and cross correlation functions of the component sources, i.e. 6 R R R R R WW XX YY XY YX ( t t t t t = 6) According to the definition of autocorrelation function, we have: R E x t x t B P X t ....

C. L. Hwang, S. Q. Li, "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-MAtch Queueing (SMAQ) Tool", Proc. IEEE Infocom '95, pp. 602612, Boston, Massachussets, April 1995.

....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. On the convergence of traffic measurement and queueing analysis: a statisticalmatching and queueing (SMAQ) Tool. IEEE/ACM Transactions on Networking, 5(1):95--110, 1997.

....which CMPP model order should be imposed. In order to guarantee a certain demanded accuracy of the cumulative distribution function, the minimal order needed can be computed from (14) Our new method for the identification of the first order parameters of a CMPP is more accurate than the method of Li and Hwang (1997) but it is more time consuming. However, by simplifying our method, we obtain an efficient and accurate alternative for Li and Hwang s approach. For a comparison between both methods and more details on the simplified version of our method we refer to (De Cock and De Moor, 1997) 4.2 The ....

Li S.Q. and Hwang C.L. (1997) On the convergence of traffic measurement and queueing analysis: a statistical-matching and queueing (SMAQ) tool. IEEE/ACM Transactions on Networking 5(1), 95-110.

....queueing analysis highly depend on the model order. For the identification of the autocorrelation O(N 3 ) operations are needed per function evaluation in the optimisation algorithm and the computational complexity of the existing queueing analysis techniques is at least proportional to N 3 [1, 3]. Therefore it is advantageous to reduce the model order. In our approach it is possible to reduce the model order after the identification of the first order parameters, i.e. before the stochastic matrix P is determined. The number of MMPP states is reduced by replacing similar states (with ....

S.Q. Li and C.L. Hwang. "On the Convergence of Traffic Measurement and Queueing Analysis: A StatisticalMatching and Queueing (SMAQ) Tool", IEEE/ACM Transactions on Networking, vol. 5, 1997, pp. 95-110.

....E mail: katrien.decock esat.kuleuven.ac.be ABSTRACT In this paper we discuss a new method for the identification of the first order parameters of a circulant modulated Poisson process. We compare 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 ....

....be integrated in other approaches. We describe the structure of the CMPP in Section II. The first order statistics of the MMPP and of the CMPP are given in Section III. In Section IV we treat three first order identification methods. In Section A we give an overview of the method of Li and Hwang [8] and in Section B our new first order identification method is explained. Our approach is based on a new method for the identification of the first order parameters of the MMPP. A simplified, more efficient version of our method is given in Section C. A comparison between the different methods is ....

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S.Q. Li and C.L. Hwang. "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-Matching and Queueing (SMAQ) Tool", IEEE/ACM Transactions on Networking, vol. 5, 1997, pp. 95-110.

....connections and burstiness of individual cell streams at possibly different time scales. One popular approach is to approximate such complex non renewal input processes by analytically tractable Markovian models either at the connection [34] 10] or at the link (physical or logical) level [18] [19], 27] Markovian Arrival Process (MAP) 26] and Batch Markovian Arrival Process (BMAP) 24] have been used extensively in ATM performance evaluation in continuous time. For example, the well known Markov Modulated Poisson Process (MMPP) is a sub case of MAP [18] Various other Markovian traffic ....

C. L. Hwang and S. Q. Li. On the convergence of traffic measurement and queueing analysis: A statistical-match queueing (SMAQ) tool. In Proc. IEEE INFOCOM, pages 602--612, 1995.

....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 ....

S.Q. Li. and C.L. Hwang. On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-Matching and Queueing (SMAQ) Tool. IEEE/ACM Transactions on Networking, vol. 5, no. 1, Feb. 1997, pp. 95-110.

....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, ....

....in practice can t be guaranteed to fall within the third class, so we conclude that the behavior of a queue cannot be predicted solely based on the mean and autocorrelation functions of its arrival processes. This conclusion is consistent with recent trends in the literature. In particular, [3] demonstrated that the family of circulant modulated Poisson processes is sufficiently rich to match not only a given autocorrelation function in a large class, but also to approximately match the first order stationary distribution of the input rate process. Tests run on data generated by MMP ....

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C. L. Hwang and S. Q. Li, "On the convergence of traffic measurement and queueing analysis: A statistical-match queueing (SMAQ) tool," Proc. IEEE Infocom'95, pp. 602-613, April 1995.

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C. L. Hwang, and S. Q. Li, "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-MAtch Queueing (SMAQ) Tool," Accepted by IEEE Infocom'95 for publication.

....be x with real b and real A; f(x) is limited to a convolved binomial function [4] They are certainly insufficient to capture the diversed traffic correlation and burstiness behavior, especially the strong pseudoperiodic nature as found in MPEG video traces and feedback controlled ABR traffic. In [5, 6], Li and Hwang proposed a structure of circulant modulated Poisson process (CMPP) whose R(r) has the form be k with real b but complex A and whose cumulative function F(x) f f(u)du is expressed as a piece wise step function. It is obvious that the sum of complex exponentials represent a much ....

....expressed as a piece wise step function. It is obvious that the sum of complex exponentials represent a much wider class of correlation functions than the sum of real exponentials. One may question the validity of using circulant for traf fic modeling. A comprehensive, blind numerical study in [6] compared queueing loss rate solutions between vastly different circulant and Markov chain, both of which are designed to match with identical R(r) and f(x) The two solutions were found generally in excellent agreement. In other words, the underlying structural difference between circulant and ....

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C. L. Hwang and S. Q. Li, "On the Convergence of Traffic Measurement and Queueing Analysis: A StatisticalMAtch Queueing (SMAQ) Tool," IEEE Infocorn'g5 Conference, April 1995, pp. 602-613.

....The former describes traffic first order statistics, and the latter captures traffic secondorder statistics. It is shown that the PBC in (2) is essentially determined by and of each session, whereas the higher order statistics of session can be neglected to a certain extent. Recently in [20], Li has developed an approach to the construction of a Markov modulated Poisson process (MMPP) to match a wide range of and The same approach is applied here in traffic modeling to reflect various statistical properties of real multimedia traffic (e.g. MPEG JPEG video and PCM voice) Based on ....

.... the other two types of arrival processes, fixing mean and autocorrelation is not sufficient to fix and CHONG AND LI: PBC BASED CONNECTION CONTROL 1077 thus the mean queue length can vary according to variations in For Markovian traffic modeling, we use a novel statistical matching technique in [20]. Using this technique, one can construct a special form of multistate MMPP, the circulant modulated Poisson process (CMPP) whose statistical functions match with measured and As demonstrated in [20] a multistate CMPP can cover a wide range of the statistical functions and In contrast, for the ....

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C. L. Hwang and S. Q. Li, "On the convergence of traffic measurement and queueing analysis: A statistical-match queueing (SMAQ) tool," in Proc. IEEE INFOCOM'95, Apr. 1995, pp. 602--612.

....Therefore it improves traffic predictability. The conclusions in this section will be verified later by quantitative analysis of real traffic traces. C. Roles of Traffic Properties in Traffic Predictability What traffic properties characterize the inherent traffic predictability By ( 10] [11]) traffic statistics of orders higher than two has little effect on queueing performance. Therefore, we will use the Gaussian traffic process of a bell shaped power spectrum for analysis in that it provides a clear picture about traffic statistical structure. With this picture we show that the ....

....for the prediction interval (1sec) used in [1] IV. TRAFFIC PREDICTABILITY ANALYSIS WITH MMPP MODEL Up to now, we have examined traffic predictability using ARMA model. Will the analysis be consistent if using the markov modulated poission process (MMPP) model instead By our previous research [11], circulant markov modulated poisson process (CMPP) as a special MMPP can be used to match real traces. It captures not only the 2nd order statistics, just as ARMA does, but also the 1st order statistics that may not be Guassian distributed. This model performs well in queueing analysis. Next we ....

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S. Q. Li and C. Hwang, On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-Match and Queueing (SMAQ) Tool, IEEE/ACM Transactions on Networking, April 1997, pp. 95-110.

....may represent the number of packet arrivals at the time interval [t; t Delta) Most queueing analyses of multimedia traffic so far have focused on wireline networks such as ATM, where the service rate is assumed to be constant. Under the assumption of a constant service rate, the studies in [13, 14, 15] indicate that only the first and second order statistics of the arrival process are important to steady state queue length and loss rate solutions, whereas its higher order statistics can be neglected, given a properly selected frequency range for the measurement. Most importantly, the queueing ....

....the individual impact of these factors on the network performance. The fading channel statistics in downtown Austin area is used as an example of typical large scale fading scenario in this paper. Similar to the modeling of the arrival process, one can use a measurement based modeling technique [13], called SMAQ, to build a Markov modulated process (MMP) to match the measured first and second order channel statistics. An MMP process is defined by both rate vector fl and Markov chain transition rate matrix Q. While fl defines the service rate (or, arrival rate in case of R a (t) in each ....

[Article contains additional citation context not shown here]

S.Q. Li and C.L. Hwang, "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-MAtch Queueing(SMAQ) Tool," IEEE/ACM Transactions on Networking, Feb. 1997, pp 95-110,

....tool in system analysis and design. Most of the examples presented are current challenges facing system designers in the network industry. The lack of a measurement based analytical tool sometimes prevents designers from obtaining an optimally designed network. The introduction of the SMAQ tool [2] provides a step towards resolving the current network design issues. The following sections provide various applications of the SMAQ tool with examples of resolving the current design issues. 1 2 Source Library The SMAQ tool provides a source library that consists of three types of ....

S. Q. Li and C. Hwang, "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-Match and Queueing (SMAQ) Tool," IEEE/ACM Transactions on Networking, pp. 95-110, Feb. 1997.

....may represent the number of packet arrivals at the time interval [t; t Delta) Most queueing analyses of multimedia traffic so far have focused on wireline networks such as ATM, where the service rate is assumed to be constant. Under the assumption of a constant service rate, the studies in [9, 10, 11] indicate that only the first and second order statistics of the arrival process are important to steady state queue length and loss rate solutions, whereas its higher order statistics can be neglected, given a properly selected frequency range for the measurement. Most importantly, the queueing ....

....significant low frequency energy as compared to the arrival process, both first and second order statistics in a low frequency band are important for the channel modeling in queueing analysis. Similar to the modeling of the arrival process, one can use a measurement based modeling technique [9], called SMAQ, to build a Markov modulated process (MMP) to match the measured first and second order channel statistics. An MMP process is defined by both rate vector fl and Markov chain transition rate matrix Q. While fl defines the service rate (or, arrival rate in case of R a (t) in each ....

[Article contains additional citation context not shown here]

S.Q. Li and C.L. Hwang, "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-MAtch Queueing(SMAQ) Tool," Proc. IEEE Infocom'95, Apr. 1995, pp. 602-613.

....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 ....

....the Internet. Using a Web based tool is expected to motivate collaborations over the Internet to improve the design and analysis of complex systems. In recent years, there have been significant development in both traffic modeling and queueing analysis. One may refer to the references listed in [4, 8] for the related work. Other papers published in this issue also provide an excellent source of the recent development in this field. Note that most traffic modeling techniques have been developed to characterize certain specific nature of second order statistics, or to match the statistics of a ....

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S. Q. Li and C. Hwang, "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-Match and Queueing (SMAQ) Tool," IEEE/ACM Transactions on Networking, pp. 95-110, April 1997.

....a steady state rate distribution such as Gaussian or Gamma. This represents a correlation in the arrival process at multiple time scales as indicated in Section 2. We will refer to this arrival process as Case 4. In order to model such traffic, we need a circulant of larger order. The SMAQ tool ([25]) is a measurement based technique that was developed to design MMPPs to match the accumulated statistics of real traffic sequences. In particular, it may be used to model traffic based on the measurement of the power spectrum and distribution of its rate trace. The reason why we focus on these ....

C.L. Hwang and S. Q. Li, "On the Convergence of Traffic Measurement and Queueing analysis: A Statisitical-MAtch Queueing (SMAQ) Tool," Proc. IEEE INFOCOM'95, vol. 2, 1995, pp. 602-612.

....sources. For instance, the rate process of the superposition of heterogeneous 2 state MMPP s can only represent monotonic decreasing power spectrum peaked at zero frequency, whereas the realistic traffic can have multiple bell, nonzero peak spectrum, according to recent empirical measurements[7]. Second, it is difficult to use the above source models to match the entire arrival rate distribution: previous techniques are usually limited to match the first few moments of the arrival process and fail to capture some important features, e.g. the tail of the input rate distribution, which ....

....as the eigenvalue decomposition approach proposed in [20, 11] can only be applied to the superposition of MMPP s with no more than 4 states since closed form expressions for the eigenvalues of the corresponding Markov Chain are required. With a newly developed Statistical Matching technique [7], the above limitations have been overcome: By using a special type of MMPP, called Circulant Modulated Poisson Process (CMPP) we can construct an analytical source model of tractable size to match the power spectrum and the rate distribution of a given traffic stream. As a result, the ....

[Article contains additional citation context not shown here]

C.L. Hwang and S.Q. Li, "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-MAtch Queueing (SMAQ) Tool," Proc. of INFOCOM'95, April 1995, pp. 602612.

....on basis of sample path deterministic analysis subject to zero loss, where conjecturs are made for the best LF sample path and the worst HF sample path. It is then verified in stochastic analysis with random traffic subject to a negligible cell loss rate, where we use a programming approach [17] for construction of circulant 1 The study in [10, 19, 23, 13, 25] also explored the concept of buffer noneffectiveness for transport of LF (large timescale) traffic, but none of them were able to quantitatively develop guidelines for transport of generic traffic subject to a maximum queueing ....

....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 ....

[Article contains additional citation context not shown here]

C. L. Hwang and S. Q. Li, "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-MAtch Queueing (SMAQ) Tool," Proc. IEEE Infocom'95, April 1995, pp. 602612, also accepted by IEEE/ACM Trans. Networking.

....and obtain sojourn time results for systems of practical interest. While previous studies mostly limit the traffic input to the superposition of a handful of 2 3 state Markov modulated sources [13, 14, 3] our approach allows the incorporation of more sophisticated and accurate traffic models [15] in the analysis. With the GFA, we can analyze the sojourn time distributions of a relatively large system in addition to the moment analysis described in [13, 14, 12] This paper is organized as follows: In the next section, we study the sojourn time analysis of a queue with level dependent ....

....in Section 6. 2 Formulation of Overload Underload Sojourn time Analysis Consider a network node modeled as a FCFS queue of buffer size K and a server with mean service time 1= The arrival stream may consist of one or more traffic sources. Using the statisticalmatching techniques proposed in [15], an N state Markov Modulated Poisson Process (MMPP) with a transition matrix Q and an input rate vector fl is constructed to model the input traffic. Based on this setting, two different modeling approaches are considered: In the first approach, the service time is assumed to follow a phase type ....

[Article contains additional citation context not shown here]

C.L. Hwang and S.Q. Li, "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-MAtch Queueing (SMAQ) Tool," Proc. of IEEE INFOCOM'95, pp. 602-612.

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Li, S.-Q. and Hwang, C.-L. "On the convergence of traffic measurement and queueing analysis: a statistical-matching and queueing (SMAQ) tool," IEEE/ACM Trans. on Networking, 1997, Vol. 5, 95-110. 16

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Li S.-Q. and Hwang C.-L "On the convergence of traffic measurement and queueing analysis: a statistical-matching and queueing (SMAQ) tool". IEEE/ACM Trans. on Networking, 5:95-110, 1997.

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