Hong-Dah Sheng, San-qi, Li, "Second order effect of binary sources on characteristics of queue and loss rate", IEEE INFOCOM'93, pp 18-27  Home/Search   Document Details and Download   Summary   Related Articles   Check

....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 ....

Sheng, H.D. and Li, S.Q., "Second Order Effect of Binary Sources on Characteristics of Queue and Loss Rate," IEEE Trans. on Communications, Vol. 42,

....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 ....

....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 not capture the stochastic aspects of a prescribed traffic process. To this end, multi state MMPP traffic are used in Sheng and Li [86] to characterize binary sources (on off traffic) and to study the effect of their second order statistical properties on queue length and loss rate statistics. A modeling technique for constructing Markovian traffic processes, which match a prescribed power spectrum, is introduced in Li and ....

Sheng, H.D. and Li, S.Q., "Second Order Effect of Binary Sources on Characteristics of Queue and Loss Rate," IEEE Trans. on Communications 42:3 (1994), 1162--1173.

.... 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 allocation ....

H.D. Sheng and S.Q. Li, "Second Order Effect of Binary Sources on Characteristics of Queue and Loss Rate," Proc. IEEE Infocom'93, pp. 18-27, 1993. (also accepted by IEEE Trans. Commu.).

....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. ....

H. D. Sheng and S. Q. Li, "Second Order Effect of Binary Sources on Characteristics of Queue and Loss Rate," IEEE Trans. Commu., Vol. 42, No. 3, March 1994, pp. 1162-1173.

....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 ....

....circulant modulated Poisson process (CMPP) for each given lorentzian component. One significant advantage of using CMPP is that one can identify the impact of power spectrum, bispectrum, trispectrum and distribution of the input process on the characteristics of queue and loss rate. The study in [2, 3] clearly shows that the input power spectrum, especially in the low frequency band, plays a dominant role in queueing analysis. As in many system theories, the input power spectrum is of great importance to queueing system analysis. This observation has important potential applications to traffic ....

H. D. Sheng and S. Q. Li, "Second Order Effect of Binary Sources on Characteristics of Queue and Loss Rate," IEEE Trans. Commu., Vol. 42, No. 3, March 1994, pp. 1162-1173.

.... 4 = 1 Gamma ff 1 Gamma ff 2 Gamma ff 3 = 1 Gamma ff) Delta (1 Gamma j) where ff and j are given by: ff = 1 2 (1 s C 2 ON Gamma 1 C 2 ON 1 ) 4) and j = fl b fl a fl b : Similarly, we also have: fi = 1 2 (1 s C 2 OFF Gamma 1 C 2 OFF 1 ) Please refer to [7] for derivation of formulae relating CON , COFF , C I with ff 0 i s and fi. Based on this general source model, the aggregate input traffic to a node will be the superposition of multiple, independent 6 state Markov modulated sources. To check the validity of negligible source distortion ....

H.D. Sheng, S.Q. Li. Second order effect of binary sources on characteristics of queue and loss rate. IEEE INFOCOM'93., pages 18--27, April 1993, also to appear on IEEE Trans. on Commu..

....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. ....

H. D. Sheng and S. Q. Li, "Second Order Effect of Binary Sources on Characteristics of Queue and Loss Rate," IEEE Trans. Commu., Vol. 42, No. 3, March 1994, pp. 1162-1173.

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H. D. Sheng and S. Q. Li, "Second Order Effect of Binary Sources on Characteristics of Queue and Loss Rate," Proc. IEEE Infocom'93, April 1993, pp. 18-27.

....transform analysis of nonperiodic functions for input correlation. Such an extension is carried out in [16] Further, the inter relationship between the source secondorder dynamics in time domain and the input power spectrum in frequency domain for queueing performance has been well explored in [17]. Appendix To derive (11) we define R a (n) Efa(m)a(n m)g and R(n) Effl(m)fl(n m)g, where a(n) represents the number of packets generated by MMPP in the n th time unit and fl(n) is the input rate process as described in Eq. 4) For n = 0, R a (0) Efa(m) 2 g = X k k 2 ....

H.D. Sheng and S.Q. Li "Second Order Effect of Binary Sources on Characteristics of Queue and Loss Rates," to appear at IEEE Infocom'93.

....for a non negative input rate. Therefore, it is the eigenstructure of Q that captures the input rate spectral properties. In principle, the power spectrum describes the magnitude of input rate variation in the frequency domain. It characterizes both input correlation and burstiness features [14]. As shown in Figure 1, each eigenvalue component, b l ( in (7) represents a bell shape curve located at the central frequency l = Imf l g and weighted by 1 l . The shape of each bell, before being weighted, is measured by its half power bandwidth BW l = Gamma2Ref l g. Both l and BW ....

....rate process is slow (i.e. more input power is in the low frequency band) Such an approximation has been commonly used in the voice and video queueing analyses. The success and accuracy of this approximation, to a great extent, are due to the dominant lowfrequency input power for voice and video [6, 11, 15, 14]. Since the queueing behavior is mainly captured by the input power in the low frequency band, the fluid flow approximation is expected overload period underload period q(t) 1 q(t) 0 q(t) K BLOCKING PERIOD r(t) r(t) Figure 6: Abstracted state flow diagram of the queueing system with fluid flow ....

H.D. Sheng and S.Q. Li, "Second Order Effect of Binary Sources on Characteristics of Queue and Loss Rate," Proc. of IEEE Infocom'93, April 1993, pp. 18-27 (also to appear in IEEE Trans. Commu.).

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Hong-Dah Sheng, San-qi, Li, "Second order effect of binary sources on characteristics of queue and loss rate", IEEE INFOCOM'93, pp 18-27

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Hong-Dah Sheng, San-qi, Li, "Second order effect of binary sources on characteristics of queue and loss rate", IEEE INFOCOM'93, pp 18-27

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