Willinger, W., Taqqu, M., Sherman, R. and Wilson, D. (1995) Self-- similarity in high--speed packet traffic: analysis and modelling of ethernet traffic measurements. Statistical Science 10, 67--85.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....paper, we propose a QoS framework for wireless data, along with scheduling strategies that are well matched to this framework. The research reported here accounts for several key observations: a) It is well known that aggregate Internet traffic is long range dependent, or heavy tailed [7] 8] [13]. The conventional approach of handling this via more conservative provisioning is unattractive in resource constrained wireless networks. b) Flat rate charging is an attractive paradigm for data applications. While it is clearly appropriate on corporate or campus This work was supported by the ....

....it is composed of. A transaction may be interpreted, for example, as a TCP connection, or a group of TCP connections, for a given source destination pair. The long range dependence in aggregate Internet traffic can be explained in terms of the heavytailed distribution of the transaction lengths [13], which vary widely, ranging from a large file transfer or an image laden web page download to short emails or a stock quote. We propose to alleviate the resource provisioning penalty due to long range dependence by penalizing the long transactions that contribute to the heavy tails in the event ....

W. Willinger, M. S. Taqqu, W. E. Leland, D. V. Wilson, "Self-similarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements, " Statistical Science, vol. 10, pp. 67-85, 1995.

....simulation results are given for several example M M 1, M D 1, and D M 1 queues. The simulation results are compared with the analytic results where appropriate. Third, TDEV results are given for several sets of measured Local Area Network (LAN) traffic data that are publicly available [3] [4]. The examples include both total LAN traffic and the portion of LAN traffic that enters or leaves the LAN (i.e. internet traffic) The contribution is organized as follows. Section 2 summarizes basic queueing theory definitions and results needed in the remainder of the contribution. Section 3 ....

....the first million Ethernet LAN packet arrivals beginning at 11:25 A.M. on 29 August 1989. The second data set is limited to external traffic, i.e. internet IP traffic entering the LAN. This data set consists of the first million arrivals beginning at 11:46 P.M. on 3 October 1989. See [3] and [4] for additional details. We emphasize again that, at this point, we present this data only as an illustrative example. It is not intended nor proposed, at present, that this should be used to represent ATM network traffic. The arrival data is illustrated in Figures 5(a) and 6(a) for the ....

Walter Willinger, Muard S. Taqqu, Will E. Leland, and Daniel V. Wilson, Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements, Statistical Science, Vol. 10, No. 1, 1995, pp. 67-85.

....[14] are based on GPS. Achieving differentiated QoS is a challenging task due to the highly bursty traffic characteristics in high speed communication networks. In contrast to traditional assumptions, the burstiness extends over a wide range of time scales. Statistical data analysis [13] [16] has in fact shown that traffic patterns may look similar when observed on various time scales. This behaviour is usually referred to as self similarity. Several studies, e.g. 9] further offered evidence of a closely related property called long range dependence, which means that correlations in ....

W. WILLINGER, M.S. TAQQU, W.E. LELAND AND D.V. WILSON. Self-similarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements. Statistical Science 10, 67 -- 85, 1995.

....To what extent can we predict traces and what are appropriate models 6. How do 1 5 depend on the granularity at which we bin Notice that an implicit assumption that we make is that the traces are stationary. There is debate within the networking community over whether this is indeed the case [4, 12]. Many of the traces that we examine are clearly stationary. Others are not. We addressed these questions in several steps. To start, we collected three sets of packet traces for our study. The first set, which we refer to as the NLANR traces, are a random sample of short traces collected from ....

WILLINGER,W.,TAQQU, M. S., LELAND, W. E., AND WILSON, D. V. Self-similarity in highspeed packet traffic: Analysis and modeling of ethernet traffic measurements. Statistical Science 10,1 (January 1995), 67--85.

....by now concluded that network traffic exhibits time dependencies at a much larger number of time scales than had been traditionally observed. This long range dependence has been detected in a wide range of applications and over multiple networking infrastructures, e.g. Ethernet LANs [12] 17] [39], VBR traffic [7] 14] Web traffic [10] and WAN traffic [31] Roughly speaking, long range dependence amounts to correlations in the packet stream spanning multiple time scales, which are individually rather small but which decay so slowly as to be non summable. This is expected to affect ....

W. Willinger, M.S. Taqqu, W.E. Leland and D.V. Wilson, "Self-- similarity in high--speed packet traffic: Analysis and modeling of ethernet traffic measurements," Statistical Science 10 (

....at the applications that make up the bulk of the measured traffic. Only the applications (with well known port numbers) that have over 0.9 percent of the total bytes or total packets are reported. 3 LRD processes Characterization We follow the self similarity and LRD definitions given in [12] [18]. Let X = X t : t = 0; 1; 2; be a covariance stationary stochastic process with mean , 5 Port Packets Percent Application 6000 24.73 X Windows 513 6.543 login 23 5.87 Telnet 80 3.849 http (World Wide Web) 119 3.42 nntp 514 1.855 Syslog 20 1.596 FTP data 515 1.483 printer Table ....

W. Willinger, M. S. Taqqu, et. al., Self-Similarity in High-Speed Packet Traffic: Analysis of Modeling of Ethernet Traffic Measurements. Statistical Science, 10, no. 1, (1995) 7186.

.... these processes do not accurately reflect the characteristics of Internet traffic [11] For a more realistic model of Internet traffic sources, we employ self similar traffic models [12] Detailed discussion of self similarity in time series data and the accompanying statistical tests are found in [13]. The time series distributions of self similar traffic are usually heavy tailed. The simplest heavy tailed distribution is the Pareto distribution. The Pareto distribution is hyperbolic over its entire range with probability mass function: k x k x k x p # = 0 , 1 # # # # . ....

W. Willinger, M. S. Taqqu, W.E. Leland, and D.V. Wilson, "Selfsimilarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements." Statistical Science 10, pp. 67-85, 1995.

....series plus noise. As the load increases, the variance of the noise goes to 1, and the variance of the long range dependent series goes to 0. One important implication is that the spectrum very close to the origin is always the same. But the behavior at the origin determines the Hurst parameter [24]. This suggests that as the load increases, remains constant, or at least close to it, even though the long range dependence decreases. This says that is not by itself an effective measure of long range dependence, and that a measure in the spirit of is needed as well. 4.7 Dependence: ....

W. Willinger, M. S. Taqqu, W. E. Leland, and D. V. Wilson. Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements. Statistical Science, 10:67--85, 1995.

....of the current demand D (s) III. MODELING BROADBAND SATELLITE NETWORK A. Traffic Sources Due to increasing dominance of Internet traffic, we focus on the transport of Internet traffic and model our traffic sources accordingly. It is well known that Internet traffic exhibits self similarity [6, 12 14]. Most previous evaluations of satellite communication protocols are based on simple ON OFF or Poisson traffic sources, which do not accurately reflect the behavior of Internet traffic [13] Therefore we employ self similar processes with long range dependence in our traffic sources to better ....

....normal, or Poisson distributions. In practical terms, a random variable that follows a Pareto distribution can give rise to extremely large values with non negligible probability. In this paper, the following two traffic models are applied, which are based on results in [6] and [12 14]. # Superposition of Fractal Renewal Processes (Sup FRP) A different fractal point process results from the superposition of a number of independent and identical FRPs. Although the resulting fractal point process model is no longer renewal, the marginal distribution of the inter arrival times ....

W. Willinger, M.S. Taqqu, W. E. Leland, and Daniel V. Wilson, "Self-similarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements." Statistical Science, vol. 10, no. 1, pp. 67-85, 1995.

....However, these methods are not reliable for empirical records with small sample sizes. In practice, R S analysis is based on a heuristic graphical approach. The feature that makes R S statistics particularly attractive is its relative robustness against changes in the marginal distribution [25]. With respect to the effectiveness of R S analysis dependent on the sample size, similar comments as in the case of the previous two methods are also relevant. 11 The absence of any results for the limit laws of the previously mentioned statistics make them inappropriate when a more refined data ....

....when a more refined data analysis is required. In contrast, a more refined data analysis is possible using periodogram based methods in the frequency domain. Several periodogram based estimators can be found in the literature, such as maximum likelihood type estimates (MLE) and related methods [25]. In particular, for Gaussian processes Whittle s estimate MLE has been studied extensively [25] Using these approaches, more information can be collected on the H estimate, such as confidence intervals. In practice, when the required preliminary conditions for the statistical tests are not ....

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W. Willinger, M. S. Taqqu, W. E. Leland, and D. V. Wilson. Self-similarity in high-speed packet traffic: Analysis and modeling of Ethernet traffic measurements. Statistical Science, 10(1):67--85, 1995.

....and designing data networks based on traditional traffic models. Interest in self similar traffic was first stimulated by the measurements of Ethernet traffic at Bellcore [8] The analysis of the collected traffic traces led to the discovery that traffic looks the same on all time scales [8, 15, 16] and to the introduction of the term self similar (or fractal) traffic. Since then, this feature has been discovered in many other traffic traces, such as Transmission Control Protocol (TCP) 10, 11] Motion Pictures Experts Group (MPEG) video [5] World Wide Web [3] and Signaling System 7 [4] ....

.... our simulations imply the importance of capturing long range characteristics of traffic models in wireless networks, and indicate the end of simple traffic models [9, 10] Self similarity has emerged as one of the most important characteristics that needs to be captured by network traffic models [8, 15, 16]. Traditional traffic models provide limited insight into the true nature of genuine traffic data, often fail to capture the properties of genuine traffic, have no meaningful physical interpretation, and have limited value in the engineering of future networks. In contrast, characteristics ....

[Article contains additional citation context not shown here]

W. Willinger, M. S. Taqqu, W. E. Leland, and D. V. Wilson, "Self-similarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements," Statistical Science, vol. 10, no. 1, pp. 67 - 85, 1995.

....1) and 1 2. Queueing systems in which the tail of the service time behaves like (1.1) have recently become important in the performance modelling and analysis of communication traffic. The main reason for this is that extensive traffic measurements for traffic in Ethernet Local Area Networks [39], Wide Area Networks [33] and VBR video [7] exhibit phenomena like self similarity and long range 1 also: Tilburg University, Faculty of Economics, P.O. Box 90153, 5000 LE Tilburg, The Netherlands. 1. Introduction 2 dependence phenomena that can be explained by the occurrence of service ....

W. Willinger, M.S. Taqqu, W.E. Leland, and D.V. Wilson. Self-similarity in high-speed packet traffic: Analysis and modeling of ethernet traffic measurements. Statistical Science, 10:67-85, 1995.

....distributions as one of the fundamental characteristics of Internet traffic. 1. INTRODUCTION 1. 1 Fundamental Characteristics of Traffic Long range dependence and heavy tailed marginal distributions have been established as important, fundamental characteristics of Internet traffic ( 17] [26]) Here, we show that nonstationarity needs to be added to this list of fundamentals, because nonstationarity is pervasive and affects many traffic variables that are measured through time on an Internet link. In addition, we provide technical detail about the nature of the nonstationarity. The ....

....displays are available for interested readers on www.anonymousfornow. 2. PREVIOUS RESULTS The traffic variables characterized here have been studied widely in the literature, and long range dependence and heavy tailed marginal distributions have been established as important characteristics [17, 26, 27]. These two characteristics are in fact closely related: the heavy tailed marginal distribution of file sizes [21, 1, 22, 9] are a major factor in long range dependence [9, 20] Connection and packet inter arrival times have been found to be long range dependent and have a distribution that is ....

W. Willinger, M. S. Taqqu, W. E. Leland, and D. V. Wilson. Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements. Statistical Science, 10:67--85, 1995.

....algorithms [16] are based on GPS. Achieving differentiated QoS is a challenging task due to the highly bursty traffic characteristics in high speed communication networks. In contrast to traditional assumptions, the burstiness extends over a wide range of time scales. Statistical data analysis [14, 17] has in fact shown that traffic patterns may look similar when observed on various time scales. This behaviour is usually referred to as self similarity. Several studies, e.g. 10] further offered evidence of a closely related property called long range dependence, which means that correlations ....

W. Willinger, M.S. Taqqu, W.E. Leland and D.V. Wilson. Self-similarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements. Statistical Science 10, 67 -- 85, 1995.

....series plus noise. As the load increases, the variance of the noise goes to 1, and the variance of the long range dependent series goes to 0. One important implication is that the spectrum very close to the origin is always the same. But the behavior at the origin determines the Hurst parameter H [24]. This suggests that as the load increases, H remains constant, or at least close to it, even though the long range dependence decreases. This says that H is not by itself an effective measure of long range dependence, and that a measure in the spirit of is needed as well. 4.7 Dependence: ....

W. Willinger, M. S. Taqqu, W. E. Leland, and D. V. Wilson. Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements. Statistical Science, 10:67--85, 1995.

....by the need for explanations of both large time scale long range dependence and self similarity in measured network traffic as well as perception of small time scale multifractality. See Kulkarni et al. 2001) Misra and Gong (1998) Mannersalo et al. 1999) Carlsson and Fiedler (2000) Riedi and Willinger (2000). The usual scheme is to consider a process fZ (n) t) Q n i=1 I (n) j (t) t 0g where I (n) j ( Delta) j = 1; n are iid on off processes or perhaps the iid structure is varied by allowing a progressive scaling of time. An on off process is an alternating renewal processes ....

W. Willinger, M. Taqqu, M. Leland and D. Wilson (1995a): Self--similarity in high--speed packet traffic: analysis and modelling of ethernet traffic measurements. Statistical Science 10:67--85.

....in wormhole switched networks. The legacy from standard traffic theory strongly suggests that a Poisson model is appropriate [72,91] However, recent studies on buffered networks of various kinds argue that the Poisson assumption fails [77, 128] Instead, the traffic has a self similar nature [101,151,156,159,160]. This is attributed to high variability and long range dependence [42, 131] We conjecture that the traffic in wormhole switched networks has similar characteristics. Study if the GSMP view facilitates a parallel implementation [48] of GMSim. We believe that the consistent structure and ....

WILLINGER, W., TAQQU, M., LELAND, W., AND WILSON, D. Self-similarity in high-speed packet traffic: Analysis and modeling of Ethernet traffic measurements. Statistical Science 10, 1 (1995), 67--85.

....in determining which properties are relevant and whether all of the possibly relevant properties have been discovered. Both the networking and load balancing communities have histories of choosing the wrong properties, resulting in unfortunate system designs that have only recently been corrected [13, 8]. When we studied the statistical properties of host load signals, we found complex properties such as a strong autocorrelation structure, self similarity and epochal behavior [5] Predictive models use these properties to create forecasts, and thus it is vital to get them right in the model that ....

Willinger, W., Taqqu, M. S., Leland, W. E., and Wilson, D. V. Selfsimilarity in high-speed packet traffic: Analysis and modeling of ethernet traffic measurements. Statistical Science 10, 1 (January 1995), 67--85.

....our measurements of user inter request times, we explore reasons for the heavy tailed distribution of quiet times needed for self similarity. 2 Background 2. 1 Definition of Self Similarity For detailed discussion of self similarity in timeseries data and the accompanying statistical tests, see [1, 27]. Our discussion in this subsection and the next closely follows those sources. A self similar time series has the property that when aggregated (leading to a shorter time series in which each point is the sum of multiple original points) the new series has the same autocorrelation function as the ....

....Thus, for self similar series, 1 D 2 :FBG: 1. As BC7 1, the degree of self similarity increases. Thus the fundamental test for self similarity of a series reduces to the question of whether B is significantly different from 1 2. The effect of self similarity in network traffic is shown in [27], which compares a self similar series with a compound Poisson series with the same distributional characteristics. The paper shows that Poisson models for network traffic become essentially uniform when aggregated by a factor of 1,000; while actual network traffic shows no such decrease in ....

Walter Willinger, Murad S. Taqqu, Will E. Leland, and Daniel V. Wilson. Self-similarity in highspeed packet traffic: Analysis and modeling of Ethernet traffic measurements. Statistical Science, 10(1):67--85, 1995.

....In the absence of methods that can permit the routine analysis of fractal queueing systems, simulation methods are suggested for routine analysis. The generation and statistical analysis of traffic with long range dependence heavy tails is an active area of current research (see for example [14] [27], 28] 10] 24] There are nevertheless several analytical results which provide considerable insights into the engineering impacts of fractal traffic. These are discussed next. IV. Engineering Impacts In this section, we will briefly review current insights into the performance and ....

W. Willinger, M.S. Taqqu, W. Leland and D.V. Wilson. SelfSimilarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements. Statistical Science, Vol. 10,

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Willinger, W., Taqqu, M., Sherman, R. and Wilson, D. (1995) Self-- similarity in high--speed packet traffic: analysis and modelling of ethernet traffic measurements. Statistical Science 10, 67--85.

No context found.

Walter Willinger, Muard S. Taqqu, Will E. Leland, and Daniel V. Wilson, Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements, Statistical Science, Vol. 10, No. 1, 1995, pp. 67-85.

No context found.

W. Willinger, M. Taqqu, W. Leland and D. Wilson, "Selfsimilarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements," Stat. Sci. vol. 10, pp. 67--85, 1995.

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W. Willinger, M. S. Taqqu, W. E. Leland, and D. V. Wilson, "Self-similarity in high speed packet traffic: Analysis and modeling of ethernet traffic measurements," Statistical Science 10(1), pp. 67--85, 1995.

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Willinger, W., Taqqu, M.S., Leland, W.E. and Wilson D.V. (1995). Selfsimilarity in high-speed packet traffic: analysis and modelling of ethernet traffic measurements. Statistical Science, 10, 67-85.

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