A. Erramilli and W. Willinger. Fractal properties in packet traffic measurements. In Proceedings of the St. Petersburg Regional ITC Seminar, pages 144--158, St. Petersburg, Russia, June 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and simulated queueing performance of the ATM traffic and show the strong robustness of self similar properties identified. 1. INTRODUCTION In the last decade a number of extensive studies of high resolution traffic measurements from a wide range of packet traffic networks have been reported [1,6,7,10,11,14,22]. The most important finding of these studies is the identified fractal like behaviour implying the so called long range dependence and self similarity properties. As a result of intensive research at Bellcore a series of papers reported these findings in Ethernet LAN [7,9,11,12] The ....

....reported [1,6,7,10,11,14,22] The most important finding of these studies is the identified fractal like behaviour implying the so called long range dependence and self similarity properties. As a result of intensive research at Bellcore a series of papers reported these findings in Ethernet LAN [7,9,11,12]. The comprehensive study of Leland s group with the conclusion that this traffic is self similar was published in detail in [11] The study of Duffy et al. 6] revealed the self similarity traffic property in common channel signalling network. Meier Hellstern et al. 14] found that the Pareto ....

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A. Erramilli and W. Willinger. Fractal properties in packet traffic measurements. In ITC Regional Seminar, pages 144--158, St. Petersburg, Russia, 1993.

....real VBR video data. In all these Markovian models, the autocorrelation function decays exponentially for large lags. In the case of real data, the autocorrelation function drops off much more slowly, in a manner indicating significant long range dependence. This phenomenon is explored further in [1, 4], where it is suggested that VBR video traffic may have certain fractal properties. In [7] an ATM switch fed by sixteen independent VBR video sources is examined using simulation. The cell loss probability when a set of real teleconference data is used in the simulation is compared to predictions ....

....structure VBR video traffic. However, the results presented here suggest that many useful cell loss statistics can be calculated accurately in spite of this deficiency in the models. The following points are suggested as worthy of further work: 1. Autocorrelation It has been observed previously [1, 4, 5] that there exists long range dependence in many types of traffic in packet networks, including both video and LAN traffic. This long range dependence leeds to autocorrelation functions that do not decay exponentially for large lags, but have polynomial order. The temporal behaviour of such ....

A. Erramilli and W. Willinger. Fractal properties in packet traffic measurements. In Proceedings of the St. Petersburg Regional ITC Seminar, pages 144--158, St. Petersburg, Russia, June 1993.

....bursts, right down to the level of packets. They argued decisively that any feasible variant of traditional models would not show such features. The results were similar across the different LAN s, over widely varying load conditions, and through network reconfigurations. Erramilli and Willinger [9] and Leyland et al. 16] analyse the above data sets, as well as VBR video sequences compiled by Beran et al. [4] Several quantities characterising the correlation structure of the data sets were measured, and in each case results indicating long term correlations, slowly decaying variances, and ....

A. Erramilli and W. Willinger, "Fractal Properties in Packet Traffic Measurements," Proc. ITC Seminar, St. Petersburg, 1993.

.... recent statistical analyses of very large traffic data sets obtained from high quality traffic measurements over various network environments have revealed that the statistical characteristics of real world traffic may be best described by self similarity (see Section 2 for its definition) [4, 7, 8, 14]. One of the main reasons for this result is that there exist various factors (e.g. collision, flow control, and human response) that consistently affect traffic behavior during the entire lifetime of a connection, resulting in an extreme degree of fluctuation over a wide range of time scales ....

....the entire measurement periods. We observe that LAN II was about 3.5 times more active in terms of average arrival rate than LAN I. Daily cycles are visible in both traces, and traffic fluctuation is indeed very high. We use the IDC, among other equivalent techniques suggested in the literature [7], to detect self similarity of each data set and estimate its Hurst parameter. For a self similar process Z, the IDCZ (m) defined in (4) has the following form [14, 23] IDCZ (m) 1 am D with a positive constant a and 0 D 1. D represents the slope of an IDC curve on a log log plot and is ....

A. Erramilli and W. Willinger. Fractal properties in packet traffic measurements. In Proc. St. Petersburg Regional ITC Seminar, 1993.

....to the modeling of broadband ISDN and ATM networked systems. Leland et.al. at Bellcore Morristown Research Center have analyzed millions of packets on several Ethernet LAN s and millions of frame data by Variable Bit Rate (VBR) video services [11, 12] In [11, 12] and in numerous other studies [1, 2, 3, 4, 8, 10] network packet traffic is characterized by high variability or burstiness over a wide range of time scales. In other words, the network traffic looks the same when measured over time intervals ranging from milliseconds to minutes to hours, etc. 5] Data traffic of this type is said to be ....

A. Erramilli and W. Willinger, "Fractal properties in packet traffic Measurements," in Proc. St. Petersburg Regional ITC Seminar, St. Petersburg, Russia, 1993, pp. 144-158.

.... three characteristics over a wider range of time or frequency scales: 3 F (T ) a 1 T ff (slowly decaying variance) r(k; T s ) a 2 k Gamma(1 Gammaff) long range dependence) 2) S(f) a 3 f Gammaff (1=f noise) for 0 ff 1 4 and some positive constants a i ; i = 1; 2; 3 [3, 8, 14, 15]. The constant ff is called the fractal exponent and related to the Hurst parameter H by ff = 2H Gamma 1. The relations in (2) are all of power law form, since scaling and fractals are closely related [14, references therein] If the process X is constructed from an FPP model, then X is ....

A. Erramilli and W. Willinger. Fractal properties in packet traffic measurements. In Proc. St. Petersburg Regional ITC Seminar, 1993.

....of broadband ISDN and ATM networked systems. For instance, Leland et.al. at Bellcore Morristown Research Center have analyzed millions of packets on several Ethernet LAN s and millions of frame data by Variable Bit Rate (VBR) video services [17, 18] In [17, 18] and in numerous other studies [1, 3, 5, 6, 10, 13] network packet traffic appears similar when measured over a wide range of time scales. That is, the network traffic looks the same when measured over time intervals ranging from milliseconds to minutes to hours, etc. 7] Data traffic of this type is said to be self similar or fractal in nature ....

....develop a means to study the impact of self similar data traffic upon telecommunication systems using analytic queueing models. For instance, with respect to item (1) there have been many studies indicating that the effect of self similar data traffic upon networks seriously degrades performance [6, 7]. Concerning item (2) the development of queueing models to study self similar traffic poses a serious challenge for researchers. The problem lies in the difficulty of obtaining Laplace transforms for power tail distributions. Pertaining to item (3) power tails exhibit many properties of ....

A. Erramilli and W. Willinger, "Fractal properties in packet traffic Measurements," in Proc. St. Petersburg Regional ITC Seminar, St. Petersburg, Russia, 1993, pp. 144-158.

....traffic measurements, in the recent past it has benefited from a tremendous flood of high resolution, high quality, and high volume traffic data from a wide range of live packet networks that carry real applications generated by real users. Subsequent measurement studies (e.g. see [20] [7], 15] 5] 13] 23] 11] 1] 28] have contributed greatly to new insights into the nature of traffic in actual networks, and have indicated that there exists a considerable gap between traditional traffic models and empirically observed traffic processes. The tractability that is so ....

A. Erramilli and W. Willinger. Fractal Properties in Packet Traffic Measurements. Proc. Regional ITC Seminar , pp. 144--158, St. Petersburg, Russia, 1993.

....insights into the traffic management of high speed networks. 1 Introduction In the past 2 3 years, large amounts of traffic measurements from working packet networks (including Ethernet LANs, WANs, CCSN SS7, ISDN, and VBR video over ATM) have been collected and analyzed. The results reported in [1, 5, 7, 13, 25, 26, 40, 23, 33, 35, 36] have been striking for two reasons: 1) these studies demonstrate that it is possible to clearly distinguish between actual packet network traffic and traffic generated by widely employed theoretical models, and (2) in sharp contrast to the traditional packet traffic models, aggregate packet ....

....contributions is to add to the current efforts of gaining a better understanding of queueing performance when the input to the queue is not given by a traditional traffic process but is instead fractal in nature. For recent analytic results and simulation studies in this area, see for example [4, 8, 7, 12, 13, 26, 34]. Given the statistical significance of the finding of selfsimilarity or LRD in measured packet traffic (e.g. in case of the Ethernet data see [26] and its demonstrated significance for queueing performance, stochastic modeling of long range phenomena becomes of crucial importance. Traditional ....

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A. Erramilli and W. Willinger, "Fractal Properties in Packet Traffic Measurements", Proc. of the St. Petersburg Regional ITC Seminar , St. Petersburg, Russia, pp. 144-158, 1993.

....in the design and operation of telephone networks. In contrast, traffic arrival processes in packet based networks are much more bursty and intermittent. A number of recent measurement studies from the full range of packet based networks and services (ISDN packet, Ethernet, SS7, VBR Video) 2] 4][9] [11] 12] 13] indicate that packet traffic is characterized by interarrival times that decay with heavy tails, by variances that decay as a fractional power of the sample size, by a power spectrum that is divergent near the origin, and by correlations that are long range dependent. A number of ....

....call (which can span many time scales) followed by another burst corresponding to the termination of the call. It is a reasonable conjecture that the sustained inactivity modeled by the single intermittency map is at the root of the self similarity observed in traffic from existing SS7 networks [9]. Note that the limited burst scenario may not be valid when signaling data from new services such as PCS, mobile computing, etc. make up a substantial portion of signaling traffic. The sojourn times in the inactive state are heavy tailed with infinite variance when (3 2 m 2) The effect of is to ....

A. Erramilli and W. Willinger, "Fractal Properties in Packet Traffic Measurements", Proc. of ITC Regional Seminar, St. Petersburg 1993.

.... that between 1966 and 1987, several thousand papers on queueing problems have been published, but only about 50 on traffic measurement results) more recently, enormous volumes of traffic data from working networks have been collected and made available to researchers: CCSN SS7 [106,107] ISDN [122,304], Ethernet LANs [173 175, 255 260, 293, 378, 409 412] WANs and NSFNet [41, 68, 69, 88, 181, 220, 314, 331 333, 335] and VBR traffic [26, 145, 146, 186, 199] Other traffic measurement studies we are aware of include [346] Ethernet traffic to a file server) 5] FASTPAC, an Australian ....

....from weeks to months years (e.g. 69,333] The former are typically used for traffic characterization purposes, and the latter yield insight into long term growth trends and network utilizations. Extensive recent statistical analyses of high time resolution traffic measurements reported in [26,107,122,146,150,199,220,256,331,410,411] have provided convincing evidence that actual traffic data from working packet networks are consistent with statistical self similarity or fractal characteristics. Moreover, these empirically observed features often distinguish clearly between traffic generated by traditional models and measured ....

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A. Erramilli and W. Willinger. Fractal properties in packet traffic measurements. In Proceedings of the St. Petersburg Regional ITC Seminar, St. Petersburg, Russia, pages 144--158, 1993. A Bibliographical Guide 15

....source, and as a result, the superposition of many such sources behaves like white noise in the sense that the aggregate traffic stream is void of any significant correlations, beyond possibly, in the short range. This behavior is in clear contrast with the measured network traffic described in [5]. Beyond this mathematical explanation, Willinger et al. 19] revisit the Bellcore Ethernet LAN traffic traces (see [5] and extract from the aggregate traffic the traces generated by individual source destination pairs. Subsequent statistical analysis of these traces (for a given hour, there are ....

....traffic stream is void of any significant correlations, beyond possibly, in the short range. This behavior is in clear contrast with the measured network traffic described in [5] Beyond this mathematical explanation, Willinger et al. 19] revisit the Bellcore Ethernet LAN traffic traces (see [5]) and extract from the aggregate traffic the traces generated by individual source destination pairs. Subsequent statistical analysis of these traces (for a given hour, there are typically between 100 1000 active source destination pairs, i.e. traffic traces) reveals that (i) the traffic ....

A. Erramilli and W. Willinger, "Fractal Properties in Packet Traffic Measurements ", ITC Regional Seminar, St. Petersburg, 1993.

....arithmetic mean of a traffic sample (consisting of the time series of packet counts) decays inversely as the sample size, asymptotically. Erramilli and Willinger 93 6 Modeling Packet Traffic with Chaotic Maps Ashok Erramilli, R.P. Singh, Parag Pruthi Template filename: ba tmplt TM.fm Version [14] show that this rate of decay is far slower in traffic samples from ISDN, Ethernet and Variable Bit Rate (VBR) Video. Long Range Dependence: The autocovariance function of conventional traffic processes decays exponentially, and correlations are assumed to exist for only short time scales. In ....

....Ethernet traffic by Leland et al. 93 [17] 1 f noise: This is a frequency domain manifestation of long range dependence. The power spectra of real traffic processes diverge at low frequencies, in contrast to widely used theoretical models that are flat at low frequencies. Erramilli and Willinger [14] demonstrate 1 f noise in ISDN, Ethernet and VBR traffic samples. Fractal Dimensions: Conventional traffic processes are characterized by a dimension of 1, according to several commonly used measures. Over time scales of engineering interest, however, actual traffic is observed to have fractal ....

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A. Erramilli and W. Willinger, "Fractal Properties in Packet Traffic Measurements ", Proc. of ITC Regional Seminar, St Petersburg 1993.

....U.S.A. b Royal Institute of Technology, Department of Teleinformatics, Electrum 204, S 164 40 Kista, Sweden Abstract At the 1993 ITC seminar in St. Petersburg, we presented results from traffic measurement studies that demonstrated the self similar ( fractal ) nature of measured packet traffic [15]. In the meantime, a flurry of new results has been published on applications of fractal (or self similar) processes to measurements, modeling and analysis of bursty packet traffic in high speed communications networks. The main purpose of this paper is to summarize the current state of the art in ....

....in its infancy, and many of the papers discussed in this article are available only as preprints. There is considerable scope for further research on highly relevant problems of practical interest. Work in this area to this point can be divided into three categories: 1. Measurement Studies: In [15], we summarized measurement results from ISDN, Ethernet LAN and VBR traffic. Recently, measurement data from a variety of other sources, such as individual Ethernet sources and specific services (such as VBR Video, Internet MBONE traffic) have been further analyzed, as well as Ethernet LAN traffic ....

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A. Erramilli and W. Willinger, "Fractal Properties in Packet Traffic Measurements", ITC Regional Seminar, St. Petersburg, June 1993.

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A. Erramilli, W. Willinger, "Fractal Properties of Packet Traffic Measurements", preprint, 1993.

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A. Erramilli, W. Willinger, "Fractal Properties of Packet Traffic Measurements", Proc. of the St. Petersburg Regional ITC Seminar, pp. 144-158, St. Petersburg, Russia, 1993.

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A. Erramilli, W. Willinger, "Fractal Properties of Packet Traffic Measurements", Proc. of the St. Petersburg Regional ITC Seminar, pp. 144158, St. Petersburg, Russia, 1993.

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A. Erramilli and W. Willinger. Fractal properties in packet traffic measurements. In Proceedings of the St. Petersburg Regional ITC Seminar, pages 144--158, St. Petersburg, Russia, June 1993.

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