B. Mandelbrot. Self-similar error clusters in communication systems and the concept of conditional stationarity. In IEEE Transactions on Communication Technology COM-13, pages 71--90, 1965.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are using to examine the trace. Figure 3 shows that GSM trace consists of error and errorfree bursts, where the length of error free bursts are significantly longer than the length of error bursts. In other words, the traces consist of long error free segments interrupted by small error clusters [13]. Note that for channels with relatively small error clusters, examining traces using a large window size value not only lowers the perceived channel error Figure 3. Burst length in GSM trace. rate, but also distorts the statistics needed by DTMCs, resulting in less accurate models. As the window ....

B. Mandelbrot, Self-similar error clusters in communication systems and the concept of conditional stationarity, IEEE Transactions on Communication Technology COM-13 (1965) 71--90.

....of Poisson measurements and in [279] for the modeling of tra#c in communication networks. The idea of modeling counting processes at multiple resolutions has a substantial history, including a number of examinations of models for self similar counting processes for a variety of applications [311, 231, 165, 318, 221, 201, 202]. The models introduced in [322, 188] make use of very simple properties of Poisson counting processes, namely the facts that (a) the numbers of counts of such a process over non overlapping intervals are independent; and (b) the sum of independent Poisson random variables is also Poisson. For a ....

B.B. Mandelbrot. Self-similar error clusters in communication systems and the concept of conditional stationarity. IEEE Trans. Commun, 13:71--90, 1965. 76

....[1] 5] Consequently, an approximation result based on British data is only presented here, and Fig. 3 illustrates such an approximation. The corresponding modeling parameters together with some parameters deduced from German data are given in Table II. IV. INTER ARRIVAL STATISTICS MODEL In [7], it was observed that errors in communication circuits appeared in self similar clusters despite the fact that the error Although some modeling parameters are given in this paper, the binding reference for such parameters is in Annex C of the corresponding ETSI Permanent Document TM6 (98)10. ....

....FOR ONE BT MEASUREMENT AND TYPICAL PARAMETERS DERIVED FROM GERMAN MEASUREMENTS events themselves were independent and identically distributed. In other words, the errors that appeared were grouped in bursts which in turn were grouped in bursts of bursts and so on. This apparent self similarity [7] of error clusters indicates the invariance of the generating mechanism with respect to multiplication of time by a constant. The class of model proposed by Berger and Mandelbrot belongs to that which is known in the literature as a renewal process model [8] 9] It is worth noting that ....

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B. Mandelbrot, "Self-similar error clusters in communication systems and the concept of conditional stationarity," IEEE Trans. Commun. Technol., pp. 71--90, Jan. 1965.

....heavy tailed) and persistent (i.e. long range dependent) phenomena. In principle, any empirical distribution, whether heavy tailed or light tailed, can be represented by mixtures of exponentials. An early example of describing bursty processes in this fashion is the approach commented on in [18] of modeling inter error times in digital transmission systems. In his criticism of this approach, Mandelbrot [18] points out several limitations and practical problems with the proposed method. For one, the resulting models are highly arbitrary and generally highly parameterized, with the number ....

....whether heavy tailed or light tailed, can be represented by mixtures of exponentials. An early example of describing bursty processes in this fashion is the approach commented on in [18] of modeling inter error times in digital transmission systems. In his criticism of this approach, Mandelbrot [18] points out several limitations and practical problems with the proposed method. For one, the resulting models are highly arbitrary and generally highly parameterized, with the number of parameters required to obtain a satisfactory fit increasing with the size of the data set. In the limit, one is ....

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B.B. Mandelbrot. Self-Similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity. IEEE Trans. Communications Technology COM-13 , pp. 71--90, 1965.

....feature of FPPs; the details of this clustering, beyond that specified by H alone, is expected to have a significant e#ect on queueing behavior, a subject of future study. 4 FRACTAL RENEWAL PROCESS Perhaps the simplest fractal point process is the standard fractal renewal process [3] 16] 21] [23], 42] For the standard FRP, the times between adjacent arrivals are independent random variables drawn from the same fractal pdf. This i.i.d. property limits the applicability of the FRP as a fractal network tra#c model, since traces exhibit high correlation between packet (cell) arrivals. ....

Mandelbrot, B. B. Self-similar error clusters in communication systems and the concept of conditional stationarity. IEEE Trans. Comm. Tech., 13:71--90, 1965.

....are using to examine the trace. Figure 3 shows that GSM trace consist of error and error free bursts, where the length of error free bursts are significantly longer than the length of error bursts. In other words, the traces consist of long error free segments interrupted by small error clusters [13]. Note that for channels with relatively small error clusters, examining traces using a large window size value not only lowers the perceived channel error rate, but also distorts the statistics needed by DTMC s, resulting in less accurate models. As the window size decreases towards the length of ....

MANDELBROT, B. Self-similar error clusters in communication systems and the concept of conditional stationarity. IEEE Transactions on Communication Technology COM-13 (1965), 71--90.

....used for characterizing network traffic. Systematic sampling Stratified random sampling Simple random sampling Figure 1 Fixed granularity sampling (from [4] 3. Self Similarity of Network Traffic The concept of self similarity in the communications field was first introduced by Mandelbrot [9]. He proposed a fractal like model of random error perturbations that appeared to come in bursts not unlike those observed in the early hydrological data studied by Hurst [1] In 1994, Leland, Taqqu, Willinger and Wilson demonstrated the presence of slowly decaying packet count bursts across all ....

B. Mandelbrot, "Self-Similar Error Clusters in Communication Systems and the concept of Conditional Stationarity." IEEE Transactions on Communication Technology, Vol. COM-13, pp. 71 - 90, 1965.

....characteristics more than on the underlying mechanisms responsible for the self similarity. There exist di erent approaches to describing bursty trac. These are mainly stochastic methods based on Gaussian self similar processes, for example fractional Brownian motion and fractional Gaussian noise [3,7 12] or, on the superposition of ON OFF sources with heavy tailed ON or OFF periods [13] and chaotic maps [14 16] All these models describe successfully the burstiness of the trac but their approach is very di erent. Recently, using stochastic methods, there have been some advances in the analytic ....

B. Mandelbrot. Self-similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity. IEEE Trans. On Communication Technology, pages 71-90, March 1965.

....delays at moderate and high utilizations. In particular, this experiment suggests that the burstiness of traffic cannot simply be explained by a renewal arrival process with a singular distribution. Such models have been considered in [38] following earlier work by Mandelbrot and co workers [29] in a different context. In these models, the probability P (T t) that the interarrival time T is greater than t decays slowly with t when t is large: P (T t) t Gammaff ; as t 1; 6) with 1 ff 0. Since ff 1, the mean interarrival time, R 1 0 dt P (T t) diverges, so that the ....

B.B. Mandelbrot, "Self-Similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity", IEEE Trans. Communications Technology COM-13 , pp. 71-90, 1965.

....short term and long term file system traces. However, we have not yet attempted to explain the underlying cause of this observed phenomenon. Willinger et al. 28] proposed a physical explanation of observed self similarity in Ethernet LAN traffic, based on theory developed initially by Mandelbrot[14] and then Taqqu and Levy[25] The theory states that the aggregation of many ON OFF sources, each exhibiting a characteristic known as the Noah effect, results in self similar total traffic. An individual source is classified as being an ON OFF source if the traffic from that source appears to ....

Mandelbrot, B. Self-similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity. IEEE Transactions on Communication Technology COM-13 (1965).

....implicit arrival at the origin, m(t) has the interpretation of being the average arrival rate in an interval of length t, conditional on the fact that something has already arrived. The work here owes much to the model of errors in transmission channels of Berger and Mandelbrot [6] and Mandelbrot [17]. In the second case A e (t) is well defined (though it itself has infinite expectation) Hence we study the ERP and consider the connection between it and the covariant stationary processes (CoVSP s) with unsummable auto covariance functions used in [16] to describe long term correlation and ....

....followed by long gaps. They reveal that a nested burst structure continues to lower scales, with no preferred timescale. It is important to note that this clustering effect is a natural product of the model, despite its simplicity, and is not due to any correlation structure designed into it (see [17], 18] This is in sharp contrast to layered Markov models (for example [11] Not only do these models require complicated state spaces to generate hierarchical clustering, but they suffer from unavoidable arbitrariness, both in the choice of the number of different time scales, and their actual ....

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B. B. Mandelbrot, "`Self Similar Error Clusters in Communications Systems and the Concept of Conditional Stationarity" IEEE Transactions on Communications Technology, Volume 13, pp71-90, 1965.

....is transmitted, during off periods no transmission happens. First letting the number of sources tend to 1 and then time, the limit process is fractional Brownian motion (see Taqqu, Willinger and Sherman [48] Taqqu and Levy [49] This is an extension of a model first introduced by Mandelbrot [35]. 30 Greiner et al. Telecommunication traffic and subexponential distributions Another class of models, also with a selfsimilar limit process, has been considered by Kurtz [31] as an alternative to the classical workload process, where each arrival brings at the instant of its arrival a ....

B.B. Mandelbrot. Self-similar error clusters in communication systems and the concept of conditional stationarity. IEEE Transactions on Communictions Technology, 13:71--90, 1965.

....been discovered is economics or, more precisely, financial economics [15,17,31,50,51,54,75,83,167,168,273,284,297,342,383] The paper [14] provides an overview. For an early application of the self similarity concept and related topics to communications systems, see the seminal paper by Mandelbrot [283]. Enlightening philosophical discussions centering around the issues of traditional mathematical modeling (based on Markov processes) versus unconventional fractal modeling (based on concepts, such as self similarity or long range dependence) as well as technical issues related to the problem of ....

.... in [23, 310] Other stochastic approaches to modeling self similar features are considered in [28, 156, 160, 274, 275, 369, 371] based on shot noise processes) 373] linear models with long range dependence) 30,261, 262, 276, 284, 411, 412] renewal reward processes and their superposition) [116, 283,401] (renewal processes or zero rate processes) 165] aggregation of simple short range dependent models) and [135, 294, 414, 416] wavelet analysis) Further models are considered in [16,19,176,313,379,386,403,417] A radically different approach to modeling self similar phenomena relies on ....

B. B. Mandelbrot. Self-similar error clusters in communications systems and the concept of conditional systems and the concept of conditional stationarity. IEEE Transactions on Communications Technology, COM13: 71--90, 1965.

.... observed packets on several Ethernet LANs at the Bellcore Morristown Research and Engineering Centre [1,2] and an analysis of a few millions of observed frame data by Variable Bit Rate(VBR) video services [3] In these studies, packet traffic appears to be statistically self similar ( fractal ) [4,5]. Self similar traffic is characterized of burstiness across an extremely wide range of time scales: traffic spikes ride on longer term ripples , that in turn ride on still longer term swells , etc. 1] This fractal behaviour of aggregate Ethernet traffic is very different both from ....

B.B.Mandelbrot, "Self-Similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity", IEEE Trans. on Comm. Technology, COM-13, 1965, pp.71-90

....several orders of magnitude below the actual simulated time period. 1 Introduction In many different areas where long time series [Taq86] are available, certain correlation structures have been observed that manifest a self similar (fractal) character. To give a few examples: ffl Hydrology [Man65, Hur51], the study of the amount of daily precipitation or the influx outflux of lakes, reservoirs, or rivers. ffl Economics [Gul95, Mul95, Pet91] where the time series consist of foreign exchange rates or trading values of stocks and bonds. ffl Communications [Lel94] where the time series consist of ....

....or the influx outflux of lakes, reservoirs, or rivers. ffl Economics [Gul95, Mul95, Pet91] where the time series consist of foreign exchange rates or trading values of stocks and bonds. ffl Communications [Lel94] where the time series consist of traffic measurements or occurrences of errors [Man65]. For all the above time series, a memory effect has been discovered. In other words, the past influences the future to a certain extent. The size of this long term memory varies among different systems. The memory effect can also be expressed in terms of a positive or negative correlation. A ....

Benoit B. Mandelbrot. Self-Similar Error Clusters in Communications Systems and the Concept of Conditional Stationarity. IEEE Trans. Communications Technology COM-13, pages 71--90, 1965.

.... observed packets on several Ethernet LANs at the Bellcore Morristown Research and Engineering Centre [1, 2] and an analysis of a few millions of observed frame data by Variable Bit Rate(VBR) video services [3] In these studies, packet traffic appears to be statistically selfsimilar ( fractal ) [4, 5]. Self similar traffic is characterized of burstiness across an extremely wide range of time scales: traffic spikes ride on longerterm ripples , that in turn ride on still longer term swells , etc. 1] This fractal behaviour of aggregate Ethernet traffic is very different both from ....

B.B.Mandelbrot, "Self-Similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity", IEEE Trans. on Comm. Technology, COM-13, 1965, pp.71-90.

....Arrival process; Fractal Brownian motion; Markov modulated Poisson process; Model identification ) 1. Introduction Recently Leland et al. [9] reported that measured Ethernet traffic has self similar characteristic or fractal nature. Self similar phenomenon dates back to Hurst [8] and Mandelbrot [10]. The two main features of self similarity are (i) structural similarities across a very wide range of time scales and (ii) hyperbolically (rather than exponentially) fast decaying autocorrelations. Detailed descriptions of mathematical and statistical aspects of self similarity can be found for ....

B. B. Mandelbrot. Self-similar error clusters in communication systems and the concept of conditional stationarity. IEEE Trans. on Communications Technology, COM-13:71--90, 1965.

....the straight line corresponds to a least squares fit to the upper 75 of the distribution, giving ff = 0:90. Adopting the conservative position of neglecting the evidence of infinite mean interarrival times (for a discussion about self similarity and distributions with infinite mean, see [Ma1]) the results of these traffic studies show that for telnet, the assumption required for Cox s construction of a constant packet arrival rate during a session is a large stretch, irrespective of the possible session lifetime characteristics. On the other hand, Kurtz s construction applies ....

B. B. Mandelbrot, Self-Similar Error Clusters in Communications Systems and the Concept of Conditional Stationarity, IEEE Transactions on Communications Technology COM-13 (1965), 71--90.

....of FPPs; the details of this clustering, beyond that specified by H alone, is expected to have a significant effect on queueing behavior, a subject of future study. 4 FRACTAL RENEWAL PROCESS Perhaps the simplest fractal point process is the standard fractal renewal process [3] 16] 21] [23], 42] For the standard FRP, the times between adjacent arrivals are independent random variables drawn from the same fractal pdf. This i.i.d. property limits the applicability of the FRP as a fractal network traffic model, since traces exhibit high correlation between packet (cell) arrivals. ....

Mandelbrot, B. B. Self-similar error clusters in communication systems and the concept of conditional stationarity. IEEE Trans. Comm. Tech., 13:71--90, 1965.

No context found.

B. Mandelbrot. Self-similar error clusters in communication systems and the concept of conditional stationarity. In IEEE Transactions on Communication Technology COM-13, pages 71--90, 1965.

No context found.

MANDELBROT, B. Self-similar error clusters in communication systems and the concept of conditional stationarity. IEEE Transactions on Communication Technology COM-13 (1965), 71--90.

No context found.

B. Mandelbrot, \Self-similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity, " IEEE Trans. On Communication Technology , pp. 71-90, March 1965.

No context found.

Mandelbrot B., 1965, "Self-Similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity" IEEE Trans. On Communication Technology, 71-90.

No context found.

Mandelbrot, B.B., "Self-Similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity", IEEE Trans. Communications Technology COM-13 (1965), 71--90.

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B. B. Mandelbrot. Self-Similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity. IEEE Transactions on Communications Technology, Vol. 13, pp. 71--90, 1965.

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