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...scales by reducing it to and pointing out a plausible explanation in terms of previously observed phenomena in the dynamics of TCP-type congestion control, among them ACK-compression; see for example =-=[12, 27, 26, 32, 17]-=-, or the more recent study [20]. This empirical observation begs for a simple mathematical construction that incorporates the essence of flow control phenomena and leads to multifractal scaling behavi...

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...j) and scale j that extends over a range of fine time scales, where 1 We use the Haar wavelets primarily for exposition and we use more general wavelets (e.g., compactly supported Daubechies wavelets =-=[6]-=-) for the scaling analysis. 2 In practice, we slide a window of length five (this parameter can be varied) over the coefficients at each scale, extracting the local maxima. Scale log2(Energy(j)) pinch...

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... in detail in Section 2. Over the last few years, network-related measurementshave become a rich source for observing interesting and at times surprising scaling behaviors; e.g., self-similar scaling =-=[15, 21, 9]-=- and multifractal scaling [24, 8]. Intuitively, the ubiquity with which some of these scaling phenomena occur in measurements from today's IP networks is related to the absence of an intrinsic scale w...

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... in detail in Section 2. Over the last few years, network-related measurementshave become a rich source for observing interesting and at times surprising scaling behaviors; e.g., self-similar scaling =-=[15, 21, 9]-=- and multifractal scaling [24, 8]. Intuitively, the ubiquity with which some of these scaling phenomena occur in measurements from today's IP networks is related to the absence of an intrinsic scale w...

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...ame time, in today's Web-dominated Internet, the sizes or durations of sessions, number of HTTP requests/responses, TCP connections or IP-flows typically span up to six orders of magnitude (e.g., see =-=[5, 29, 9]-=-). Mathematically, the absence of an intrinsic scale is equivalent to high variability and can be captured in a parsimonious manner using heavy-tailed (also known as scale-invariant) distributions wit...

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...parameters required for these distributions and used in our studies can be found in the Appendix. We base our choice of distributions (including the specific parameters) on the work surrounding SURGE =-=[4]-=-, a Web workload generator designed to generate realistic Web traffic patterns, and upon [7, 18]. Note that we simulate HTTP without pipelining and without persistent connections. The protocol stack, ...

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...usible explanation in terms of previously observed phenomena in the dynamics of TCP-type congestion control, among them ACK-compression; see for example [12, 27, 26, 32, 17], or the more recent study =-=[20]-=-. This empirical observation begs for a simple mathematical construction that incorporates the essence of flow control phenomena and leads to multifractal scaling behavior. Unfortunately, we have not ...

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...ng phenomenon of measured IP traffic over small time scales that may be as plausible, intuitive, appealing and relevant as the one that has recently been found for the self-similar scaling (e.g., see =-=[30, 29, 9]-=-). This and other open problems, together with some practical applications of our scaling analysis and some limitations of our study and of the underlying network configurations are discussed in Secti...

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...our simulations by simpler versions which in essence equate a session with an infinite file transfer. While such simplifications are often convenient for analytical studies of TCP dynamics (e.g., see =-=[14]-=- and references therein), they lead in general to very different behaviors of the resulting traffic, especially in a reasonably heterogeneous network environment. To illustrate, Figure 12 shows the lo...

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...scales by reducing it to and pointing out a plausible explanation in terms of previously observed phenomena in the dynamics of TCP-type congestion control, among them ACK-compression; see for example =-=[12, 27, 26, 32, 17]-=-, or the more recent study [20]. This empirical observation begs for a simple mathematical construction that incorporates the essence of flow control phenomena and leads to multifractal scaling behavi...

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...ability, network-related variability), others remain untouched or sufficiently obscure. For example, we have not yet systematically explored issues related to traffic synchronization (see for example =-=[31, 10]-=-). Although we have observed a significant amount of synchronization effects in simulations that assume infinite sources (see Section 4.5), very little of this phenomenonseems to show up when assuming...

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... and determine qualitatively over what range of scales there exists a linear relationship between log(E j ) and scale j; that is, over what range of time scales there exists self-similar scaling (see =-=[1]-=- for more details). In all of the figures in this paper, the scale j is on the bottom axis and the corresponding time (in seconds) is plotted on the top axis for reference. The local scaling analysis ...

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...similar scaling behavior over large time scales is mainly caused by user/session characteristics and has little to do with network-specific aspects" (e.g., see [8]; for related earlier work, see =-=also [19]). In supp-=-ort of yet another conjecture that can be found in [8], we also present empirical evidence demonstrating that time scales on the order of a "typical" roundtrip time within the network are di...

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...estigations also has an impact on the problem related to simulation of "realistic " Internet scenarios. The challenges associated with simulating Internet-like environments are clearly spell=-=ed out in [22]-=- but our empirical work points towards an approach that does away with traditional simulation modeling and coincides with a number of arguments put forward in [22]. In particular, we have demonstrated...

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...scales by reducing it to and pointing out a plausible explanation in terms of previously observed phenomena in the dynamics of TCP-type congestion control, among them ACK-compression; see for example =-=[12, 27, 26, 32, 17]-=-, or the more recent study [20]. This empirical observation begs for a simple mathematical construction that incorporates the essence of flow control phenomena and leads to multifractal scaling behavi...

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...s meant by statements of the form “Self-similar scaling behavior over large time scales is mainly caused by user/session characteristics and has little to do with network-specific aspects” (e.g., see =-=[8]-=-; for related earlier work, see also [19]). In support of yet another conjecture that can be found in [8], we also present empirical evidence demonstrating that time scales on the order of a “typical”...

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...ndix. We base our choice of distributions (including the specific parameters) on the work surrounding SURGE [4], a Web workload generator designed to generate realistic Web traffic patterns, and upon =-=[7, 18]-=-. Note that we simulate HTTP without pipelining and without persistent connections. The protocol stack, network topology (including delays and bandwidths), and the sequence of Web requests define a si...

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...caling analysis, we begin with a time series derived from a conservative cascade with fixed generator W (we take W to be a truncated normal on [0; 1] with mean 1=2 and variance 0.01; for details, see =-=[8, 11, 23]). From th-=-is sequence, we construct the toy example time series "fold" by targeting a selected range of scales and replacing the wavelet coefficients at those scales by appropriately chosen fixed (pos...

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...congestion control, retransmission, ACK compression), we have gained access to a substantial body of knowledge about various aspects of the dynamics of congestion control mechanisms; for example, see =-=[13, 12, 25, 26, 32]-=- and the empirical studies of Internet traffic dynamics [17, 20]. As a result, we believe to have set the stage for a physical explanation and understanding of the multifractal scaling phenomenon of m...

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... physical explanation of the self-similar scaling of network traffic over large time scales in terms of the infinite variance or high-variability property of user session sizes (for details, e.g. see =-=[21, 9]-=-). In this sense, global scaling plots such as the ones shown in Figure 4 (see also below for global scaling plots where we explicitly change a variety of network-related features, without any signifi...

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...scales by reducing it to and pointing out a plausible explanation in terms of previously observed phenomena in the dynamics of TCP-type congestion control, among them ACK-compression; see for example =-=[12, 27, 26, 32, 17]-=-, or the more recent study [20]. This empirical observation begs for a simple mathematical construction that incorporates the essence of flow control phenomena and leads to multifractal scaling behavi...

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...nderlying network configuration. Our work relies on a set of measured traffic traces from an ISP environment and on various traces collected from a simulation environment that uses the ns-2-simulator =-=[3]-=- and exploits its ability to implement different network configurations. The ISP traces serve as benchmarks and are used for reality checks, while the ns-2-generated traces allow us to identify the ef...

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...ndix. We base our choice of distributions (including the specific parameters) on the work surrounding SURGE [4], a Web workload generator designed to generate realistic Web traffic patterns, and upon =-=[7, 18]-=-. Note that we simulate HTTP without pipelining and without persistent connections. The protocol stack, network topology (including delays and bandwidths), and the sequence of Web requests define a si...

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...congestion control, retransmission, ACK compression), we have gained access to a substantial body of knowledge about various aspects of the dynamics of congestion control mechanisms; for example, see =-=[13, 12, 25, 26, 32]-=- and the empirical studies of Internet traffic dynamics [17, 20]. As a result, we believe to have set the stage for a physical explanation and understanding of the multifractal scaling phenomenon of m...

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...ability, network-related variability), others remain untouched or sufficiently obscure. For example, we have not yet systematically explored issues related to traffic synchronization (see for example =-=[31, 10]-=-). Although we have observed a significant amount of synchronization effects in simulations that assume infinite sources (see Section 4.5), very little of this phenomenonseems to show up when assuming...

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...nd define the partition function S(q; j) as the sum over the local maxima of the (normalized) wavelet coefficients raised to the qth power at each scale j: S(q; j) = X max j2 \Gammaj=2 d j;k j q (see =-=[8, 11]-=- and the references therein) 2 . Although we need several additional transformations of the partition function to quantify rigorously the distribution of scaling exponents, for an intuitive picture an...

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...t few years, network-related measurementshave become a rich source for observing interesting and at times surprising scaling behaviors; e.g., self-similar scaling [15, 21, 9] and multifractal scaling =-=[24, 8]-=-. Intuitively, the ubiquity with which some of these scaling phenomena occur in measurements from today's IP networks is related to the absence of an intrinsic scale wherever one looks: link speedsspa...

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...ividual TCP connections where it has been shown to conform to multifractal scaling. At the aggregate level, multifractal scaling has been observed in a 7 number of measured Internet traces (e.g., see =-=[24, 16, 8]-=-). Given this empirical connection with multifractal scaling behavior over fine time scales, our aim in this subsection is to provide initial insights into and a first physical understanding for what ...

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...ame time, in today's Web-dominated Internet, the sizes or durations of sessions, number of HTTP requests/responses, TCP connections or IP-flows typically span up to six orders of magnitude (e.g., see =-=[5, 29, 9]-=-). Mathematically, the absence of an intrinsic scale is equivalent to high variability and can be captured in a parsimonious manner using heavy-tailed (also known as scale-invariant) distributions wit...

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...ipelining and without persistent connections. The protocol stack, network topology (including delays and bandwidths), and the sequence of Web requests define a simulation. Since TCP Reno and HTTP 1.0 =-=[28]-=- are assumed to be the predominant protocols in the ISP environment at hand, we emulate them in our simulations. We vary the number of sessions from 100 (low load scenarios) to 300 or 400 for high loa...

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...and the goal of a local scaling analysis is to collect characteristic information about the strengths and locations of the various scaling exponents (for a more detailed presentation see, e.g. [8] or =-=[2]-=-). To gather the statistics of the local scaling exponents, we again use the discrete wavelet transform of the underlying data and define the partition function S(q; j) as the sum over the local maxim...

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...s meant by statements of the form "Self-similar scaling behavior over large time scales is mainly caused by user/session characteristics and has little to do with network-specific aspects" (=-=e.g., see [8]; for rela-=-ted earlier work, see also [19]). In support of yet another conjecture that can be found in [8], we also present empirical evidence demonstrating that time scales on the order of a "typical"...