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252
Evidence for longtailed distributions in the Internet
 In Proceedings of ACM SIGCOMM Internet Measurment Workshop
, 2001
"... We review evidence that Internet traffic is characterized by longtailed distributions of interarrival times, transfer times, burst sizes and burst lengths. We propose a new statistical technique for identifying longtailed distributions, and apply it to a variety of datasets collected on the Intern ..."
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Cited by 39 (0 self)
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We review evidence that Internet traffic is characterized by longtailed distributions of interarrival times, transfer times, burst sizes and burst lengths. We propose a new statistical technique for identifying longtailed distributions, and apply it to a variety of datasets collected on the Internet. We find that there is little evidence that interarrival times and transfer times are longtailed, but that there is some evidence for longtailed burst sizes. We speculate on the causes of longtailed bursts. I.
Performance Impacts of MultiScaling in Wide Area TCP/IP Traffic
 Proceedings of IEEE INFOCOM
, 2000
"... Recent measurement and simulation studies have revealed that wide area network traffic has complex statisticalpossibly multifractalcharacteristics on short timescales, and is selfsimilar on long timescales. In this paper, using measured TCP traces and queueing simulations, we show that the fi ..."
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Cited by 37 (1 self)
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Recent measurement and simulation studies have revealed that wide area network traffic has complex statisticalpossibly multifractalcharacteristics on short timescales, and is selfsimilar on long timescales. In this paper, using measured TCP traces and queueing simulations, we show that the fine timescale features can affect performance substantially at low and intermediate utilizations, while the coarse timescale selfsimilarity is important at intermediate and high utilizations. We outline an analytical method for estimating performance for traffic that is selfsimilar on coarse timescales and multifractal on fine timescales, and show that the engineering problem of setting safe operating points for planning or admission controls can be significantly affected by fine timescale fluctuations in network traffic. Keywords Wide Area TCP traffic, Multifractal Scaling, Performance Analysis I. INTRODUCTION It is now generally accepted that sufficiently aggregated packet network ...
Inferring Network Characteristics via MomentBased Estimators
, 2001
"... In this work we develop simple inference models based on finite capacity single server queues for estimating the buffer size and the intensity of cross traffic at the bottleneck link of a path between two hosts. Several pairs of momentbased estimators are proposed to estimate these two quantities. ..."
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Cited by 33 (0 self)
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In this work we develop simple inference models based on finite capacity single server queues for estimating the buffer size and the intensity of cross traffic at the bottleneck link of a path between two hosts. Several pairs of momentbased estimators are proposed to estimate these two quantities. The best scheme is then identified through simulation.
LongRange Dependence and Data Network Traffic
, 2001
"... This is an overview of a relatively recent application of longrange dependence (LRD) to the area of communication networks, in particular to problems concerned with the dynamic nature of packet flows in highspeed data networks such as the Internet. We demonstrate that this new application area off ..."
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Cited by 29 (1 self)
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This is an overview of a relatively recent application of longrange dependence (LRD) to the area of communication networks, in particular to problems concerned with the dynamic nature of packet flows in highspeed data networks such as the Internet. We demonstrate that this new application area offers unique opportunities for significantly advancing our understanding of LRD and related phenomena. These advances are made possible by moving beyond the conventional approaches associated with the widespread "blackbox" perspective of traditional time series analysis and exploiting instead the physical mechanisms that exist in the networking context and that are intimately tied to the observed characteristics of measured network traffic. In order to describe this complexity we provide a basic understanding of the design, architecture and operations of data networks, including a description of the TCP/IP protocols used in today's Internet. LRD is observed in the large scale behavior of the data traffic and we provide a physical explanation for its presence. LRD tends to be caused by user and application characteristics and has little to do with the network itself. The network affects mostly small time scales, and this is why a rudimentary understanding of the main protocols is important. We illustrate why multifractals may be relevant for describing some aspects of the highly irregular traffic behavior over small time scales. We distinguish between a timedomain and waveletdomain approach to analyzing the small time scale dynamics and discuss why the waveletdomain approach appears to be better suited than the timedomain approach for identifying features in measured traffic (e.g., relatively regular traffic patterns over certain time scales) that have a direct networking interpretation (e....
LongRange Dependence and HeavyTail Modeling for Teletraffic Data
 IEEE Signal Processing Magazine
, 2002
"... Analysis and modeling of computer network traffic is a daunting task considering the amount of available data. This is quite obvious when considering the spatial dimension of the problem, since the number of interacting computers, gateways and switches can easily reach several thousands, even in a L ..."
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Cited by 26 (3 self)
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Analysis and modeling of computer network traffic is a daunting task considering the amount of available data. This is quite obvious when considering the spatial dimension of the problem, since the number of interacting computers, gateways and switches can easily reach several thousands, even in a Local Area Network (LAN) setting. This is also true for the time dimension: W. Willinger and V. Paxson in [42] cite the figures of 439 million packets and 89 gigabytes of data for a single week record of the activity of a university gateway in 1995. The complexity of the problem further increases when considering Wide Area Network (WAN) data [28]. In light of the above, it is clear that a notion of importance for modern network engineering is that of invariants, i.e. characteristics that are observed with some reproducibility and independently of the precise settings of the network under consideration. In this tutorial paper, we focus on two such invariants related to the time d...
Memory and Infrequent Breaks
, 1999
"... Memory and Infrequent Breaks We study how processes with infrequent regime switching may generate a long memory effect in the autocorrelation function. In such a case, the use of a strong fractional I(d) model for economic or financial analysis may lead to spurious results. Keywords: Long Memory, Sw ..."
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Cited by 25 (0 self)
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Memory and Infrequent Breaks We study how processes with infrequent regime switching may generate a long memory effect in the autocorrelation function. In such a case, the use of a strong fractional I(d) model for economic or financial analysis may lead to spurious results. Keywords: Long Memory, Switching Regime, Heavy Tail. JEL : C22 THIS VERSION: December 2, 1999 1 1 Introduction Inference on the dynamics of economic or financial time series is usually based on the autocorelation function whose decay pattern is used to assess the persistence range of processes. Those, displaying a geometric decay rate are modelled as Autoregressive Moving Averages whereas strong fractional I(d) models are used to fit hyperbolic decay rates of socalled long memory processes. However the analysis adequate for linear dynamics may often become misleading if the true underlying dynamics is nonlinear. This point is of special importance for the "long memory" property, which is often observed in macroe...
Modeling heterogeneous user churn and local resilience of unstructured p2p networks
 In ICNP
, 2006
"... Abstract — Previous analytical results on the resilience of unstructured P2P systems have not explicitly modeled heterogeneity of user churn (i.e., difference in online behavior) or the impact of indegree on system resilience. To overcome these limitations, we introduce a generic model of heterogen ..."
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Cited by 23 (4 self)
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Abstract — Previous analytical results on the resilience of unstructured P2P systems have not explicitly modeled heterogeneity of user churn (i.e., difference in online behavior) or the impact of indegree on system resilience. To overcome these limitations, we introduce a generic model of heterogeneous user churn, derive the distribution of the various metrics observed in prior experimental studies (e.g., lifetime distribution of joining users, joint distribution of session time of alive peers, and residual lifetime of a randomly selected user), derive several closedform results on the transient behavior of indegree, and eventually obtain the joint in/out degree isolation probability as a simple extension of the outdegree model in [13]. I.
Convergence of Scaled Renewal Processes and a Packet Arrival Model
 Bernoulli
"... We study the superposition process of a class of independent renewal processes with longrange dependence. It is known that under two different scalings in time and space either fractional Brownian motion or a stable Levy process may arise in the rescaling asymptotic limit. It is shown here that in ..."
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Cited by 22 (4 self)
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We study the superposition process of a class of independent renewal processes with longrange dependence. It is known that under two different scalings in time and space either fractional Brownian motion or a stable Levy process may arise in the rescaling asymptotic limit. It is shown here that in a third, intermediate scaling regime a new limit process appears, which is neither Gaussian nor stable. The new limit process is characterized by its cumulant generating function and some of its properties are discussed.
A compound model for TCP connection arrivals for
 LAN and WAN applications. Computer Networks, 40(3):319 – 337
, 2002
"... We propose a two level model for TCP connection arrivals in local area networks. The first level are user sessions whose arrival is timevarying Poisson. The second level are connections within a user session. Their number and mean interarrival are independent and biPareto across user session. The ..."
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Cited by 20 (0 self)
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We propose a two level model for TCP connection arrivals in local area networks. The first level are user sessions whose arrival is timevarying Poisson. The second level are connections within a user session. Their number and mean interarrival are independent and biPareto across user session. The interarrivals within a user session are Weibull, and across all users are correlated Weibull. Our model has a small number of parameters which are inferred from real traffic collected a a firewall. We show that traffic synthesized with our model closely characterizes the original data. 1