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144
Simulation of nonGaussian LongRangeDependent Traffic using Wavelets
, 1999
"... In this paper, we develop a simple and powerful multiscale model for the synthesis of nonGaussian, longrange dependent (LRD) network traffic. Although wavelets effectively decorrelate LRD data, waveletbased models have generally been restricted by a Gaussianity assumption that can be unrealistic f ..."
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Cited by 35 (4 self)
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In this paper, we develop a simple and powerful multiscale model for the synthesis of nonGaussian, longrange dependent (LRD) network traffic. Although wavelets effectively decorrelate LRD data, waveletbased models have generally been restricted by a Gaussianity assumption that can be unrealistic for traffic. Using a multiplicative superstructure on top of the Haar wavelet transform, we exploit the decorrelating properties of wavelets while simultaneously capturing the positivity and "spikiness" of nonGaussian traffic. This leads to a swift O(N) algorithm for fitting and synthesizing Npoint data sets. The resulting model belongs to the class of multifractal cascades, a set of processes with rich statistical properties. We elucidate our model's ability to capture the covariance structure of real data and then fit it to real traffic traces. Queueing experiments demonstrate the accuracy of the model for matching real data. Our results indicate that the nonGaussian nature of traffic has a significant effect on queuing.
Reducedload equivalence and induced burstiness in GPS queues with longtailed traffic flows
 Theory Appl
, 2000
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The Importance of Powertail Distributions for Modeling Queueing Systems
, 1999
"... Powertail distributions are those for which the reliability function is of the form x \Gammaff for large x. Although they look well behaved, they have the singular property that E(X ` ) = 1 for all ` ff. Thus it is possible to have a distribution with an infinite variance, or even an infinite ..."
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Cited by 34 (11 self)
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Powertail distributions are those for which the reliability function is of the form x \Gammaff for large x. Although they look well behaved, they have the singular property that E(X ` ) = 1 for all ` ff. Thus it is possible to have a distribution with an infinite variance, or even an infinite mean. As pathological as these distributions seem to be, they occur everywhere in nature, from the CPU time used by jobs on mainframe computers to sizes of files stored on discs, earthquakes, or even healthinsurance claims. Recently, traffic on the "electronic super highway" was revealed to be of this type, too. In this paper we first describe these distributions in detail and show their suitability to model selfsimilar behavior e.g. of the traffic stated above. Then we show how these distributions can occur in computersystem environments and develop a socalled truncated analytical model that in the limit is powertail. We study and compare the effects on system performance of a GI/M/1 ...
Practical TimeScale Fitting of SelfSimilar Traffic with MarkovModulated Poisson Process
, 2001
"... Recent measurements of packet/cell... In this paper, we first give some definitions of selfsimilarity. Then, we propose a fitting method for the selfsimilar traffic in terms of Markovmodulated Poisson process (MMPP). We construct an MMPP as the superposition of twostate MMPPs and fit it so as to ..."
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Cited by 33 (2 self)
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Recent measurements of packet/cell... In this paper, we first give some definitions of selfsimilarity. Then, we propose a fitting method for the selfsimilar traffic in terms of Markovmodulated Poisson process (MMPP). We construct an MMPP as the superposition of twostate MMPPs and fit it so as to match the variance function over several timescales. Numerical examples show that the variance function of the selfsimilar process can be well represented by that of resulting MMPPs. We also examine the queueing behavior of the resulting MMPP/D/1 queueing systems. We compare the analytical results of MMPP/D/1 with the simulation ones of the queueing system with selfsimilar input.
Application of the Many Sources Asymptotic and Effective Bandwidths to Traffic Engineering
, 1999
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FixedPoint Models for the EndtoEnd Performance Analysis of IP Networks
 IN PROCEEDINGS OF THE 13TH ITC SPECIALIST SEMINAR: IP TRAFFIC MEASUREMENT, MODELING AND MANAGEMENT, SEPT 2000
, 2000
"... This paper presents a new approach to modeling endtoend performance for IP networks. Unlike earlier models, in which end stations generate traffic at a constant rate, the work discussed here takes the adaptive behaviour of TCP/IP into account. The approach is based on a fixed  point method which d ..."
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Cited by 33 (4 self)
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This paper presents a new approach to modeling endtoend performance for IP networks. Unlike earlier models, in which end stations generate traffic at a constant rate, the work discussed here takes the adaptive behaviour of TCP/IP into account. The approach is based on a fixed  point method which determines packet loss, link utilization and TCP throughput across the network. Results are presented for an IP backbone network, which highlight how this new model finds the natural operating point for TCP, which depends on route lengths (via roundtrip times and number of resources), endtoend packet loss and the number of user sessions.
A MeasurementAnalytic Approach for QoS Estimation in a Network Based on the Dominant Time Scale
, 2003
"... In this paper, we describe a measurementanalytic approach for estimating the overflow probability, an important measure of the quality of service (QoS), at a given multiplexing point in the network. A multiplexing point in the network could be a multiplexer or an output port of a switch or router ..."
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Cited by 31 (5 self)
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In this paper, we describe a measurementanalytic approach for estimating the overflow probability, an important measure of the quality of service (QoS), at a given multiplexing point in the network. A multiplexing point in the network could be a multiplexer or an output port of a switch or router where resources such as bandwidth and buffers are shared. Our approach impinges on using the notion of the dominant time scale (DTS), which corresponds to the most probable time scale over which overflow occurs. The DTS provides us with a measurement window for the statistics of the traffic, but is in fact itself defined in terms of the statistics of the traffic over all time. This, in essence, results in a chickenandegg type of unresolved problem. For the DTS to be useful for online measurements, we need to be able to break this chickenandegg cycle, and to estimate the DTS with only a bounded window of time over which the statistics of the traffic are to be measured. In this paper, we present a stopping criterion to successfully break this cycle and find a bound on the DTS. Thus, the result has significant implications for network measurements. Our approach is quite different from other works in the literature that require offline measurements of the entire trace of the traffic. In our case, we need to measure only the statistics of the traffic up to a bound on the DTS. We also investigate the characteristics of this upper bound on the DTS, and provide numerical results to illustrate the utility of our measurement analytic approach.
AFEC: An Adaptive Forward ErrorCorrection Protocol for EndtoEnd Transport of RealTime Traffic
 In Proc. IEEE IC3N
, 1997
"... This paper presents an adaptive protocol for packetlevel forward error correction in dynamic networks. The objective is to facilitate endtoend transporti.e., without special network supportof realtime traffic whose timing constraints rule out the use of retransmissionbased congestion cont ..."
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Cited by 31 (4 self)
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This paper presents an adaptive protocol for packetlevel forward error correction in dynamic networks. The objective is to facilitate endtoend transporti.e., without special network supportof realtime traffic whose timing constraints rule out the use of retransmissionbased congestion control and quality of service (QoS) provision schemes. The degree of redundancy injected into the network is adjusted as a function of network state, decreasing when the network is wellbehaved and increasing when it is not. The control problem is nontrivial due to the fact that increased redundancy, beyond a certain point, can backfire resulting in selfinduced congestion which impedes the timely recovery of information at the receiver. In the first part of the paper, we give a comprehensive analysis of the control problem associated with adaptive forward error correction, concentrating on the dynamics of a particular protocol called Adaptive Forward Error Correction (AFEC). We show that insta...
QoSSensitive Transport of RealTime MPEG Video using Adaptive Redundancy Control
 In Proceedings of IEEE Multimedia Systems
, 2000
"... This paper presents an adaptive endtoend protocol for quality of servicesensitive transport of realtime MPEG video using packetlevel forward error correction in dynamic networks. The objective is to facilitate a userspecified QoS endtoend  i.e., without special network support  for realti ..."
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Cited by 29 (3 self)
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This paper presents an adaptive endtoend protocol for quality of servicesensitive transport of realtime MPEG video using packetlevel forward error correction in dynamic networks. The objective is to facilitate a userspecified QoS endtoend  i.e., without special network support  for realtime MPEG video whose timing constraints rule out the use of retransmissionbased congestion control and QoS provisioning schemes. The degree of redundancy  overcode in forward error correction  injected into the network is adjusted as a function of network state, decreasing when the network is wellbehaved to minimize unnecessary network resource consumption, and increasing when it is not to compensate for adverse network effects so as to maintain an invariant level of endtoend QoS. We describe an adaptive packetlevel FEC protocol called AFEC and analyze its properties with respect to optimality and stability. The optimal control problem is nontrivial due to the fact that increased redundancy, b...
Multiscale queuing analysis of longrangedependent network traffic
 Proc. IEEE INFOCOM
, 2000
"... Abstract—Many studies have indicated the importance of capturing scaling properties when modeling traffic loads; however, the influence of longrange dependence (LRD) and marginal statistics still remains on unsure footing. In this paper, we study these two issues by introducing a multiscale traffic ..."
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Cited by 29 (7 self)
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Abstract—Many studies have indicated the importance of capturing scaling properties when modeling traffic loads; however, the influence of longrange dependence (LRD) and marginal statistics still remains on unsure footing. In this paper, we study these two issues by introducing a multiscale traffic model and a novel multiscale approach to queuing analysis. The multifractal wavelet model (MWM) is a multiplicative, waveletbased model that captures the positivity, LRD, and “spikiness ” of nonGaussian traffic. Using a binary tree, the model synthesizes anpoint data set with only computations. Leveraging the tree structure of the model, we derive a multiscale queuing analysis that provides a simple closed form approximation to the tail queue probability, valid for any given buffer size. The analysis is applicable not only to the MWM but to treebased models in general, including fractional Gaussian noise. Simulated queuing experiments demonstrate the accuracy of the MWM for matching real data traces and the precision of our theoretical queuing formula. Thus, the MWM is useful not only for fast synthesis of data for simulation purposes but also for applications requiring accurate queuing formulas such as call admission control. Our results clearly indicate that the marginal distribution of traffic at different timeresolutions affects queuing and that a Gaussian assumption can lead to overoptimistic predictions of tail queue probability even when taking LRD into account. I.