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Inverting Sampled Traffic
 In Proceedings of the 3rd ACM SIGCOMM conference on Internet measurement
, 2003
"... Routers have the ability to output statistics about packets and flows of packets that traverse them. Since however the generation of detailed tra#c statistics does not scale well with link speed, increasingly routers and measurement boxes implement sampling strategies at the packet level. In this pa ..."
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Cited by 104 (4 self)
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Routers have the ability to output statistics about packets and flows of packets that traverse them. Since however the generation of detailed tra#c statistics does not scale well with link speed, increasingly routers and measurement boxes implement sampling strategies at the packet level. In this paper we study both theoretically and practically what information about the original tra#c can be inferred when sampling, or `thinning', is performed at the packet level. While basic packet level characteristics such as first order statistics can be fairly directly recovered, other aspects require more attention. We focus mainly on the spectral density, a second order statistic, and the distribution of the number of packets per flow, showing how both can be exactly recovered, in theory. We then show in detail why in practice this cannot be done using the traditional packet based sampling, even for high sampling rate. We introduce an alternative flow based thinning, where practical inversion is possible even at arbitrarily low sampling rate. We also investigate the theory and practice of fitting the parameters of a Poisson cluster process, modelling the full packet tra#c, from sampled data.
Modeling and Analysis of PowerTail Distributions via Classical Teletraffic Methods
, 2000
"... e of exponentials The research was performed while this author was a Ph.D student at the Technion  Israel Institute of Technology This work was supported by the Israel Science Foundation administrated by the Academy of Science and Humanities 2 Starobinski and Sidi / Modeling and Analysis of ..."
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Cited by 22 (2 self)
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e of exponentials The research was performed while this author was a Ph.D student at the Technion  Israel Institute of Technology This work was supported by the Israel Science Foundation administrated by the Academy of Science and Humanities 2 Starobinski and Sidi / Modeling and Analysis of PowerTail Distributions 1. Introduction Recent studies have revealed that network trac exhibits burstiness over multiple time scales [15,22]. In many circumstances, powertail probability distributions have been found appropriate for capturing this salient feature (see [19] and references therein). A random variable X has a powertail distribution if its complementary cumulative distribution function (ccdf) F (t) satises F (t) = PrfX > tg ct as t !
Computable convergence rates for subgeometric ergodic Markov chains
 Bernoulli
, 2007
"... Abstract. In this paper, we give quantitative bounds on the ftotal variation distance from convergence of an Harris recurrent Markov chain on an arbitrary under drift and minorisation conditions implying ergodicity at a subgeometric rate. These bounds are then specialized to the stochastically mon ..."
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Cited by 10 (1 self)
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Abstract. In this paper, we give quantitative bounds on the ftotal variation distance from convergence of an Harris recurrent Markov chain on an arbitrary under drift and minorisation conditions implying ergodicity at a subgeometric rate. These bounds are then specialized to the stochastically monotone case, covering the case where there is no minimal reachable element. The results are illustrated on two examples from queueing theory and Markov Chain Monte Carlo.
Fractal Network Traffic Modeling: Past, Present, and Future
 In Proc. 25th Allerton Conference on Communication, Control and Computing
, 1996
"... The discovery of a fractal phenomenon in computer network and compressed packet video traffic has added a new dimension to teletraffic modeling and analysis. But some of the recent research effort on the modeling and analysis of the fractal phenomena have generated results that are seemingly confusi ..."
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Cited by 2 (0 self)
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The discovery of a fractal phenomenon in computer network and compressed packet video traffic has added a new dimension to teletraffic modeling and analysis. But some of the recent research effort on the modeling and analysis of the fractal phenomena have generated results that are seemingly confusing or contradictory. The goal of this study is to correctly digest the recent contributions, examine the current status, and lay out research directions of teletraffic research in the area of fractal network traffic modeling and analysis. By doing so, we hope to provide a unified approach to the understanding of the role and implications of fractal behavior in traffic engineering for emerging networks such as BISDN and Integrated Services Internet. 1 Introduction No one would argue against the claim that the establishment and discovery of a fractal phenomenon in computer network [15, 22, 14] and compressed packet video traffic [9, 2] has added a new dimension to teletraffic modeling and an...
QueueLength Distributions for MultiPriority Queueing Systems
 in IEEE INFOCOM
, 1999
"... The bottleneck in many telecommunication systems has often been modeled by an M/G/1 queueing system with priorities. While the probability generating function for the occupancy distribution of each traffic classes can be readily obtained, the occupancy distributions have been obtainable only rarely. ..."
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Cited by 2 (0 self)
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The bottleneck in many telecommunication systems has often been modeled by an M/G/1 queueing system with priorities. While the probability generating function for the occupancy distribution of each traffic classes can be readily obtained, the occupancy distributions have been obtainable only rarely. However, the occupancy distribution is of great importance, particularly in those cases where the moments are not all finite. We present a method of obtaining the occupancy distribution from the PGF and demonstrate its validity by obtaining the occupancy distributions for a number of cases, including those with regularly varying service time distributions. I. INTRODUCTION The bottleneck in telecommunication systems has often been modeled by an M/G/1 queueing system having nonpreemptive priority service, where the probability generating function (PGF) for the occupancies of the various traffic classes can be obtained using either classical approaches [17] or FuhrmannCooper decomposition [1...
On the Convergence to Fairness in Overloaded FIFO Systems
"... Abstract—Many of today’s computing and communication systems are based on FIFO queues whose performance, e.g., in terms of throughput and fairness, is highly impacted by load fluctuations, especially in the case of shortterm overload. This paper analytically proves that overloaded FIFO queues are f ..."
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Abstract—Many of today’s computing and communication systems are based on FIFO queues whose performance, e.g., in terms of throughput and fairness, is highly impacted by load fluctuations, especially in the case of shortterm overload. This paper analytically proves that overloaded FIFO queues are fair in the sense that each flow or aggregate of flows receives a proportional fair share of the service rate. The convergence rate is evaluated with respect to flow sizes and intensity of overutilization for two broad and distinctive arrival classes: Markovian and heavytailed/selfsimilar. For the former class the paper shows smaller convergence times at higher utilizations, which is exactly the opposite behavior characteristic to underloaded queueing systems. I.
Modeling and analysis of powertail distributions via classical teletraffic methods
, 1999
"... We propose a new methodology for modeling and analyzing powertail distributions, such as the Pareto distribution, in communication networks. The basis of our approach is a fitting algorithm which approximates a powertail distribution by a hyperexponential distribution. This algorithm possesses sev ..."
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We propose a new methodology for modeling and analyzing powertail distributions, such as the Pareto distribution, in communication networks. The basis of our approach is a fitting algorithm which approximates a powertail distribution by a hyperexponential distribution. This algorithm possesses several key properties. First, the approximation can be achieved within any desired degree of accuracy. Second, the fitted hyperexponential distribution depends only on a few parameters. Third, only a small number of exponentials are required in order to obtain an accurate approximation over many time scales. Once equipped with a fitted hyperexponential distribution, we have an integrated framework for analyzing queueing systems with powertail distributions. We consider the GI/G/1 queue with Pareto distributed service time and show how our approach allows to derive both quantitative numerical results and asymptotic closedform results. This derivation shows that classical teletraffic methods can be employed for the analysis of powertail distributions. Keywords: communication networks, GI/G/1 queue, multiple timescale traffic, fitting, heavytail distribution, hyperexponential distribution, mixture of exponentials 1.
SUBMITTED IN TOTAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
, 2004
"... A mes parents, pour leur amour, encouragement et constant support, sans qui rien ne serait. iii This thesis concerns measuring, understanding and modelling Internet traffic. We first study the origins of the statistical properties of Internet traffic, in particular its scaling behaviour, and propose ..."
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A mes parents, pour leur amour, encouragement et constant support, sans qui rien ne serait. iii This thesis concerns measuring, understanding and modelling Internet traffic. We first study the origins of the statistical properties of Internet traffic, in particular its scaling behaviour, and propose a constructive model of packet traffic with physically motivated parameters. We base our analysis on a large amount of empirical data measured on different networks, and use a so called semiexperimental approach to isolate certain features of traffic we seek to model. These results lead to the choice of a particular Poisson cluster process, known as BartlettLewis point process, for a new packet traffic model. This model has a small number of parameters with simple networking meaning, and is mathematically tractable. It allows us to gain valuable insight on the underlying mechanisms creating the observed statistics. In practice, Internet traffic measurements are limited by the very large amount of data generated by high bandwidth links. This leads us to also investigate traffic sampling strate
REQUIREMENTS FOR THE DEGREE OF
, 2004
"... Measuring understanding and modelling internet traffic Terms and Conditions: Terms and Conditions: Copyright in works deposited in Minerva Access is retained by the ..."
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Measuring understanding and modelling internet traffic Terms and Conditions: Terms and Conditions: Copyright in works deposited in Minerva Access is retained by the