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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 105 (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.
Regular variation in the mean and stable limits for Poisson shot noise
, 2001
"... Poisson shot noise is a natural generalization of a compound Poisson process when the summands are stochastic processes starting at the points of the underlying Poisson process. We study the limiting behavior of Poisson shot noise when the limits are infinite variance stable processes. In this con ..."
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Cited by 18 (5 self)
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Poisson shot noise is a natural generalization of a compound Poisson process when the summands are stochastic processes starting at the points of the underlying Poisson process. We study the limiting behavior of Poisson shot noise when the limits are infinite variance stable processes. In this context a sufficient condition for this convergence turns up which is closely related to multivariate regular variation. We call it regular variation in the mean. We also show that the latter condition is necessary and sufficient for the weak convergence of the point processes constructed from the normalized noise sequence and also for the weak convergence of its extremes.
A Class of Shot Noise Models for Financial Applications
, 1996
"... We describe a class of nonMarkov shot noise processes that can be used as models for rates of return on securities, exchange rate processes and other processes in finance. These are continuous time processes that can exhibit heavy tails that become lighter when sampling interval increases, clusteri ..."
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Cited by 7 (1 self)
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We describe a class of nonMarkov shot noise processes that can be used as models for rates of return on securities, exchange rate processes and other processes in finance. These are continuous time processes that can exhibit heavy tails that become lighter when sampling interval increases, clustering and long memory. 1 Introduction A "typical" stochastic process fY (t); t 0g can be the logprice process of a particular security S (a stock in particular), the logexchange rate process between major currencies, etc. Understanding of the structure of the random process fY (t); t 0g is of obvious importance, and many researchers in academia as well as those associated with the banking industry have taken a hard look on the data that accumulated throughout the years. Both the properties of the marginal distributions of the process and its dependence structure (in particular, correlations) have been thoroughly discussed, simply because those are the factors that affect the risk associate...
Dependability Issues in Smart Networks
 Proc. 5th IFIP Conference on Intelligence in Networks
, 1999
"... The dependency of society and business on telecommunication services is commonly recognized, but is this conception taken into account in our effort towards smarter and more autonomous networks? The objective of the paper is to discuss some dependability issues in the context of these networks and t ..."
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Cited by 2 (0 self)
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The dependency of society and business on telecommunication services is commonly recognized, but is this conception taken into account in our effort towards smarter and more autonomous networks? The objective of the paper is to discuss some dependability issues in the context of these networks and to pinpoint some challenges. As an introduction, a brief review of dependability concepts is given. Next the following issues are discussed: a) strategies for providing a survivable transport network; b) faulttolerant network nodes vs. faulttolerant functionality on a distributed platform; c) software faults and their consequences like error propagation and network wide failure modes.
Verifying Cell Loss Requirements in HighSpeed Communication Networks
, 1998
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PREDICTION IN A POISSON CLUSTER MODEL
, 2010
"... Abstract. We consider a Poisson cluster model which is motivated by insurance applications. At each claim arrival time, modeled by a point of a homogeneous Poisson process, we start a cluster process which represents the number or amount of payments triggered by the arrival of a claim in a portfolio ..."
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Abstract. We consider a Poisson cluster model which is motivated by insurance applications. At each claim arrival time, modeled by a point of a homogeneous Poisson process, we start a cluster process which represents the number or amount of payments triggered by the arrival of a claim in a portfolio. The cluster process is a Lévy or truncated compound Poisson process. Given the observations on the process over a finite interval we consider the expected value of the number and amount of payments in a future time interval. We also give bounds for the error encountered in this prediction procedure.
AREA ft WORK UNIT NUMBERS
, 1976
"... Approved for public release: distribution unlimited ..."
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Reproduction of all or part of this report is authorized. Prepared by:
, 1916
"... The work reported herein was supported by funds provided directly from ..."
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