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51
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 23 (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....
NeymanPearson detection of GaussMarkov signals in noise: Closedform error exponent and properties,” preprint
, 2004
"... Abstract — The performance of NeymanPearson detection of correlated stochastic signals using noisy observations is investigated via the error exponent for the miss probability with a fixed level. Using the statespace structure of the signal and observation model, a closedform expression for the er ..."
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Cited by 22 (11 self)
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Abstract — The performance of NeymanPearson detection of correlated stochastic signals using noisy observations is investigated via the error exponent for the miss probability with a fixed level. Using the statespace structure of the signal and observation model, a closedform expression for the error exponent is derived, and the connection between the asymptotic behavior of the optimal detector and that of the Kalman filter is established. The properties of the error exponent are investigated for the scalar case. It is shown that the error exponent has distinct characteristics with respect to correlation strength: for signaltonoise ratio (SNR)> 1 the error exponent decreases monotonically as the correlation becomes stronger, whereas for SNR < 1 there is an optimal correlation that maximizes the error exponent for a given SNR. I.
Exponential Bounds with Applications to Call Admission
, 1996
"... In this paper we develop a framework for computing upper and lower bounds of an exponential form for a large class of single resource systems with Markov additive inputs. Specifically, the bounds are on quantities such as backlog, queue length, and response time. Explicit or computable expressions f ..."
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Cited by 21 (10 self)
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In this paper we develop a framework for computing upper and lower bounds of an exponential form for a large class of single resource systems with Markov additive inputs. Specifically, the bounds are on quantities such as backlog, queue length, and response time. Explicit or computable expressions for our bounds are given in the context of queueing theory and numerical comparisons with other bounds are presented. The paper concludes with two applications to admission control in multimedia systems. Keywords: Tail distribution; Exponential bound; Large deviation principle; Ergodicity; Markov chain; Matrix analysis; Queues; Markov additive process; Effective bandwidth; Call admission control. P. Nain was supported in part by NSF under grant NCR9116183. This work was done when this author was visiting the University of Massachusetts in Amherst during the academic year 199394. y D. Towsley was supported in part by NSF under grant NCR9116183. 0 1 Introduction We are witnessing a ph...
Fast Simulation of Packet Loss Rates in a Shared Buffer Communications Switch
 ACM Transactions on Modeling and Computer Simulation
, 2001
"... This paper describes an efficient technique for estimating, via simulation, the probability of buffer overows in a queueing model that arises in the analysis of ATM (Asynchronous Transfer Mode) communication switches. There are multiple streams of (autocorrelated) traffic feeding the switch that has ..."
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Cited by 19 (1 self)
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This paper describes an efficient technique for estimating, via simulation, the probability of buffer overows in a queueing model that arises in the analysis of ATM (Asynchronous Transfer Mode) communication switches. There are multiple streams of (autocorrelated) traffic feeding the switch that has a buffer of finite capacity. Each stream is designated as either being of high or low priority. When the queue length reaches a certain threshold, only high priority packets are admitted to the switch's buffer. The problem is to estimate the loss rate of high priority packets. An asymptotically optimal importance sampling approach is developed for this rare event simulation problem. In this approach, the importance sampling is done in two distinct phases. In the first phase, an importance sampling change of measure is used to bring the queue length up to the threshold at which low priority packets get rejected. In the second phase, a different importance sampling change of measure is used to move the queue length from the threshold to the buffer capacity.
Effective Bandwidth in High Speed Digital Networks
 IEEE Journal on Selected Areas in Communications
, 1999
"... The theory of large deviations provides a simple unified basis for statistical mechanics, information theory and queueing theory. The objective of this paper is to use large deviation theory and the Laplace method of integration to provide an simple intuitive overview of the recently developed theor ..."
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Cited by 18 (5 self)
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The theory of large deviations provides a simple unified basis for statistical mechanics, information theory and queueing theory. The objective of this paper is to use large deviation theory and the Laplace method of integration to provide an simple intuitive overview of the recently developed theory of effective bandwidth for high speed digital networks, especially ATM networks. This includes (i) identification of the appropriate energy function, entropy function and effective bandwidth function of a source, (ii) the calculus of the effective bandwidth functions, (iii) bandwidth allocation and buffer management, (iv) traffic descriptors, and (v) envelope processes and conjugate processes for fast simulations and bounds.
Exceptions to the Multifractal Formalism for Discontinuous Measures
, 1997
"... In an earlier paper [MR] the authors introduced the inverse measure y (dt) of a given measure (dt) on [0; 1] and presented the `inversion formula' f y (ff) = fff(1=ff) which was argued to link the respective multifractal spectra of and y . A second paper [RM2] established the formula under ..."
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Cited by 18 (9 self)
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In an earlier paper [MR] the authors introduced the inverse measure y (dt) of a given measure (dt) on [0; 1] and presented the `inversion formula' f y (ff) = fff(1=ff) which was argued to link the respective multifractal spectra of and y . A second paper [RM2] established the formula under the assumption that and y are continuous measures. Here, we investigate the general case which reveals telling details of interest to the full understanding of multifractals. Subjecting selfsimilar measures to the operation 7! y creates a new class of discontinuous multifractals. Calculating explicitly we find that the inversion formula holds only for the `fine multifractal spectra' and not for the `coarse' ones. As a consequence, the multifractal formalism fails for this class of measures. A natural explanation is found when drawing parallels to equilibrium measures. In the context of our work it becomes natural to consider the degenerate Holder exponents 0 and 1.
Large Deviations in the Supercritical Branching Process
, 1993
"... The tail behaviour of the limit of the normalized population size in the simple supercritical branching process, W, is studied. Most of the results concern those cases when a tail of the distribution function of W decays exponentially quickly. In essence, knowledge of the behaviour of transforms can ..."
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Cited by 17 (0 self)
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The tail behaviour of the limit of the normalized population size in the simple supercritical branching process, W, is studied. Most of the results concern those cases when a tail of the distribution function of W decays exponentially quickly. In essence, knowledge of the behaviour of transforms can be combined with some `large deviation' theory to get detailed information on the oscillation of the distribution function of W near zero or at infinity. In particular we show how an old result of Harris (1948) on the asymptotics of the moment generating function of W translates to tail behaviour.
How Fast Does A General Branching Random Walk Spread?
, 1997
"... New results on the speed of spread of the onedimensional spatial branching process are described. Generalizations to the multitype case and to d dimensions are discussed. The relationship of the results with deterministic theory is also indicated. Finally the theory developed is used to reprove s ..."
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Cited by 14 (2 self)
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New results on the speed of spread of the onedimensional spatial branching process are described. Generalizations to the multitype case and to d dimensions are discussed. The relationship of the results with deterministic theory is also indicated. Finally the theory developed is used to reprove smoothly (and improve slightly) results on certain datastorage algorithms arising in computer science.
The Large Deviation Principle For Stochastic Processes
, 2002
"... this paper either #(x) = p 1 x p , for some p > 0 or #(x) = e x 1. We also see that under certain conditions, the rate function in the LDP for some certain stochastic processes has the form I(z) = # # # # # # # # M #(z # (t)) dt, if z(0) = 0 and z is absolutely continuous ot ..."
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Cited by 14 (10 self)
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this paper either #(x) = p 1 x p , for some p > 0 or #(x) = e x 1. We also see that under certain conditions, the rate function in the LDP for some certain stochastic processes has the form I(z) = # # # # # # # # M #(z # (t)) dt, if z(0) = 0 and z is absolutely continuous otherwise
Classspecific quality of service guarantees in multimedia communication networks
, 1999
"... An admission control approach that can provide per class packet loss and delay Quality of Service guarantees is developed. The proposed approach is based on large deviations performance analysis results. We consider the problem of qualityofservice (QoS) provisioning in modern highspeed, multimedi ..."
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Cited by 11 (1 self)
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An admission control approach that can provide per class packet loss and delay Quality of Service guarantees is developed. The proposed approach is based on large deviations performance analysis results. We consider the problem of qualityofservice (QoS) provisioning in modern highspeed, multimedia, communication networks. We quantify QoS by the probabilities of loss and excessive delay of an arbitrary packet, and introduce the model of a multiclass node (switch) which provides network access to users that may belong to multiple service classes. We treat such a node as a stochastic system which we analyze and control. In particular, we develop an analytical approach to estimate both the delay and the buffer overflow probability per service class, based on ideas from large deviations and optimal control. We exploit these performance analysis results by devising a call admission control algorithm which can provide per class QoS guarantees. We compare the proposed approach to alternative worstcase and effective bandwidthbased schemes and argue that it leads to increased efficiency. Finally, we discuss extensions to the network case in order to provide endtoend QoS guarantees.