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Stochastically Bounded Burstiness for Communication Networks
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1999
"... We develop a network calculus for processes whose burstiness is stochastically bounded by general decreasing functions. This calculus enables us to prove the stability of feedforward networks and obtain statistical upper bounds on interesting performance measures such as delay, at each buffer in the ..."
Abstract

Cited by 57 (4 self)
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We develop a network calculus for processes whose burstiness is stochastically bounded by general decreasing functions. This calculus enables us to prove the stability of feedforward networks and obtain statistical upper bounds on interesting performance measures such as delay, at each buffer in the network. Our bounding methodology is useful for a large class of input processes, including important processes exhibiting "subexponentially bounded burstiness" such as fractional Brownian motion. Moreover, it generalizes previous approaches and provides much better bounds for common models of realtime traffic, like Markov modulated processes and other multiple timescale processes. We expect that this new calculus will be of particular interest in the implementation of services providing statistical guarantees.
Quality Of Service In High Speed Networks With Multiple TimeScale Traffic
 PH.D. DISSERTATION
, 1999
"... ..."
The Statistical EndtoEnd Delay Guarantee for Networks with Selfsimilar Traffic
, 2003
"... this paper, we further extend our statistical delay analysis to cover the entire network. We first show that the superposition of two selfsimilar processes remains selfsimilar. Then we show that the selfsimilar properties will not be altered by any server mechanism (e.g. switch with different ..."
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this paper, we further extend our statistical delay analysis to cover the entire network. We first show that the superposition of two selfsimilar processes remains selfsimilar. Then we show that the selfsimilar properties will not be altered by any server mechanism (e.g. switch with different scheduling policies). With the above, we can derive the statistical endtoend delay guarantee for a switched network
Some New Findings on the Selfsimilarity Property in Communications Networks and on Statistical Endtoend Delay Guarantee
"... Realtime communication requires performance guarantee from the underlying network. In order to analyse the network performance, we must find the traffic characterization in every server of the network. Due to the strong experimental evidence that network traffic is selfsimilar in nature, it is imp ..."
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Realtime communication requires performance guarantee from the underlying network. In order to analyse the network performance, we must find the traffic characterization in every server of the network. Due to the strong experimental evidence that network traffic is selfsimilar in nature, it is important to study the problems to see whether the superposition of two self similar processes retains the property of selfsimilarity and whether the service of a server changes the selfsimilarity property of the input traffic. In this paper, we first discusses some definitions and superposition properties of selfsimilar processes. Then we gives a model of a single server with infinite buffer and prove that when the queue length has finite secondorder moment, the input process being strong asymptotically secondorder selfsimilar(sass) is equivalent to the output process also bearing the sass property. Given the method for determinating the worst case cell delay for an ATM switch with self similar input traffic, we can determine the endtoend delay for such realtime communications in an ATM network by summing the cell delay experienced by each of the ATM switch along each connection.