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 real-time traffic, like Markov modulated processes and other multiple time-scale processes. We expect that this new calculus will be of particular interest in the implementation of services providing statistical guarantees.

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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 self-similar processes remains self-similar. Then we show that the self-similar properties will not be altered by any server mechanism (e.g. switch with different scheduling policies). With the above, we can derive the statistical end-to-end delay guarantee for a switched network

Real-time 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 self-similar in nature, it is important to study the problems to see whether the superposition of two self- similar processes retains the property of self-similarity and whether the service of a server changes the self-similarity property of the input traffic. In this paper, we first discusses some definitions and superposition properties of self-similar processes. Then we gives a model of a single server with infinite buffer and prove that when the queue length has finite second-order moment, the input process being strong asymptotically second-order self-similar(sas-s) is equivalent to the output process also bearing the sas-s property. Given the method for determinating the worst case cell delay for an ATM switch with self- similar input traffic, we can determine the end-to-end delay for such real-time communications in an ATM network by summing the cell delay experienced by each of the ATM switch along each connection.