2007 12th IEEE Symposium on Computers and Communications
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Abstract

Exponential distributions have traditionally been used to model the traffic (e.g. inter-arrival and service distributions) experienced in computer networks. They are attractive as they are amenable to analysis typically utilised in queueing models. However, modern traffic analysis has shown that many computing workloads are in fact 'heavy-tailed' and highly variable, and are better represented by general distributions such as Log-normal and Pareto. The use of General distributions can make an analytical analysis of some queueing metrics (e.g. waiting time, busy period, slowdown) difficult due to the fact that the Markovian properties of certain stochastic processes in queues are no longer in force. For such distributions Prony 's method can be utilised to fit a series of exponentials to the original General distribution, resulting in a Hyper-exponential distribution that represents the characteristics of the original workload, but is more amenable to analysis. Bounded representations of general distributions (such as Bounded Pareto) are frequently used, but by default, Prony's method is not ideally suited to fitting such distributions. We present two ways of addressing this issue: by normalising the Hyper-exponential resulting from Prony's method between the bounds of the workload distribution being approximated, and by re-evaluating Prony's method to fit directly to a Bounded Hyper-exponential.
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