Abstract
Recently, there has been frequent discussion of whether communication traffic is long-range dependent or not. This paper gives another insight to this issue by discussing the problem of estimating the tail probability P(Q > x) of a Gaussian fluid queue under finite measurement of input processes.
We show that if the mean m and the autocovariance function {Λ(t)}0≤t≤T of an input rate process can be estimated from traffic data of a finite length, P(Q > x) for x in a finite interval can be evaluated by an approximation formula determined only from m, {Λ(t)}0≤t≤T and the output rate c. This result implies that as long as we evaluate P(Q > x) in a finite region of x, it is not important whether the input rate process is long-range dependent or not.
We also apply the approximation formula to the performance evaluation of an ATM multiplexer with VBR Video traffic. We see that Λ(t) can be estimated in a sufficient range to evaluate P(Q > x) for x in the practical range and that the formula provides a good approximation except for a scale parameter.
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© 1998 Springer Science+Business Media Dordrecht
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Kobayashi, K., Takahashi, Y. (1998). Tail Probability of a Gaussian Fluid Queue under Finite Measurement of Input Processes. In: Hasegawa, T., Takagi, H., Takahashi, Y. (eds) Performance and Management of Complex Communication Networks. IFIP — The International Federation for Information Processing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35360-9_3
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DOI: https://doi.org/10.1007/978-0-387-35360-9_3
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