Abstract
In the past few years a large number of teletraffic measurements have been extensively studied by many contributors. Most of the authors agree on saying that the traffic measured on today’s broadband networks is long-range dependent. Oddly enough these contributors do not question the stationarity of the traffic on these long time scales when the hypothesis of stationarity is essential to speak of long-range dependence. Concurrently it has been demonstrated that some kind of non stationarities in a short-range dependent process can lead, if they are not detected, to the untrue conclusion of long-range dependence.
We prove on the basis of different tests of stationarity that the hypothesis of short range dependence and the hypothesis of stationarity are contradictory on long time-scales. Contrary to many authors who decide in favor of the long-range dependence we propose to model the measured traffic as a locally stationary and markovian process. We exhibit a new markovian model and we show how one can track the varying parameters of this model by means of a recursive maximum likelihood algorithm.
We then generate a non stationary markovian traffic whose varying parameters are matching the parameters of the measured traffic. We verify that the use of a classical visual index of long-range dependence brings to the same conclusion of long-range dependence for the non stationary and markovian model than for the measured traffic.
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Vaton, S., Moulines, E. (1998). A Locally Stationary Semi-Markovian Representation for Ethernet LAN Traffic Data. In: Kühn, P.J., Ulrich, R. (eds) Broadband Communications. BC 1998. IFIP — The International Federation for Information Processing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35378-4_41
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DOI: https://doi.org/10.1007/978-0-387-35378-4_41
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