Derivations of error bound on recording traffic time series with long-range dependence

Abstract

Measurement of traffic time series plays a key role in the research of communication networks though theoretic research has a considerable advances. Differing from analytical analysis, quantities of interest are estimates experimentally analyzed from measured real life data. Hence, accuracy should be taken into account from a view of engineering. In practical terms, it is inappropriate to record data series that is either too short or over-long as too short record may not provide enough data to achieve a given degree of accuracy of an estimate while over-long record is usually improper for real-time applications. Consequently, error analysis based on record length has practical significance. This paper substantially extends our previous work [20,21] by detailing the derivations of error bound relating to record length and the Hurst parameter of a long-range dependent fractional Gaussian noise and by interpreting the effects of long-range dependence on record length. In addition, a theoretical evaluation of some widely used traces in the traffic research is also given. © Springer-Verlag Berlin Heidelberg 2005.