Internet traffic exhibits self-similarity and long-range dependence (LRD) on various timescales. A well studied issue is the estimation of statistical parameters characterizing traffic selfsimilarity and LRD, such as the Hurst parameter H. In this paper, we propose to adapt the Modified Allan Variance (MAVAR), a time-domain quantity originally conceived to discriminate fractional noise in frequency stability measurement, to estimate the Hurst parameter of LRD traffic traces and, more generally, to identify fractional noise components in network traffic. This novel method is validated by comparison to one of the best techniques for analyzing self-similar and LRD traffic: the logscale diagram based on wavelet analysis. Both methods are applied to pseudo-random LRD data series, generated with assigned values of H. The superior spectral sensitivity of MAVAR achieves outstanding accuracy in estimating H, even better than the logscale method. The behaviour of MAVAR with most common deterministic signals that yield nonstationarity in data under analysis is also studied. Finally, both techniques are applied to a real IP traffic trace, providing a sound example of the usefulness of MAVAR also in traffic characterization, to complement other established techniques as the logscale method.
NoteThis paper is based in part on ideas presented in the preliminary version "The Modified Allan Variance as Time-Domain Analysis Tool for Estimating the Hurst Parameter of Long-Range Dependent Traffic", by S. Bregni and L.
Clock stability characterization and measurement for telecommunications pose peculiar issues and requirements. This paper aims to provide an overview on this subject. After briefly recalling the background work, the key features and issues of clock stability characterization and measurement in telecommunications are described. The timing signal reference model and the stability quantities adopted in the new international standards are introduced and the impact of the measurement configuration and of the time error sampling period on their behavior are elucidated. The measurement of clock stability in telecommunications is then addressed, and a standard practical measurement procedure is outlined. Several measurement results are provided to support the concepts expounded with experimental evidence. The results shown have been chosen among those obtained throughout the last three years by testing clocks of digital switching exchanges, clocks for synchronous digital hierarchy (SDH) equipment, and state-of-the-art stand-alone slave clocks for synchronization networks. They thus represent a survey of the actual performance of clocks currently deployed in telecommunications networks.
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