19238

Автор(ы): 

Автор(ов): 

1

Параметры публикации

Тип публикации: 

Тезисы доклада

Название: 

Extremes of Time Series with Application to Peer-to-Peer Overlay Networks

Наименование конференции: 

  • The 8th World Congress in Probability and Statistics, Istanbul July 9-14, 2012

Наименование источника: 

  • Proceedings of the 8th World Congress in Probability and Statistics (Istanbul, 2012)

Город: 

  • Istanbul

Издательство: 

  • Kos University

Год издания: 

2012

Страницы: 

159
Аннотация
Extremes of Time Series with Application to Peer-to-Peer Overlay Networks Natalia Michailovna Markovich Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia In practice it is important to evaluate the impact of clusters of exceedances over sufficiently high thresholds. Such exceedances correspond to anomalous observations. The clusters are caused by the dependence of heavy-tail distributed time series. They contain consecutive exceedances of a time series that are separated by return intervals with consecutive observations running below the threshold. A stationary sequence of random variables with some marginal distribution and an extremal index is considered. We derive asymptotically equal distributions of two random variables, namely, the number of exceedances inside clusters and the number of non-exceedances between clusters. After a specific normalization these random variables are shown to be geometrically distributed with a probability depending on the extremal index of the underlying process. The asymptotically equal means of the latter random variables are derived. Sufficiently high quantiles of the underlying process are proposed as required threshold values. The models are validated by autoregressive maxima and moving maxima processes. It is shown that the geometric models fit well the underlying distributions of the latter processes. Moreover, we consider the durations of clusters and return intervals as sums of weakly dependent regularly varying inter-arrival times between events of interest with a positive tail index less than two. We derive upper and lower bounds for the limit distributions of the cluster durations and return intervals between clusters as sums of stable and exponentially distributed components. The achievements are applied to evaluate the quality-of-service metric of a packet stream transmitted by a peer-to-peer overlay network like Skype and IPTV. For this purpose the rates associated with packet transmissions are considered as an underlying time series. The capacity of a channel shared by several active packet streams is regarded as a threshold. A packet will be lost if its associated rate exceeds the capacity. Then the return interval and the cluster duration are interpreted as lossless and lossy periods, respectively.

Библиографическая ссылка: 

Маркович Н.М. Extremes of Time Series with Application to Peer-to-Peer Overlay Networks / Proceedings of the 8th World Congress in Probability and Statistics (Istanbul, 2012). Istanbul: Kos University, 2012. С. 159.