Tail approximation in models that involve long range dependence: The distribution of overflows

Benjamin Yakir*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Long range dependence in stationary processes of increments corresponds to the situations where the variance of cumulative sums is dominated by the accumulation of the covariances between increments. The Hurst parameter, the exponent of the standard deviation of the sum as a function of the number of increments involved, is a characteristic of long range dependence. Models of long range dependence, models that involve an Hurst parameter 0:5 < H < 1, are frequently used to model the incoming workload in computer networks and communication. Consider a Gaussian arrival process with long range dependence, a buffer, and a departure process bounded by the bandwidth. This paper present an analytical approximations of the probability of a buffer overflow within a given time interval. The analysis uses and demonstrates a measure-transformation technique.

Original languageAmerican English
Pages (from-to)1657-1672
Number of pages16
JournalStatistica Sinica
Volume23
Issue number4
DOIs
StatePublished - Jul 2013

Keywords

  • Cusum
  • Likelihood-ratio identity
  • Long-range dependence
  • Maxima of a random field
  • Overshoot correction

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