Exact overflow asymptotics for queues with many Gaussian inputs

Krzysztof Debicki, M.R.H. Mandjes

Research output: Contribution to journalArticleAcademicpeer-review

32 Citations (Scopus)

Abstract

In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.
Original languageUndefined
Pages (from-to)704-720
Number of pages17
JournalJournal of applied probability
Volume40
Issue number3
DOIs
Publication statusPublished - 2003

Keywords

  • EWI-17782
  • METIS-213638
  • integrated Gaussian process
  • Fluid queue
  • IR-70357
  • Overflow probability
  • Extremes
  • fractional Brownian motion
  • exact asymptotics
  • Gaussian process

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