Asymptotic behavior of a multiplexer fed by a long-range dependent process

Zhen Liu, Philippe Nain, Don Towsley, Zhi Li Zhang

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


In this paper we study the asymptotic behavior of the tail of the stationary backlog distribution in a single server queue with constant service capacity c, fed by the so-called M/G/∞ input process or Cox input process. Asymptotic lower bounds are obtained for any distribution G and asymptotic upper bounds are derived when G is a subexponential distribution. We find the bounds to be tight in some instances, e.g. when G corresponds to either the Pareto or lognormal distribution and c − ρ < 1, where ρ is the arrival rate at the buffer.

Original languageEnglish (US)
Pages (from-to)105-118
Number of pages14
JournalJournal of Applied Probability
Issue number1
StatePublished - Jan 1 1999


  • Asymptotic self-similar process
  • Large deviations
  • Long-range dependence
  • Pareto distribution
  • Queues
  • Subexponential distributions


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