Stationary M/G/1 excursions in the presence of heavy tails

Søren Asmussen, Claudia Klüppelberg

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11 Scopus citations


It is shown that the stationary excursions above level x for the stationary M/G/1 queue with the service time distribution belonging to a certain class ℐ* of subexponential distributions are asymptotically of two types as x → ∞: either the excursion starts with a jump from a level which is O(1) and the initial excess over x converges to ∞ or it starts from a level of the form x - O(1) and the excess has a proper limit distribution. The two types occur with probabilities ρ, resp. 1 - ρ.

Original languageEnglish
Pages (from-to)208-212
Number of pages5
JournalJournal of Applied Probability
Issue number1
StatePublished - Mar 1997
Externally publishedYes


  • Excursion
  • Overshoot
  • Palm theory
  • Queueing theory
  • Regular variation
  • Spatially homogeneous process
  • Subexponential distribution


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