1 results
Stationary M/G/1 excursions in the presence of heavy tails
- Part of
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- Journal:
- Journal of Applied Probability / Volume 34 / Issue 1 / March 1997
- Published online by Cambridge University Press:
- 14 July 2016, pp. 208-212
- Print publication:
- March 1997
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- Article
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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
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.
of subexponential distributions are asymptotically of two types as 