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

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Søren Asmussen  and
Claudia Klüppelberg
Søren Asmussen*
Affiliation:
University of Lund
Claudia Klüppelberg*
Affiliation:
Johannes Gutenberg University
*
∗ Postal address: Department of Mathematical Statistics, University of Lund, Box 118, S-221 00 Lund, Sweden.
∗∗ Postal address: Department of Mathematics, Johannes Gutenberg University, D-55099 Mainz, Germany.
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Abstract

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.

Keywords

EXCURSIONOVERSHOOTQUEUEING THEORYREGULAR VARIATIONPALM THEORYSPATIALLY HOMOGENEOUS PROCESSSUBEXPONENTIAL DISTRIBUTION

MSC classification

Primary: 60G17: Sample path properties 60K25: Queueing theory

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 208 - 212
Copyright
Copyright © Applied Probability Trust 1997 

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