Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times

A. Baltrunas; Daryl J. Daley; C. Klüppelberg

doi:10.1016/j.spa.2004.01.005

Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times

A. Baltrunas, Daryl J. Daley, C. Klüppelberg

Chair of Mathematical Statistics

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

This paper considers a stable GI/GI/1 queue with subexponential service time distribution. Under natural assumptions we derive the tail behaviour of the busy period of this queue. We extend the results known for the regular variation case under minimal conditions. Our method of proof is based on a large deviations result for subexponential distributions.

Original language	English
Pages (from-to)	237-258
Number of pages	22
Journal	Stochastic Processes and their Applications
Volume	111
Issue number	2
DOIs	https://doi.org/10.1016/j.spa.2004.01.005
State	Published - Jun 2004

Keywords

Busy period
GI/GI/1 queue
Precise large deviations
Subexponential distribution
Transient random walk

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10.1016/j.spa.2004.01.005

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title = "Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times",

abstract = "This paper considers a stable GI/GI/1 queue with subexponential service time distribution. Under natural assumptions we derive the tail behaviour of the busy period of this queue. We extend the results known for the regular variation case under minimal conditions. Our method of proof is based on a large deviations result for subexponential distributions.",

keywords = "Busy period, GI/GI/1 queue, Precise large deviations, Subexponential distribution, Transient random walk",

author = "A. Baltrunas and Daley, {Daryl J.} and C. Kl{\"u}ppelberg",

note = "Funding Information: We thank A.P. Zwart as well as P. Jelenkovi{\'c} and P. Mom{\u c}ilovi{\'c} for pre-publication copies of their papers. DJD's work was done mostly at the Munich University of Technology supported by an Alexander von Humboldt Foundation Prize. We thank the referees and editor for their thoughtful attentive comments.",

year = "2004",

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T1 - Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times

AU - Baltrunas, A.

AU - Daley, Daryl J.

AU - Klüppelberg, C.

N1 - Funding Information: We thank A.P. Zwart as well as P. Jelenković and P. Momc̆ilović for pre-publication copies of their papers. DJD's work was done mostly at the Munich University of Technology supported by an Alexander von Humboldt Foundation Prize. We thank the referees and editor for their thoughtful attentive comments.

PY - 2004/6

Y1 - 2004/6

N2 - This paper considers a stable GI/GI/1 queue with subexponential service time distribution. Under natural assumptions we derive the tail behaviour of the busy period of this queue. We extend the results known for the regular variation case under minimal conditions. Our method of proof is based on a large deviations result for subexponential distributions.

AB - This paper considers a stable GI/GI/1 queue with subexponential service time distribution. Under natural assumptions we derive the tail behaviour of the busy period of this queue. We extend the results known for the regular variation case under minimal conditions. Our method of proof is based on a large deviations result for subexponential distributions.

KW - Busy period

KW - GI/GI/1 queue

KW - Precise large deviations

KW - Subexponential distribution

KW - Transient random walk

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U2 - 10.1016/j.spa.2004.01.005

DO - 10.1016/j.spa.2004.01.005

M3 - Article

AN - SCOPUS:2342504595

SN - 0304-4149

VL - 111

SP - 237

EP - 258

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times

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Keywords

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