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Extreme value theory for queues via cycle maxima

Asmussen, Sören LU (1998) In Extremes 1(2). p.137-168
Abstract
The present state of extreme value theory for queues is surveyed. The exposition focuses on the regenerative properties of queueing systems, which reduces the problem to the study of the tail of the maximum $overline X( au)$ of the queueing process ${X(t)}$ during a regenerative cycle $ au$. For simple queues, methods for obtaining the distribution of $overline X( au)$ both explicitly and asymptotically are reviewed. In greater generality, the study leads to Wiener-Hopf problems. Extensions to queues in a Markov regime, for example, to those governed by Markov-modulated Poisson arrivals, are also considered.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Extremes
volume
1
issue
2
pages
137 - 168
publisher
Kluwer
ISSN
1572-915X
language
English
LU publication?
yes
id
beb37897-64d4-4c97-bc63-86315d903019 (old id 1273193)
alternative location
http://www.springerlink.com/content/mt6v802523201516/fulltext.pdf
date added to LUP
2008-12-09 14:27:58
date last changed
2016-04-16 04:31:57
@article{beb37897-64d4-4c97-bc63-86315d903019,
  abstract     = {The present state of extreme value theory for queues is surveyed. The exposition focuses on the regenerative properties of queueing systems, which reduces the problem to the study of the tail of the maximum $overline X(	au)$ of the queueing process ${X(t)}$ during a regenerative cycle $	au$. For simple queues, methods for obtaining the distribution of $overline X(	au)$ both explicitly and asymptotically are reviewed. In greater generality, the study leads to Wiener-Hopf problems. Extensions to queues in a Markov regime, for example, to those governed by Markov-modulated Poisson arrivals, are also considered.},
  author       = {Asmussen, Sören},
  issn         = {1572-915X},
  language     = {eng},
  number       = {2},
  pages        = {137--168},
  publisher    = {Kluwer},
  series       = {Extremes},
  title        = {Extreme value theory for queues via cycle maxima},
  volume       = {1},
  year         = {1998},
}