Extreme value theory for queues via cycle maxima
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1273193
- author
- Asmussen, Sören LU
- organization
- publishing date
- 1998
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Extremes
- volume
- 1
- issue
- 2
- pages
- 137 - 168
- publisher
- Springer
- 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
- 2016-04-01 16:33:41
- date last changed
- 2018-11-21 20:42:22
@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 = {{Springer}}, series = {{Extremes}}, title = {{Extreme value theory for queues via cycle maxima}}, url = {{http://www.springerlink.com/content/mt6v802523201516/fulltext.pdf}}, volume = {{1}}, year = {{1998}}, }