Exact buffer overflow calculations for queues via martingales
(2002) In Queueing Systems 42(1). p.63-90- Abstract
- Let tau(n) be the first time a queueing process like the queue length or workload exceeds a level n. For the M/M/1 queue length process, the mean Etaun and the Laplace transform Ee(-staun) is derived in closed form using a martingale introduced in Kella and Whitt (1992). For workload processes and more general systems like MAP/PH/1, we use a Markov additive extension given in Asmussen and Kella (2000) to derive sets of linear equations determining the same quantities. Numerical illustrations are presented in the framework of M/M/1 and MMPP/M/1 with an application to performance evaluation of telecommunication systems with long-range dependent properties in the packet arrival process. Different approximations that are obtained from... (More)
- Let tau(n) be the first time a queueing process like the queue length or workload exceeds a level n. For the M/M/1 queue length process, the mean Etaun and the Laplace transform Ee(-staun) is derived in closed form using a martingale introduced in Kella and Whitt (1992). For workload processes and more general systems like MAP/PH/1, we use a Markov additive extension given in Asmussen and Kella (2000) to derive sets of linear equations determining the same quantities. Numerical illustrations are presented in the framework of M/M/1 and MMPP/M/1 with an application to performance evaluation of telecommunication systems with long-range dependent properties in the packet arrival process. Different approximations that are obtained from asymptotic theory are compared with exact numerical results. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/329957
- author
- Asmussen, Sören LU ; Jobmann, M and Schwefel, HP
- organization
- publishing date
- 2002
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- regenerative, queue length, power tail, martingale, Markov-modulation, local time, Levy process, exponential martingale, extreme value theory, process, Wald martingale
- in
- Queueing Systems
- volume
- 42
- issue
- 1
- pages
- 63 - 90
- publisher
- Springer
- external identifiers
-
- wos:000177630100003
- scopus:0036362030
- ISSN
- 0257-0130
- DOI
- 10.1023/A:1019994728099
- language
- English
- LU publication?
- yes
- id
- 25f15bb0-f8d7-4546-95f2-df4e7391b9b3 (old id 329957)
- date added to LUP
- 2016-04-01 16:38:37
- date last changed
- 2022-04-22 23:28:57
@article{25f15bb0-f8d7-4546-95f2-df4e7391b9b3,
abstract = {{Let tau(n) be the first time a queueing process like the queue length or workload exceeds a level n. For the M/M/1 queue length process, the mean Etaun and the Laplace transform Ee(-staun) is derived in closed form using a martingale introduced in Kella and Whitt (1992). For workload processes and more general systems like MAP/PH/1, we use a Markov additive extension given in Asmussen and Kella (2000) to derive sets of linear equations determining the same quantities. Numerical illustrations are presented in the framework of M/M/1 and MMPP/M/1 with an application to performance evaluation of telecommunication systems with long-range dependent properties in the packet arrival process. Different approximations that are obtained from asymptotic theory are compared with exact numerical results.}},
author = {{Asmussen, Sören and Jobmann, M and Schwefel, HP}},
issn = {{0257-0130}},
keywords = {{regenerative; queue length; power tail; martingale; Markov-modulation; local time; Levy process; exponential martingale; extreme value theory; process; Wald martingale}},
language = {{eng}},
number = {{1}},
pages = {{63--90}},
publisher = {{Springer}},
series = {{Queueing Systems}},
title = {{Exact buffer overflow calculations for queues via martingales}},
url = {{http://dx.doi.org/10.1023/A:1019994728099}},
doi = {{10.1023/A:1019994728099}},
volume = {{42}},
year = {{2002}},
}