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Exact buffer overflow calculations for queues via martingales

Asmussen, Sören LU ; Jobmann, M and Schwefel, HP (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)
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author
organization
publishing date
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
Kluwer
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
2007-08-07 16:14:31
date last changed
2017-01-01 07:10:52
@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},
  keyword      = {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    = {Kluwer},
  series       = {Queueing Systems},
  title        = {Exact buffer overflow calculations for queues via martingales},
  url          = {http://dx.doi.org/10.1023/A:1019994728099},
  volume       = {42},
  year         = {2002},
}