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Transient properties of many-server queues and related QBDs

Asmussen, S and Pihlsgård, Mats LU (2004) In Queueing Systems 46(3-4). p.249-270
Abstract
The time tau(n) of first passage from queue length x to queue lengthn > x in a many-server queue with both the arrival process and service intensities governed by a finite Markov process is considered. The mean and the Laplace transform are computed as solutions of systems of linear equations coming out by optional stopping of a martingale obtained as a stochastic integral of the exponential Wald martingale for Markov additive processes. Compared to existing techniques for QBD's, the approach has the advantage of being far more efficient for large n.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Levy process, transform, Laplace, Kella-Whitt martingale, heterogeneous servers, passage problem, first, exponential martingale, birth-death process, buffer overflow, MMM/MMM/c queue, Markov additive process, optional stopping
in
Queueing Systems
volume
46
issue
3-4
pages
249 - 270
publisher
Kluwer
external identifiers
  • wos:000221461500004
  • scopus:3543068154
ISSN
0257-0130
DOI
10.1023/B:QUES.0000027986.41904.05
language
English
LU publication?
yes
id
2ddc18e5-7f14-431e-9f1f-48873194d181 (old id 277468)
date added to LUP
2007-10-16 14:09:19
date last changed
2017-01-01 07:28:51
@article{2ddc18e5-7f14-431e-9f1f-48873194d181,
  abstract     = {The time tau(n) of first passage from queue length x to queue lengthn > x in a many-server queue with both the arrival process and service intensities governed by a finite Markov process is considered. The mean and the Laplace transform are computed as solutions of systems of linear equations coming out by optional stopping of a martingale obtained as a stochastic integral of the exponential Wald martingale for Markov additive processes. Compared to existing techniques for QBD's, the approach has the advantage of being far more efficient for large n.},
  author       = {Asmussen, S and Pihlsgård, Mats},
  issn         = {0257-0130},
  keyword      = {Levy process,transform,Laplace,Kella-Whitt martingale,heterogeneous servers,passage problem,first,exponential martingale,birth-death process,buffer overflow,MMM/MMM/c queue,Markov additive process,optional stopping},
  language     = {eng},
  number       = {3-4},
  pages        = {249--270},
  publisher    = {Kluwer},
  series       = {Queueing Systems},
  title        = {Transient properties of many-server queues and related QBDs},
  url          = {http://dx.doi.org/10.1023/B:QUES.0000027986.41904.05},
  volume       = {46},
  year         = {2004},
}