Transient properties of many-server queues and related QBDs
(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:
https://lup.lub.lu.se/record/277468
- author
- Asmussen, S and Pihlsgård, Mats LU
- organization
- publishing date
- 2004
- 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
- Springer
- 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
- 2016-04-01 17:15:53
- date last changed
- 2022-01-29 01:28:03
@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}}, 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}}, language = {{eng}}, number = {{3-4}}, pages = {{249--270}}, publisher = {{Springer}}, 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}}, doi = {{10.1023/B:QUES.0000027986.41904.05}}, volume = {{46}}, year = {{2004}}, }