Loss rate asymptotics in a GI/G/1 queue with finite buffer
(2005) In Stochastic Models 21(4). p.913-931- Abstract
- We consider the stationary loss rate l(K) of a GI/G/1 queue with finite buffer of size K. Let X-n = U-n - T-n, n >= 1 where U-n is the service time, T-n is the interarrival time and let rho be the traffic intensity. We derive sharp asymptotics for the loss rate as K -> infinity, in the cases (i): rho > 1, and (ii): rho < 1 and X-n non-lattice with light tails. We also look at another reflection, related to Moran's dam model. As an example, we look at the PH/PH/1 case, where we show how to compute the asymptotic loss rate as well as the exact one and illustrate our results numerically.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/211964
- author
- Pihlsgård, Mats LU
- organization
- publishing date
- 2005
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- random walk, phase-type distribution, Lundberg's inequality, Lundberg equation, asymptotics, Cramer-Lundberg approximation, stationary loss rate, reflection
- in
- Stochastic Models
- volume
- 21
- issue
- 4
- pages
- 913 - 931
- publisher
- Taylor & Francis
- external identifiers
-
- wos:000233431400004
- scopus:33644974373
- ISSN
- 1532-6349
- DOI
- 10.1080/15326340500294637
- language
- English
- LU publication?
- yes
- id
- 5092f532-9803-4ca0-b41f-97063dc6b73b (old id 211964)
- date added to LUP
- 2016-04-01 16:29:54
- date last changed
- 2022-01-28 20:06:53
@article{5092f532-9803-4ca0-b41f-97063dc6b73b, abstract = {{We consider the stationary loss rate l(K) of a GI/G/1 queue with finite buffer of size K. Let X-n = U-n - T-n, n >= 1 where U-n is the service time, T-n is the interarrival time and let rho be the traffic intensity. We derive sharp asymptotics for the loss rate as K -> infinity, in the cases (i): rho > 1, and (ii): rho < 1 and X-n non-lattice with light tails. We also look at another reflection, related to Moran's dam model. As an example, we look at the PH/PH/1 case, where we show how to compute the asymptotic loss rate as well as the exact one and illustrate our results numerically.}}, author = {{Pihlsgård, Mats}}, issn = {{1532-6349}}, keywords = {{random walk; phase-type distribution; Lundberg's inequality; Lundberg equation; asymptotics; Cramer-Lundberg approximation; stationary loss rate; reflection}}, language = {{eng}}, number = {{4}}, pages = {{913--931}}, publisher = {{Taylor & Francis}}, series = {{Stochastic Models}}, title = {{Loss rate asymptotics in a GI/G/1 queue with finite buffer}}, url = {{http://dx.doi.org/10.1080/15326340500294637}}, doi = {{10.1080/15326340500294637}}, volume = {{21}}, year = {{2005}}, }