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Loss rate asymptotics in a GI/G/1 queue with finite buffer

Pihlsgård, Mats LU (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:
author
organization
publishing date
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
2007-08-16 14:53:32
date last changed
2017-01-01 07:06:56
@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 &gt;= 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 -&gt; infinity, in the cases (i): rho &gt; 1, and (ii): rho &lt; 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},
  keyword      = {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},
  volume       = {21},
  year         = {2005},
}