Loss rate asymptotics in a GI/G/1 queue with finite buffer
(2005) In Stochastic Models 21(4). p.913931 Abstract
 We consider the stationary loss rate l(K) of a GI/G/1 queue with finite buffer of size K. Let Xn = Un  Tn, n >= 1 where Un is the service time, Tn 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 Xn nonlattice 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:
http://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, phasetype distribution, Lundberg's inequality, Lundberg equation, asymptotics, CramerLundberg 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
 15326349
 DOI
 10.1080/15326340500294637
 language
 English
 LU publication?
 yes
 id
 5092f53298034ca0b41f97063dc6b73b (old id 211964)
 date added to LUP
 20070816 14:53:32
 date last changed
 20170101 07:06:56
@article{5092f53298034ca0b41f97063dc6b73b, abstract = {We consider the stationary loss rate l(K) of a GI/G/1 queue with finite buffer of size K. Let Xn = Un  Tn, n >= 1 where Un is the service time, Tn 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 Xn nonlattice 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 = {15326349}, keyword = {random walk,phasetype distribution,Lundberg's inequality,Lundberg equation,asymptotics,CramerLundberg approximation,stationary loss rate,reflection}, language = {eng}, number = {4}, pages = {913931}, 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}, }