Paper Info
Title
A sufficient condition for the subexponential asymptotics of GI/G/1-type Markov chains with queueing applications
Abstract
The main contribution of this paper is to present a new sufficient condition for the subexponential asymptotics of the stationary distribution of a GI/G/1-type Markov chain with the stochastic phase transition matrix in non-boundary levels, which implies no possibility of jumps from level “infinity” to level zero. For simplicity, we call such Markov chains because they are used to analyze semi-Markovian queues without “disasters”, which are negative customers who remove all the customers in the system (including themselves) on their arrivals. We first demonstrate the application of our main result to the stationary queue length distribution in the standard BMAP/GI/1 queue. Thereby we present new asymptotic formulas and derive the existing formulas under weaker conditions than those in the literature. We also apply our main result to the stationary queue length distributions in two queues: One is a MAP//1 queue with the -bulk-service rule (i.e., MAP//1 queue); and the other is a MAP//1 retrial queue with constant retrial rate.
Year
DOI
Venue
2016
https://doi.org/10.1007/s10479-015-1893-6
Annals of Operations Research
Keywords
Field
DocType
Subexponential asymptotics,GI/G/1-type Markov chain,Disaster,BMAP/GI/1 queue,Bulk-service queue,Retrial queue,60K25,60J10
M/M/1 queue,Discrete mathematics,Mathematical optimization,Bulk queue,G/G/1 queue,M/M/c queue,M/G/1 queue,M/G/k queue,Burke's theorem,M/D/c queue,Mathematics
Journal
Volume
Issue
ISSN
247
1
0254-5330
Citations 
PageRank 
References 
0
0.34
4
Authors
1
Name
Order
Citations
PageRank
Hiroyuki Masuyama18611.53