Abstract
This paper discusses the asymptotic behavior of the loss probability for general queues with finite GI/M/1 type structure such as GI/M/c/K, SM/M/1/K and GI/MSP/1/K queues. We find an explicit expression for the asymptotic behavior of the loss probability as K tends to infinity. With the result, it is shown that the loss probability tends to 0 at a geometric rate.
| Original language | English |
|---|---|
| Pages (from-to) | 47-55 |
| Number of pages | 9 |
| Journal | Queueing Systems |
| Volume | 57 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2007 Sep 1 |
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Keywords
- GI/M/1 type Markov chain
- Loss probability
- Matrix-valued function
- Maximal eigenvalue
- Stationary distribution
ASJC Scopus subject areas
- Computer Science Applications
- Computational Theory and Mathematics
- Management Science and Operations Research
Cite this
Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure. / Kim, Jeongsim; Kim, Bara.
In: Queueing Systems, Vol. 57, No. 1, 01.09.2007, p. 47-55.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure
AU - Kim, Jeongsim
AU - Kim, Bara
PY - 2007/9/1
Y1 - 2007/9/1
N2 - This paper discusses the asymptotic behavior of the loss probability for general queues with finite GI/M/1 type structure such as GI/M/c/K, SM/M/1/K and GI/MSP/1/K queues. We find an explicit expression for the asymptotic behavior of the loss probability as K tends to infinity. With the result, it is shown that the loss probability tends to 0 at a geometric rate.
AB - This paper discusses the asymptotic behavior of the loss probability for general queues with finite GI/M/1 type structure such as GI/M/c/K, SM/M/1/K and GI/MSP/1/K queues. We find an explicit expression for the asymptotic behavior of the loss probability as K tends to infinity. With the result, it is shown that the loss probability tends to 0 at a geometric rate.
KW - GI/M/1 type Markov chain
KW - Loss probability
KW - Matrix-valued function
KW - Maximal eigenvalue
KW - Stationary distribution
UR - http://www.scopus.com/inward/record.url?scp=35548951896&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=35548951896&partnerID=8YFLogxK
U2 - 10.1007/s11134-007-9045-6
DO - 10.1007/s11134-007-9045-6
M3 - Article
VL - 57
SP - 47
EP - 55
JO - Queueing Systems
JF - Queueing Systems
SN - 0257-0130
IS - 1
ER -