Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure

Jeongsim Kim; Bara Kim

doi:10.1007/s11134-007-9045-6

Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure

Jeongsim Kim, Bara Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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	https://doi.org/10.1007/s11134-007-9045-6
Publication status	Published - 2007 Sep

Keywords

GI/M/1 type Markov chain
Loss probability
Matrix-valued function
Maximal eigenvalue
Stationary distribution

ASJC Scopus subject areas

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

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title = "Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure",

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.",

keywords = "GI/M/1 type Markov chain, Loss probability, Matrix-valued function, Maximal eigenvalue, Stationary distribution",

author = "Jeongsim Kim and Bara Kim",

note = "Funding Information: This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).",

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AU - Kim, Jeongsim

AU - Kim, Bara

N1 - Funding Information: This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).

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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

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Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure

Abstract

Keywords

ASJC Scopus subject areas

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