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

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 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

Kim, J., & Kim, B. (2007). Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure. Queueing Systems, 57(1), 47-55. https://doi.org/10.1007/s11134-007-9045-6

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10.1007/s11134-007-9045-6