Asymptotics in the MAP/G/1 queue with critical load

Jeongsim Kim; Bara Kim

doi:10.1080/07362990903415866

Asymptotics in the MAP/G/1 queue with critical load

Jeongsim Kim, Bara Kim

Department of Mathematics

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

Abstract

When the offered load ρ is 1, we investigate the asymptotic behavior of the stationary measure for the MAP/G/1 queue and the asymptotic behavior of the loss probability for the finite buffer MAP/G/1/K + 1 queue. Unlike Baiocchi [Stochastic Models 10(1994):867-893], we assume neither the time reversibility of the MAP nor the exponential moment condition for the service time distribution. Our result generalizes the result of Baiocchi for the critical case ρ = 1 and solves the problem conjectured by Kim et al. [Operations Research Letters 36(2008):127-132].

Original language	English
Pages (from-to)	157-168
Number of pages	12
Journal	Stochastic Analysis and Applications
Volume	28
Issue number	1
DOIs	https://doi.org/10.1080/07362990903415866
Publication status	Published - 2009

Bibliographical note

Funding Information:
Received March 5, 2009; Accepted June 22, 2009 This research was supported by a Korea University Grant and 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).

Keywords

Loss probability
Markovian arrival process
Stationary measure
Stationary probability vector
Wiener-Hopf theory

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1080/07362990903415866

Cite this

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abstract = "When the offered load ρ is 1, we investigate the asymptotic behavior of the stationary measure for the MAP/G/1 queue and the asymptotic behavior of the loss probability for the finite buffer MAP/G/1/K + 1 queue. Unlike Baiocchi [Stochastic Models 10(1994):867-893], we assume neither the time reversibility of the MAP nor the exponential moment condition for the service time distribution. Our result generalizes the result of Baiocchi for the critical case ρ = 1 and solves the problem conjectured by Kim et al. [Operations Research Letters 36(2008):127-132].",

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Asymptotics in the MAP/G/1 queue with critical load

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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