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 - 2010 Jan

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].",

keywords = "Loss probability, Markovian arrival process, Stationary measure, Stationary probability vector, Wiener-Hopf theory",

author = "Jeongsim Kim and Bara Kim",

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).",

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N2 - 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].

AB - 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

Keywords

ASJC Scopus subject areas

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