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

Jeongsim Kim, Bara Kim

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)157-168
Number of pages12
JournalStochastic Analysis and Applications
Volume28
Issue number1
DOIs
Publication statusPublished - 2010 Jan 1

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Critical Load
Operations research
Stochastic models
Queue
Asymptotic Behavior
Time Reversibility
Stationary Measure
Finite Buffer
Loss Probability
Moment Conditions
Critical Case
Operations Research
Stochastic Model
Generalise
Asymptotic behavior
Time reversibility
Moment conditions
Finite buffer
Stochastic model

Keywords

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

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability

Cite this

Asymptotics in the MAP/G/1 queue with critical load. / Kim, Jeongsim; Kim, Bara.

In: Stochastic Analysis and Applications, Vol. 28, No. 1, 01.01.2010, p. 157-168.

Research output: Contribution to journalArticle

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