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

Jeongsim Kim, Bara Kim

Research output: Contribution to journalArticlepeer-review


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
Issue number1
Publication statusPublished - 2010 Jan


  • 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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