Asymptotics in the MAP/G/1 Queue with Critical Load |
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Authors: | Jeongsim Kim |
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Institution: | Department of Mathematics Education , Chungbuk National University , Chungbuk , Korea |
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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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Keywords: | Loss probability Markovian arrival process Stationary measure Stationary probability vector Wiener-Hopf theory |
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