Asymptotics in the MAP/G/1 Queue with Critical Load

Abstract

When the offered load 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 =1 and solves the problem conjectured by Kim et al. [Operations Research Letters 36(2008):127-132].