Asymptotic behavior of the stationary distribution in a finite QBD process with zero mean drift

We consider a finite QBD process with mm levels. Assuming that the mean drift is 0, we obtain an asymptotic behavior πm(m)∼(1/m)c as m→∞m→∞ in the stationary distribution (π0(m),…,πm(m)), by finding an explicit expression for vector cc. This solves the problem that was conjectured by Miyazawa et al. [Asymptotic behaviors of the loss probability for a finite buffer queue with QBD structure, StochasticModels 23 (2007) 79–9579–95].