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

Abstract

We consider a finite QBD process with m levels. Assuming that the mean drift is 0, we obtain an asymptotic behavior pi((m))(m) similar to (1/m)c as m -> infinity in the stationary distribution (pi((m))(0), ... , pi((m))(m)), by finding an explicit expression for vector c. 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, Stochastic Models 23 (2007) 79-951. (c) 2007 Elsevier B.V. All rights reserved.