The matrices R and G of matrix analytic methods and the time-inhomogeneous periodic Quasi-Birth-and-Death process

Authors:
B. H. Margolius
Affiliations:
Department of Mathematics, Cleveland State University, Cleveland, USA 44114-2214
Venue:
Queueing Systems: Theory and Applications
Year:
2008

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Abstract

We solve for the asymptotic periodic distribution of the continuous time quasi-birth-and-death process with time-varying periodic rates in terms of $\hat{\mathbf{R}}$ and $\hat{\mathbf{G}}$ matrix functions which are analogues of the R and G matrices of matrix analytic methods. We evaluate these QBDs numerically by solving for $\hat{\mathbf{R}}$ numerically.