We solve for the asymptotic periodic distribution of the continuous time quasi-birth-and-death process with time-varying periodic rates in terms of R^ and G^ matrix functions which are analogues of the R and G matrices of matrix analytic methods. We evaluate these QBDs numerically by solving for R^ numerically.
Margolius, Barbara H., "The Matrices R and G of Matrix Analytic Methods and The Time-Inhomogeneous Periodic Quasi-Birth-and-Death Process" (2008). Mathematics Faculty Publications. 238.
The final publication is available at Springer via http://dx.doi.org/10.1007/s11134-008-9090-9