Abstract
We derive the transient distribution and periodic family of asymptotic distributions and the transient and periodic moments for the quasi-birth-and-death processes with time-varying periodic rates. The distributions and moments are given in terms of integral equations involving the related random-walk process. The method is a straight-forward application of generating functions.
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Margolius, B.H. Transient and periodic solution to the time-inhomogeneous quasi-birth death process. Queueing Syst 56, 183–194 (2007). https://doi.org/10.1007/s11134-007-9027-8
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DOI: https://doi.org/10.1007/s11134-007-9027-8