Transient and periodic solution to the time-inhomogeneous quasi-birth death process
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.
quasi-birth-and-death process time-inhomogeneous markov chain queueing model