Transient and periodic solution to the time-inhomogeneous quasi-birth death process

Authors:
B. H. Margolius
Affiliations:
Department of Mathematics, Cleveland State University, Cleveland, USA 44114-2214
Venue:
Queueing Systems: Theory and Applications
Year:
2007

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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.