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

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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.

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  1. Department of Mathematics, Cleveland State University, 1515 Rhodes Tower, 2121 Euclid Ave., Cleveland, OH, 44114-2214, USA

    B. H. Margolius

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  1. B. H. Margolius
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Correspondence to B. H. Margolius.

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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

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