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The matrices R and G of matrix analytic methods and the time-inhomogeneous periodic Quasi-Birth-and-Death process

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Abstract

We solve for the asymptotic periodic distribution of the continuous time quasi-birth-and-death process with time-varying periodic rates in terms of \(\hat{\mathbf{R}}\) and \(\hat{\mathbf{G}}\) matrix functions which are analogues of the R and G matrices of matrix analytic methods. We evaluate these QBDs numerically by solving for \(\hat{\mathbf{R}}\) numerically.

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  1. Department of Mathematics, Cleveland State University, 1515 Rhodes Tower, 2121 Euclid Avenue, 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. The matrices R and G of matrix analytic methods and the time-inhomogeneous periodic Quasi-Birth-and-Death process. Queueing Syst 60, 131–151 (2008). https://doi.org/10.1007/s11134-008-9090-9

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  • DOI: https://doi.org/10.1007/s11134-008-9090-9

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