Abstract
In this paper, a generalization of the level dependent Quasi-Birth-and-Death (QBD) chains is presented. We analyze nested level dependent QBD chains and provide the complete characterization of their fundamental matrices in terms of minimal non-negative solutions of a number of matrix quadratic equations. Our results provide mixed matrix-geometric solution for the stationary distribution of nested QBD chains. Applications in overload control in communication networks are also discussed.
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Choi, S.H., Kim, B., Sohraby, K. et al. On Matrix-Geometric Solution of Nested QBD Chains. Queueing Systems 43, 5–28 (2003). https://doi.org/10.1023/A:1021884213344
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DOI: https://doi.org/10.1023/A:1021884213344