On Matrix-Geometric Solution of Nested QBD Chains

Authors:
Sung Ho Choi;Bara Kim;Khosrow Sohraby;Bong Dae Choi
Affiliations:
Global Standards and Strategy Telecommunication R&D Center, Information & Communication Business, Samsung Electronics Co. LTD Suwon, P.O. Box 105 416, Maetan-3dong, Paldal-gu Suwon-si, Gye ...;School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA bkim@isye.gatech.edu;School of Interdisciplinary Computing and Engineering, University of Missouri-Kansas City, 5100 Rockhill Road, Kansas City, MO 64110-2499, USA sohrabyk@umkc.edu;Telecommunication Mathematics Research Center and Department of Mathematics, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Korea bdchoi@semi.korea.ac.kr
Venue:
Queueing Systems: Theory and Applications
Year:
2003

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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.