QBD processes provided a useful tool in the study of stochastic models, such as queueing systems, manufacturing systems and computer networks. Chapter 3 of Neuts [1981] gave a complete picture of a level independent QBD process. Latouche and Ramaswami [1993] gave a logarithmic reduction algorithm for the rate matrix. Ramaswami [1996] gave an excellent overview for the QBD processes. Bright and Taylor [1995] provided effective algorithms for computation of level dependent QBD processes. Naoumov [1996] proposed an algebraically matrix-multiplicative approach to study the stationary probability vector of a QBD process. Ramaswami and Taylor [1996] discussed useful properties of the rate operator in a level dependent QBD processes with a countable number of phases. Li and Cao [2004] gave two types of RG-factorizations, which lead to a unified and complete framework to deal with stationary (or transient) solution to performance of various QBD processes. Li and Liu [2005] provided a sensitivity analysisfor a perturbed QBD process. Nielsen and Ramaswami [1997] and Li and Lin [2006] studied QBD processes with continuous phases.

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QBD processes with either finitely-many levels or infinitely-many levels have provided a useful mathematical tool in the study of stochastic models, such as queueing systems, manufacturing systems and computer networks. Chapter 3 of Neuts [1981] gave a complete picture of level independent QBD processes. Li's 2010 book provides a detailed analysis for level dependent QBD processes and various useful generalized models.
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QBD processes