期刊
STOCHASTIC MODELS
卷 22, 期 1, 页码 77-98出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/15326340500481747
关键词
equilibrium distribution; lattice path counting; matrix-geometric method; quasi-birth-and-death processes; rate matrix
We determine the equilibrium distribution for a class of quasi-birth-and-death (QBD) processes using the matrix-geometric method, which requires the determination of the rate matrix R . In contrast to most QBD processes, the class under consideration allows for an explicit description of R , by exploiting its probabilistic interpretation. We show that the problem of finding each element of R reduces to counting lattice paths in the transition diagram. For resolving this counting problem, we present an extended version of the classical Ballot theorem. We also present various examples of queueing models that fit into the class.
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