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Quasi-birth-and-death processes with level-geometric distribution. (English) Zbl 1012.60068

Quasi birth and death processes are important in the performance evaluation of communication systems [M. F. Neuts, “Structured stochastic matrices of M/G/1 type and their applications” (1989; Zbl 0695.60088)]. The authors consider a special class of homogeneous continuous-time quasi birth and death processes which possess level-geometric distribution where each pair of stationary subvectors that belong to consecutive levels is related by the same scalar. They establish necessary and sufficient conditions for the existence of such a distribution and illustrate with suitable examples.

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
65H10 Numerical computation of solutions to systems of equations
65F05 Direct numerical methods for linear systems and matrix inversion
65F10 Iterative numerical methods for linear systems
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F50 Computational methods for sparse matrices

Citations:

Zbl 0695.60088
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