Dayar, Tuugrul; Quessette, Franck Quasi-birth-and-death processes with level-geometric distribution. (English) Zbl 1012.60068 SIAM J. Matrix Anal. Appl. 24, No. 1, 281-291 (2002). 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. Reviewer: P.R.Parthasarathy (Chennai / Madras) Cited in 3 Documents 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 Keywords:parallel system; cold standby Citations:Zbl 0695.60088 PDFBibTeX XMLCite \textit{T. Dayar} and \textit{F. Quessette}, SIAM J. Matrix Anal. Appl. 24, No. 1, 281--291 (2002; Zbl 1012.60068) Full Text: DOI