On matrix-geometric solution of nested QBD chains
The authors study a nested quasi-birth-and-death (QBD) process, which is a three-dimensional generalization of a QBD process. It is shown that the stationary distribution of the process may be expressed in terms of the fundamental matrices of certain submatrices of the generator of the process, while these fundamental matrices themselves may be expressed in terms of the minimal nonnegative solutions of sets of quadratic matrix equations. An application is given to overload control in communication networks.
scientific article; zbMATH DE number 1896715