Analysis of a QBD process that depends on background QBD processes

Abstract: "We define a class of Markov chains that are called recursive foreground-background quasi-birth-and-death (RFBQBD) processes, and describe approximate (nearly exact) analyses of an RF-BQBD process. An RFBQBD process consists of a foreground QBD process whose transitions depend on the level of a background QBD process, where the transitions of the background QBD process may depend on the level of another background QBD process, and this dependency may be repeated recursively. We also evaluate the running time and accuracy of the analyses numerically by applying them to analyze the performance of a particular task assignment policy in a multiserver system."