Computer Science Department
School of Computer Science, Carnegie Mellon University
Analysis of a QBD Process that Depends on
Background QBD Processes
Takayuki Osogami
September 2004
CMU-CS-04-163.ps
CMU-CS-04-163.pdf
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 RFBQBD
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.
27 pages
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