Kronecker-based infinite level-dependent QBDS : matrix analytic solution versus simulation
Author
Orhan, Muhsin Can
Advisor
Dayar, Tuğrul
Date
2011Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
Markovian systems with multiple interacting subsystems under the influence of a
control unit are considered. The state spaces of the subsystems are countably in-
finite, whereas that of the control unit is finite. A recent infinite level-dependent
quasi-birth-and-death (LDQBD) model for such systems is extended by facilitating
the automatic representation and generation of the nonzero blocks in its
underlying infinitesimal generator matrix with sums of Kronecker products. Experiments
are performed on systems of stochastic chemical kinetics having two
or more countably infinite state space subsystems. Results indicate that, albeit
more memory consuming, there are many cases where a matrix analytic solution
coupled with Lyapunov theory yields a faster and more accurate steady-state
measure compared to that obtained with simulation.