Kronecker representation and decompositional analysis of closed queueing networks with phase-type service distributions and arbitrary buffer sizes
Author(s)
Advisor
Dayar, TuğrulDate
2007Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
This thesis extends two approximative fixed–point iterative methods based
on decomposition for closed queueing networks (QNs) with Coxian service distributions
and arbitrary buffer sizes from the literature to include phase–type
service distributions. It shows how the irreducible Markov chain associated with
each subnetwork in the decomposition can be represented hierarchically using
Kronecker products. The proposed methods are implemented in a software tool,
which is capable of computing the steady–state probability vector of each subnetwork
by a multilevel method at each fixed–point iteration. The two methods are
compared with others, one being the multilevel method for the closed QN itself,
for accuracy and efficiency on a number of examples using the tool, and their
convergence properties are discussed. Numerical results indicate that there is a
niche among the problems considered which is filled by the two approximative
fixed–point iterative methods.
Keywords
Closed queueing networksPhase–type service distributions
Kronecker representations
Network decomposition
Fixed–point iteration
Multilevel methods