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Title: "Polling networks with limited Service policies and Wavelet-based information fusion and dimension reduction"
Advisor: Dr. Brani Vidakovic
Co-advisor: Dr. Douglas G. Down
Summary
The thesis is comprised of two research topics.
Polling models with limited service policies is featured in the first part, while some theoretical and applied
aspects of wavelets are highlighted in the second part of the dissertation.
In the first topic, we find sharp asymptotic expressions for the event that the total queue length is large for a $k_i$-limited
exponential polling model with equal service rates and $N$ classes of customer. It is found that this behavior can be classified into
$N$ very different regimes, depending on the arrival rates to the system. Based on these analytical results we provide heuristics
for optimally choosing $k_i$ values to provide a given level of quality of service to $n$ classes while giving best effort to the
remaining $N-n$ classes.
In the second part, a novel type of wavelet shrinkage and wavelet-based binary linear classifiers are proposed and
investigated.
For the wavelet shrinkage, we propose a wavelet-based shrinkage estimation of a single data component of interest or base-line
signal, combining the information from the rest of multivariate components. This incorporation of information is done via
Stein-type shrinkage rule resulting from an Empirical Bayes argument. The proposed shrinkage estimators maximize the
predictive density under appropriate model assumptions on the wavelet coefficients.
For the wavelet-based binary linear classifier, we consider wavelet-based binary linear classifiers. Both consistency results
and implementation issues are addressed. We show that under mild assumptions on the design density wavelet discrimination rules are
$L_2$-consistent.
