| 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 ki-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 ki 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 classifiers, we show good classification performance by using wavelet regularization. We address both consistency results and implementation issues of these classifiers. We show that under mild assumptions these design density wavelet discrimination rules are L 2-consistent. |
