| Summary: | 博士 === 國立交通大學 === 電子工程系所 === 96 === In the first part of this dissertation, we propose a filter-based generator for the synthesization of self-similar traffics. It can produce long range dependent traffics with adjustable levels of bustiness and correlation, and is parsimonious in the number of model parameters. By comparing it with existing self-similar traffic synthesizers, e.g., the RMD and the Paxson IFFT algorithms, the proposed filter-based synthesizer has the advantages that the synthetic traffic can be generated on the fly, and always produces non-negative-valued traffic. The implications between the correlation coefficient (a quantity that only measures the linear dependence) and mutual information (a quantity that can represent the general dependence) is subsequently investigated. The obtained results suggest that for weakly correlated random variables such as two instances of a self-similar process with a long time lag, half the square of the correlation coefficients might be a reasonable approximation to the mutual information.
Continuing from the synthesization of processes with heavy tails, we turn to study the impact of such processes on decentralized detection. Several interesting results are found. Firstly, the optimality of identical sensor system for the exponential distribution family has been verified. A side result along this research line is that
the optimal performance of the serial two-sensor system is the same as that of the parallel two-sensor system for exponential sources. This is somewhat surprising because it is generally considered that the serial two-sensor system has better performance than the parallel two-sensor system.
Secondly, for a more general class of distribution families, we propose several propositions on the optimality of the identical system. A straightforward approach to test the optimality of identical sensor system often results in searching all local minimums in the solution space that is defined through a set of nonlinear equations.
However, this approach is not tractable in certain situations. Our propositions then provide an alternative for optimality test of identical sensor system. Besides, they can be applied to other decentralized detection problems like the detection of lifetime encountered in survival analysis and failure time analysis or the determination of the degree of self-similarity of the whole network system based on geographically dispersed measurements of the packet inter-arrival times on different links.
Finally, with the help of numerical study on functions and equations, we analytically confirm the optimality of identical sensor system over Gaussian sources.
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