| Summary: | 博士 === 國立交通大學 === 應用數學系 === 91 === For nonblocking switching networks, there are different levels of nonblockingness: strictly (SNB), wide-sense (WSNB), and rearrangeable (RNB). Traditionally, the blocking condition of classical networks occurs when two connections are attempting to use the same links. However, due to the limitation of current optical technology, researchers studies different blocking conditions for optical switching networks. One of the most important blocking conditions is the node-blocking condition, which reflects the crosstalk-free constraint by using directional couplers as switching elements.
In this thesis, we study the degree of blockingness for classical strictly nonblocking networks. By extending the definition of the degree of blockingness, we also study the degree of node-blockingness, which is used for crosstalk-free networks. Further, we give a simple argument to transform classical SNB (RNB) results to crosstalk-free results. At the same time, we also give some new results.
Besides studying the nonblockingness in the literature, we also study a new class of nonblocking networks called noninterruptive rearrangeable (NIR) networks, which are rearrangeable under the additional condition that existing connections are not interrupted while their paths are rerouted. In this thesis, we give a complete characterization of NIR Clos networks built of switching elements of various nonblocking properties. Our approaches provide recursive constructions of NIR networks, and thus deduce many cost-efficient NIR networks. We also give comparisons between our constructions and previous known results.
In 1973, Bassalygo proposed an idea to rearrange existing connections for RNB Clos networks that can connect requests with fewer rearrangements. He claimed an upper bound of the rearrangements and gave an outline of proof but no detail. In this thesis, we give a series of examples invalidating his upper bound and also give a new upper bound. Further, we modify the routing algorithm to fit NIR networks.
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