| Summary: | 碩士 === 國立清華大學 === 通訊工程研究所 === 99 === One of the main problems in all-optical packet-switched networks is the lack of optical buffers, and one feasible technology for the constructions of optical buffers is to use optical crossbar Switches and fiber Delay Lines (SDL). In this thesis, we consider SDL constructions of optical queues with a limited number of recirculations through the optical switches and the fiber delay lines. Such a problem arises from practical feasibility considerations. We show that the constructions of optical linear compressors and optical linear decompressors (special types of optical queues) under a simple packet routing scheme and under the constraint of a limited number of recirculations can be transformed into equivalent integer representation problems under a corresponding constraint. Specifically, we show that the effective maximum delay of a linear compressor/decompressor in our constructions is equal to the maximum representable integer B(d_1^M;k) with respect to d_1^M and k (defined in (1.4) in Chapter 1), where d_1^M=(d_1, d_2,..., d_M) is the sequence of the delays of the M fibers used in our
constructions and k is the maximum number of times that a packet can be routed through the M fibers.
Given M and k, therefore, the problem of finding an optimal construction, in the sense of maximizing the maximum delay, among our constructions of linear compressors/decompressors is equivalent to the problem of finding an optimal sequence in A_M, where A_M is the set of all sequences of fiber delays allowed in our constructions
of linear compressors/decompressors. In this thesis, we consider the class of greedy constructions of 2-to-1 FIFO multiplexers proposed in [16], and extend this class of greedy constructions for the constructions of linear compressors/decompressors. We show that every optimal construction must be a greedy construction.
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