On Optimal Constructions of 2-to-1 FIFO Multiplexers With a Limited Number of Recirculations

Abstract

Recently, constructing queues for optical packet switching has received a lot of attention in the literature. Such a research interest mainly originates from the lack of optical buffers in optical packet switching networks. The only known way to store optical packets without converting them into other media is to use switched delay lines (SDL). Theoretical SDL constructions have been reported for various types of optical queues, including output-buffered switches, First-in-first-out (FIFO) multiplexers, FIFO queues, last-in-first-out (LIFO) queues, priority queues, linear compressors, non-overtaking delay lines, and flexible delay lines. In this thesis, we focus on finding optimal constructions (in the sense of maximizing the buffer size) of optical 2-to-1 FIFO multiplexers by using a feedback system consisting of an (M + 2)x(M + 2) optical crossbar switch and M fiber delay lines under a simple packet routing policy and under the limitation that each optical packet can be recirculated through the M fibers at most k times. Such a limitation on the number of recirculations comes from practical feasibility considerations. Under such a setting, it has been shown by Cheng et al. that an optimal construction belongs to a class of greedy constructions. Our contribution in this thesis is to show that an optimal construction could be found in a much smaller subset of the original class of greedy constructions. As a result, the complexity of searching for an optimal construction could be reduced from O(M^(k-1)) (which grows with the switch size), to O(1)(which does not grow with the switch size).