Abstract
To resolve packet conflicts due to limited resources, optical buffers are necessary in all-optical packet-switched networks. Recently, constructing optical buffers directly via optical Switches and fiber Delay Lines (SDL) has attracted a lot of attention. Fault tolerant capability is an important design issue in the constructions of optical buffers from a practical perspective, and such an issue has seldom been theoretically addressed before. In this thesis, we focus on fault tolerant 2-to-1 FIFO multiplexers. We consider a feedback system consisting of an (M +2)×(M +2) optical crossbar switch and M fiber delay lines with delays d1, d2, . . ., dM. In [20], a class of choices of the fiber delays d1, d2, . . ., dM such that the feedback system can still be operated as a 2-to-1 FIFO multiplexer even after up to F of the fibers are broken was provided. To compare various choices of the fiber delays, the construction efficiency was used in [20] as a performance measure for a choice of the fiber delays. In this thesis, we give some new results and observations that could be helpful in solving the conjecture in [20] regarding the closed-form expression of the asymptotic construction efficiency for the optimal choice (in the sense of maximizing the buffer size) of the fiber delays. First, we derive a closed-form expression for n_(ℓ+2)*, the number of fibers with delay 2^(ℓ+1) when the choice of fiber delays is optimal, for some values of F. Furthermore, we show that di* ≧ hi* for all i = 1, 2, . . .,M, where di* (resp. hi* ) denote the sequence of fiber delays given by the optimal choice such that the feedback system can tolerate up to F (resp. F +1) failures of the fiber delay lines. Finally, we give some conjectures which (if true) could be used to obtain the closed-form expression for the asymptotic construction efficiency.