Abstract — Despite all the recent advances in the mathematical theories for constructing optical queues by optical Switches and fiber Delay Lines (SDL), there are still many problems that need to be resolved. In this paper, we tackle the following problems: (i) is it possible to construct optical queues with switches of arbitrary sizes? (ii) is there a general theory that unifies many constructions of optical queues with known packet delays? and (iii) under what conditions can a concatenation of optical queues allow overtaking? For the first problem, we propose a new class of optical memory cells that can be made by switches of arbitrary sizes. Moreover, we propose the generalized C-transform for routing packets through such optical memory cells. For the second problem, we introduce a new class of optical queues, including FIFO, LIFO and absolute contractors. We show that both linear compressors in  and FIFO multiplexers (with multiple inputs) in ,  are special cases of contractors. An interesting finding is that overtaking can occur in LIFO and absolute contractors. I
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