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This paper considers a packet multiplexer (resp. de multiplexer) in the form of a queue with a single time-multiplexed input (resp. output) line, which is called a multiplexing queue (resp. demultiplexing queue). This queue is abstractly formulated in a way that allows recursive construction via 2-stage interconnection. The theoretic underpinning of this recursive construction is the preservation of two types of conditionally nonblocking switches through two versions of the 2-stage interconnection network. The recursive construction of a mux/demux queue emulates such switch preservation into a serial connection of fiber-switch blocks, which combine optical switches with fiber delay lines. Moreover, appropriate tandem connection between these two devices makes a FIFO queue. In terms of the physical structure, an instance of the FIFO queue so constructed coincides with the existing construction in the literature. The switching control mechanisms are different though. Inheriting the unique-routing characteristic of the 2-stage interconnection network, the present construction is under faster control, which distributes the computation task to individual blocks.