Constructions of optical FIFO queues

Discrete-time queues are infinite dimensional switches in time. Ever since Shannon published his paper ("Memory requirements in a telephone exchange", Bell Syst. Tech. J., pp. 343-349, vol. 29, 1950) on the memory requirements in a telephone exchange, there have been tremendous efforts in the search for switches with minimum complexity. Constructing queues with minimum complexity has not received the same amount of attention as queues are relatively cheap to build via electronic memory. Recent advances in optical technologies, however, have spurred interest in building optical queues with minimum complexity. In this correspondence, we develop mathematical theory of constructing discrete-time optical first-in-first-out (FIFO) queues. To our surprise, we find that many classical constructions for switches have their counterparts for constructing queues. Analogous to the three-stage construction of Clos networks, we develop a three-stage construction of optical FIFO queues via switched delay lines (SDLs). Via recursively expanding the three-stage construction, we show that an optical FIFO queue with buffer 2ⁿ-1 can be constructed by using 2n 2×2 switches with the total fiber length 3·2^n-1-2.