Recursive construction of FIFO optical multiplexers with switched delay lines

In this paper, we develop mathematical theory for recursive construction of first-in first-out (FIFO) optical multiplexers by the combination of (bufferless) crossbar switches and fiber delay lines (SDLs). We show that by cascading multistage SDL units, 2-to-1 multiplexers with a large buffer can be emulated exactly for both the departure process and the loss process from the multiplexer. Such results are extended to the case of n-to-1 multiplexers by introducing a new class of multiplexers, called delayed-loss multiplexers. A delayed-loss multiplexer has the same departure process as an ordinary multiplexer. However, lost packets due to buffer overflow in a multiplexer might be delayed. A key result from our theory is the self-routing n-to-1 multiplexer, where the routing path of a packet through the multistage SDL units can be determined upon its arrival.