In the literature, research has been published extensively on how one achieves exact emulation of First In First Out (FIFO) multiplexers for fixed-size cells (or packets) using optical crossbar Switches and fiber Delay Lines (SDL). In this paper, we go a step further and propose a new architecture that achieves exact emulation of FIFO multiplexers for variable length bursts. Our architecture consists of two blocks: a cell-scheduling block and a FIFO multiplexer for fixed-size cells. Both blocks are made of SDI, units. The objective of the cell-scheduling block is to schedule cells in a burst to the right input at the right time so that cells in the same burst depart contiguously from the multiplexer for fixed-size cells. We show that cell scheduling can be done efficiently by keeping track of a single state variable, called the total virtual waiting time in this paper. Moreover, the delay through the cell-scheduling block is bounded above by a constant that only depends on the number of inputs and the maximum number of cells in a burst. Such a delay bound provides a limit on the number of fiber delay lines needed in the cell-scheduling block.

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.

It has been studied extensively in the literature how one achieves exact emulation of First In First Out (FIFO) multiplexers for fixed size cells (or packets) using optical crossbar switches and fiber delay lines (SDL). In this paper, we take a step further and propose a new architecture that achieves exact emulation of FIFO multiplexers for variable length bursts. Our architecture consists of two blocks: a cell scheduling block and an FIFO multiplexer for fixed size cells. Both blocks are made of SDL units. The objective of the cell scheduling block is to schedule cells in a burst to the right input at the right time so that cells in the same burst depart contiguously from the multiplexer for fixed size cells. We show that cell scheduling can be done efficiently by keeping track of a single state variable, called the total virtual waiting time in this paper. Moreover, the delay through the cell scheduling block is bounded above by a constant that only depends on the number of inputs and the maximum number of cells in a burst. Such a delay bound provides a limit on the number of fiber delay lines needed in the cell scheduling block.