—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 ...