Feedforward SDL Constructions of Output-Buffered Multiplexers and Switches with Variable Length Bursts

In this paper, we study the problem of exact emulation of two types of optical queues: (i) N-to-1 output-buffered multiplexers with variable length bursts, and (ii) N times N output-buffered switches with variable length bursts. For both queues, the delay of a packet (in a burst) is known upon its arrival. As such, one can emulate such queues by finding a delay path that yields the exact delay for each packet. For emulating the delay of a packet in such queues, in this paper we consider a multistage feedforward network with optical crossbar switches and fiber delay lines (SDL). For any fixed delay d, there exist multiple delay paths in such a network. A delay path is feasible if it satisfies the following three constraints: (i) conflict constraint: no more than one packet can be scheduled at the same input/output ports of each crossbar switch at the same time, (ii) causality constraint: no packet can be scheduled before its arrival, and (iii) strong contiguity constraint: packets in the same burst should be routed through any fiber delay lines contiguously. By the worst case analysis, we find sufficient conditions for the numbers of delay lines needed in each stage of such a feedforward network to achieve exact emulation of both queues. For N-to-1 output-buffered multiplexers, our sufficient conditions are also necessary when each burst contains exactly one packet. By computer simulation, we also show that the number of delay lines in each stage can be greatly reduced due to statistical multiplexing gain.