Abstract
In this thesis, we propose the constructions of N-to-1 output-buffered first-in first-out (FIFO) multiplexers for variable length bursts. We consider a multistage feedforward network con- sisting of optical crossbar Switches and ‾ber Delay Lines (SDL) for the constructions of N-to-1 output-buffered FIFO multiplexers for variable length bursts. Since the delay of a packet (in a burst) is known upon its arrival for N-to-1 output-bu®ered FIFO multiplexers with variable length bursts, as in the previous work [28] we use the r-ary representation of the packet delay for the self-routing of a packet through such a feedforward network, and we schedule the bursts so that the following three constraints are satis‾ed: (i) Con°ict con- straint: no more than one packet can be scheduled at the same input/output port of any crossbar switch at the same time. (ii) Causality constraint: no burst can be scheduled before its arrival. (iii) Strong contiguity constraint: packets in the same burst should be routed through any ‾ber delay line contiguously. To satisfy the con°ict constraint, we provide multiple delay paths in such a feedforward network for each delay. We obtain a su±cient condition on the number of ‾ber delay lines in each stage of the feedforward network for the constructions of N-to-1 output-bu®ered FIFO multiplexers for variable length bursts. Since we schedule the bursts so that the strong contiguity constraint is satis‾ed, there is no need to perform burst segmentation and reassembly, which is a great advantage of our constructions as both the construction complexity and the routing complexity can be greatly reduced.