Constructing Sub-exponentially Large Optical Priority Queues with   Switches and Fiber Delay Lines
  Optical switching has been considered as a natural choice to keep pace with growing fiber link capacity. One key research issue of all-optical switching is the design of optical queues by using optical crossbar switches and fiber delay lines (SDL). In this paper, we focus on the construction of an optical priority queue with a single $(M+2)\times (M+2)$ crossbar switch and $M$ fiber delay lines, and evaluate it in terms of the buffer size of the priority queue. Currently, the best known upper bound of the buffer size is $O(2^M)$, while existing methods can only construct a priority queue with buffer $O(M^3)$.   In this paper, we make a great step towards closing the above huge gap. We propose a very efficient construction of priority queues with buffer $2^{\Theta(\sqrt{M})}$. We use 4-to-1 multiplexers with different buffer sizes, which can be constructed efficiently with SDL, as intermediate building blocks to simplify the design. The key idea in our construction is to route each packet entering the switch to some group of four 4-to-1 multiplexers according to its current priority, which is shown to be collision-free. 
Bin Tang, Xiaoliang Wang, Cam-Tu Nguyen, Sanglu Lu
cs.IT math.IT