Constructing sub-exponentially large optical priority queues with switches and fiber delay lines

Abstract

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)×(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 Θ( √ 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.

Construction of Subexponential-Size Optical Priority Queues With Switches and Fiber Delay Lines

“…On the other hand, the use of multiplexers imposes an additional condition on the routing policy that buffer overflow cannot happen at any multiplexer. Nevertheless, we only need to guarantee that the number of packets buffered at a multiplexer cannot exceed the buffer size of the multiplexer, since 1 Datta's work [24] and our preliminary version of this work [1] firstly appeared at almost the same time. the buffer space of a multiplexer is always used in a consecutive manner.…”

“…A preliminary version of the paper has appeared in IEEE International Symposium on Information Theory, Barcelona, Spain, July 10-15, 2016 [1].…”

“…Proper delays were further assigned to the FDLs, which leads to the first construction of optical priority queue with buffer Θ(M 2 ) [19]. This sorting-based routing policy plays a vital role in all the subsequent constructions of optical priority queues, including the ones by Chiu et al in [20] and [21] whose buffer sizes are Θ(M 2 ) and Θ(M 3 ), respectively, and the recursive construction by Datta [24], which can achieve a buffer size of Θ(M c ) for any positive integer c. 1 However, all these buffer sizes achieved are polynomial in M , which are far away from the exponential upper bound 2 M + 1.…”