Abstract : The design of optical buffers is an important issue in all-optical packet switching. One of the most general types of buffering schemes is priority queues, which includes first-in first- out (FIFO) queues and last-in first-out (LIFO) queues as special cases (where the packet arrival times are used for the assignment of packet priorities). Recently, it was shown in our previous work that an optical priority queue with buffer size 2O(√αM) can be implemented by using an optical (M + 2) × (M + 2) (bufferless) crossbar switch and M fiber delay lines under a simple priority- based routing policy, where α is a constant that depends on the parameters used in the constructions. This achieved buffer size 2O( √αM) (which is exponential in √M) is the best result currently known in the literature and significantly improves on all previous results (all of which are only polynomial in M). In this paper, we focus on our previous constructions of optical priority queues. The first contribution of this paper is to derive a closed-form expression for the maximum buffer size that can be achieved in our previous constructions. Such an expression is of sufficient theoretical interest itself and can be used to directly compute the maximum buffer size (in contrast, the maximum buffer size has to be computed recursively in our previous work). The second contribution of this paper is to use the closed-form expression to show that in the regime that s ≥ 2, k ≥ 2s + 1, and m ≥ 2, where s, k, and m are parameters used in the constructions, the maximum buffer sizeUk is given by Uk = 2O(√M log2 (2s+2) log2 m/((2s+1)m)) undera mild constraint that is applicable in practical scenarios. This result can be regarded as a complement to the approximate resultUk ≈ 2O( √M log2 (2s+2) log2 m/((2s+1)m)) in our previous work.
Index terms : FIFO multiplexers, optical buffers, optical queues, optical switches, priority queues.