In this paper, we consider Switched-Delay-Lines (SDL) constructions of optical priority queues by using optical (bufferless) crossbar switches and optical fiber delay lines. In a priority queue, each packet is associated with a priority upon its arrival, the highest-priority packet is sent out from the queue whenever there is a departure request, and the lowest-priority packet is dropped from the queue whenever there is a buffer overflow. Given any system for SDL constructions of optical priority queues, the main research problem is twofold: (i) the design of the routing policy performed by the optical crossbar switches; (ii) the choice of the delays of the optical fiber delay lines. Sarwate and Anantharam are the first to propose a feedback system consisting of an optical$(M+2)\times (M+2)$crossbar switch and M optical fiber delay lines (seeFigure 1inSection I) for SDL constructions of optical priority queues, and they have shown that the largest buffer size that can possibly be achieved by using such a feedback system is$2^{M}$. However, whether this theoretical buffer size$2^{M}$can be achieved or not remains an open research problem. Currently, the best result in the literature was obtained by Cheng et al. and the achieved buffer size is$2^{O(\sqrt {\alpha M})}$, where$\alpha $is a constant that depends on the parameters used in their constructions. In this paper, we consider a discrete-time setting and use a feedback system consisting of an optical crossbar switch and multiple groups of optical first-in first-out (FIFO) multiplexers with delay one (FM1’s) for SDL constructions of optical priority queues under apriority-based routing policy (seeFigure 2inSection I). Our contributions are as follows: (i) We extend and generalize an important class of constructions that contains the optimal constructions in the work of Cheng et al. As a result, we achieve larger buffer sizes and less construction complexities/costs than those by Cheng et al. (ii) We obtain a closed-form expression for the maximum buffer size that is achieved by the optimal construction for the scenario that each group of FM1’s has the same number of FM1’s. (iii) Our constructions possess a salient feature, namely, fault-tolerant capability, that can tolerate the malfunctioning of some FM1’s by using the generalized results obtained in this paper. (iv) We show that our constructions can be implemented by using an optical$(M+2)\times (M+2)$crossbar switch andMoptical fiber delay lines, and achieve a buffer size$2^{O(\sqrt {\alpha M})}$, where$\alpha $is a constant that depends on the parameters used in our constructions and is better, i.e., larger, than that in the work of Cheng et al. in a very broad regime.

One of the main challenges in all-optical packet switching is to design optical buffers for packet conflict resolution. In this paper, we consider a very general type of buffering schemes, namely, optical N-to-K priority queues with time-varying service capacity, where each packet is associated with a unique priority upon its arrival, at time slot t at most c(t) highest-priority packets are sent out from the queue if there are packets in the queue and the service capacity c(t) (0 ≤ c(t) ≤ K) of the queue is not zero, and up to N lowest-priority packets are dumped from the queue if there is a buffer overflow. We extend and generalize our previous constructions [8] of optical priority queues under a priority-based routing policy from single input/output to multiple inputs/outputs. The main contributions of this paper are as follows: (i) The priority queues considered in this paper subsume those considered in all previous works as special cases. (ii) Our queueing model with time-varying service capacity is not only more general but also more realistic than that with fixed service capacity previously studied in the literature. (iii) For the special case that N = K = 1, our constructions in this paper subsume those in [8] as special cases. (iv) For the special case that N = K, we show that an optical N-to-N priority queue with buffer size ${2^{O(\sqrt {M/N} )}}$ (exponential in $\sqrt {M/N} $) can be constructed by using an optical (M+2N)×(M+2N) (bufferless) crossbar switch and M fiber delay lines, which substantially improves the best result O(M3/N2) (polynomial in M/N) in the literature.