Constructions of Optical Priority Queues With Multiple Inputs and Multiple Outputs

In this paper, we consider the constructions of an N -to- K optical priority queue with buffer Σ_i=1^M d_i by using a feedback system consisting of a single (M+max[N,K]) × (M+max[N, K]) (bufferless) optical crossbar switch, min[N,K] 1× 2 (bufferless) optical crossbar switches, and M fiber delay lines with delays d₁, d₂,..., d_M, where N is the number of arrival links and K is the number of departure links of the priority queue. We first obtain two sufficient conditions [the conditions (A1) and (A2) in Section I] for our constructions of N -to-K optical priority queues. By establishing a space-time advancement property and a monotonically decreasing/increasing property for the packets stored in the fiber delay lines, we then use these sufficient conditions to show that with an appropriate choice for the delays d₁, d₂,..., d_M, we can achieve a buffer size of O([(M³/N²)]) for the case that N=K. For the special case that N=K=1, our constructions achieve a buffer size of O(M³), which is much better than the O(M²) buffer size previously known in the literature for single-input single-output optical priority queues. Therefore, other than the extension from the constructions of optical priority queues with a single input and a single output to the constructions of optical priority queues with multiple inputs and multiple outputs, our constructions also achieve a larger buffer size than previous constructions of single-input single-output optical priority queues. Furthermore, we give another sufficient condition [the condition (A3) in Section I] for our constructions of N -to-K optical priority - - queues and then use that condition to obtain choices for the delays d₁, d₂,..., d_M so that our constructions have the fault tolerant capability that can tolerate up to F broken/malfunctioning fibers (e.g., fiber cut, fiber shorting out, etc.), where 0 ≤ F ≤ M-1.