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In this paper, we consider the constructions of an N -to- K optical priority queue with buffer Σi=1M di 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,..., dM, 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,..., dM, 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,..., dM 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.