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With recent advances in optical technology, we are closer to building all-optical routers than ever before. A major problem in this area, however, is the lack of all-optical memories similar to what we have in electronics. To overcome this problem, recently, there have been several proposals that show how we can emulate First-In First-Out (FIFO) queues using a combination of fiber delay lines and switches. Unfortunately, FIFO queues cannot be used for implementing many link scheduling policies including weighted fair queuing, weighted round-robin, or strict priority, which are essential components of any modern router today. In this paper, we introduce an architecture based on fiber delay lines and optical switches that can be used for emulating Push-In First-Out (PIFO) queues. In a PIFO queue, an incoming packet can be pushed anywhere in the queue, and therefore it can be used for the implementation of various link scheduling policies. We describe a scheduling algorithm for this architecture and show that with a small speedup, we can build a PIFO queue of size N - 1 using only O(log2 N) 3 Ã 3 optical switches. The resulting system has a minimum reliability of 99.5%, and even for the small portion of departure requests that cannot be fulfilled immediately, the requested packet is ready to depart within approximately five time slots from the request time.