Constructions of Optical Queues With a Limited Number of Recirculations–Part II: Optimal Constructions

One of the main problems in all-optical packet-switched networks is the lack of optical buffers, and one feasible technology for the constructions of optical buffers is to use optical crossbar Switches and fiber Delay Lines (SDL). In this two-part paper, we consider SDL constructions of optical queues with a limited number of recirculations through the optical switches and the fiber delay lines. Such a problem arises from practical feasibility considerations. In Part I, we have proposed a class of greedy constructions for certain types of optical queues, including linear compressors, linear decompressors, and 2-to-1 FIFO multiplexers, and have shown that every optimal construction among our previous constructions of these types of optical queues under the constraint of a limited number of recirculations must be a greedy construction. Specifically, given M ≥ 2 and 1 ≤ k ≤ M − 1, we have shown that to find an optimal construction, it suffices to find an optimal sequence d∗M1 ∈ GM,k such that B(d∗M1; k) = maxdM 1 ∈GM,k B(dM1; k), where B(dM1; k) is the maximum representable integer with respect to dM1 and k (defined in Part I) and GM,k is the set of sequences dM1 = (d1, d2,..., dM) given by dsi+j = B(d si+j−1 1; i + 1) + 1 for i = 0, 1,..., k − 1 and j = 1, 2,..., ni+1 for some sequenc