Scheduling switching element (SE) disjoint connections in stage-controlled photonic banyans

We study the problem of scheduling switching element (SE)-disjoint connections in banyans and dilated banyans under stage control and show how it applies to photonic cross-connect (or switch) technology. For a given set of connections (or packets), it is desirable to establish them in as few rounds as possible where the number of rounds (i.e., schedule length) corresponds to the degree at which a cross-connect may be multiplexed in time or wavelength. For a stage-controlled banyan, three scheduling algorithms are described. The first two algorithms perform well when the number of connections to be scheduled is small and large, respectively, but perform poorly otherwise. The third algorithm is optimal in that it can generate a schedule of minimum length with a polynomial time complexity. We determine the average schedule length in a banyan using these three algorithms through both analysis and simulation and extend our analysis to dilated banyans.