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Vertically stacked optical banyan (VSOB) is an attractive architectture for constructing banyan-based optical switches. Blocking analysis is an effective approach to studying network performance and finding a graceful compromise among hardware cost, blocking probability and crosstalk tolerance; however, little has been done on analyzing the blocking behavior of VSOB networks under crosstalk constraint. In this paper, we study the overall blocking behavior of a VSOB network under various degree of crosstalk, where an upper bound on the blocking probability of the network is developed. The upper bound depicts accurately the overall performance behavior of a VSOB network as verified by extensive simulation results and it agrees with the strictly nonblocking condition of the network. The derived upper bound is significant because it reveals the inherent relationship between blocking probability and network hardware cost, by which a desirable tradeoff can be made between them under various degree of crosstalk constraint. Also, the upper bound shows how crosstalk adds a new dimension to the theory of switching systems. In particular, our bound provides network developers an effective tool to estimate the maximum blocking probability of a VSOB network in which different routing algorithms can be applied with a guaranteed performance in terms of blocking probability and hardware cost. An important conclusion drawn from our work is that the hardware cost of VSOB networks can be reduced dramatically without introducing significantly high blocking probability considering the crosstalk.

Overall Blocking Behavior Analysis on Banyan-Based Optical Switching Networks Under Crosstalk Constraint