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Horizontally expanded and vertically stacked optical banyan (HVOB) is a general architecture for constructing banyan-based optical switches. Blocking analysis is an effective approach to studying network performance and finding a graceful compromise among hardware cost, network depth and blocking probability; however, little has been done on analyzing the blocking behavior of general HVOB networks. In this paper, we study the overall blocking behavior of a HVOB network, where an upper bound on the blocking probability of the network is developed. The upper bound depicts accurately the overall performance behavior of a HVOB 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 among blocking probability, network depth, and network hardware cost, by which a desirable tradeoff can be made among them. In particular, our bound provides network developers an effective tool to estimate the maximum blocking probability of a HVOB network in which different routing algorithms can be applied with a guaranteed performance in terms of blocking probability, hardware cost and network depth. An important conclusion drawn from our work is that the hardware cost of HVOB networks can be reduced dramatically without introducing either significantly high blocking probability or a large network depth.