Design model of a three-stage folded Clos network with a decoupled first stage guaranteeing admissible blocking probability

Some data center networks have implemented optical circuit switching (OCS) to replace electrical packet switching, achieving reduced power consumption, lower latency, and increased capacity. This paper focuses on designing an OCS network to maximize the switching network size, defined as the number of terminals connected under the constraints of a fixed number of identical $N \times N$ switches and a specified maximum admissible blocking probability. An existing design for a three-stage folded Clos network encounters a limitation where the network size ceases to grow as the number of switches increases beyond a certain threshold. To address this, we propose a design model for a three-stage folded Clos network with the decoupled first stage, named 3dF, to maximize the network switching size while guaranteeing an admissible blocking probability. The 3dF model introduces an input–output layer that combines the first- and second-stage switches into a single, large switch and decouples the switching functions originally handled by a single switch at the first stage into two distinct switches. We formulate this model as an optimization problem and employ an exhaustive search-based algorithm to identify the structure with the largest switching network size in non-increasing order while ensuring that specified constraints, such as blocking probability, are satisfied. We derive theoretical results for three-stage folded Clos variants and, through numerical analysis, show that the 3dF design achieves a larger switching network size than other variants under the SNB condition or a blocking probability guarantee.