Design of Multiple-Plane Twisted and Folded Clos Network Guaranteeing Admissible Blocking Probability

Future advancements in data centers are anticipated to incorporate advanced circuit switching technologies, especially optical switching, which achieve high transmission capacity and energy efficiency. Previous studies addressed a Clos-network design problem to guarantee an admissible blocking probability to maximize the switching capacity, which is defined by the number of terminals connected to the network. However, as the number of available <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N} \times {N}$ </tex-math></inline-formula> switches increases, the switching capacity no longer increases due to the switch port limitation. This paper proposes a design of a multiple-plane twisted-folded (TF) Clos network, named MP-TF, to enhance the switching capacity, which is limited by the original TF-Clos, by guaranteeing an admissible blocking probability. MP-TF consists of identical M TF-Clos planes and pairs of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\times {M}$ </tex-math></inline-formula> selector and an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M} \times 1$ </tex-math></inline-formula> selector, each pair of which is associated with a transmitter and receiver pair. We formulate a design model of MP-TF as an optimization problem to maximize the switching capacity. We introduce connection admission control in MP-TF, named MP-CAC. We derive the theorem that the MP-TF design model using MP-CAC guarantees the admissible blocking probability. Numerical results observe that MP-TF increases the switching capacity as the number of TF-Clos planes when available <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N} \times {N}$ </tex-math></inline-formula> switches are sufficient; for example, with seven planes, the switching capacity is 1.97 times larger than that of one plane, given a request active probability of 0.6 and an admissible blocking probability of 0.01. We find that the computation time for MP-TF diminishes with an increase in the number of TF-Clos planes. Designing MP-TF is similar to designing a single TF-Clos plane, differing mainly in the handling of connection admission control. With a larger number of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N} \times {N}$ </tex-math></inline-formula> switches, MP-TF enables the design of a smaller TF-Clos plane. We provide the analyses of optical power management and network cost of MP-TF.