Optical circuit switching provides high-capacity and low-latency data transmission capabilities. A Clos network is well known as a class of non-blocking switching networks. A prior study addressed designing a three-stage twisted and folded Clos network (3TF), which has a larger switching network size, i.e., the number of terminals connected to the network, than its two-stage variants. That study used a sufficient condition for strict-sense non-blocking (SNB) in 3TF to solve an optimization design problem. However, this condition may be stricter than necessary to guarantee strict-sense non-blocking, suggesting that by using the necessary and sufficient condition, the constraints can likely be relaxed, allowing for configurations with a larger switching network size. No study has addressed the necessary and sufficient condition for SNB in the whole 3TF. A past study derived the SNB condition for the three-stage folded Clos (3F), the basis of 3TF, assuming that connections within the same first- and second-stage group loop back no further than the second stage. Its necessary and sufficient condition in the general case, however, remains unexamined, despite an initial study on the SNB condition for 3F. This paper proposes a design model of 3TF based on the necessary and sufficient condition for strict-sense non-blocking. We derive and prove the necessary and sufficient condition for strict-sense non-blocking in the whole 3TF. The proposed design model considers two cases: one where no blocking is allowed and another where the blocking probability does not exceed a given admissible threshold, based on our derived necessary and sufficient condition for strict-sense non-blocking in 3TF. We formulate the problem based on the necessary and sufficient condition to obtain the configuration of the proposed model that maximizes the switching network size. We theoretically show that the maximum switching network size obtained by solving the proposed model is always larger than or equal to that obtained by solving the existing 3TF design model. Numerical results show that the proposed model achieves a larger switching network size than the existing 3TF design model.

Air-to-ground (A2G) wireless networks comprising unnamed aerial vehicles (UAVs) can provide flexible communications services to ground users. However, battery capacity limitations of UAVs affect the stability of the A2G networks. To improve network stability, we propose an A2G Network using Circularly ORbiting UAVs (ANCOR), where UAV base stations (UAV-BSs) always move in circular orbits. ANCOR is based on the fact that hovering UAVs consume more power than moving UAVs. We also propose an arrangement method for the orbits of the UAV-BSs to improve the average energy efficiency, which is defined as the ratio of the average capacity to the average power consumption. The arrangement method comprises two steps. In the first step, the orbits of the UAV base stations are optimized to minimize coverage holes and maximize the minimum capacity in the area. In the second step, the moving speeds of the UAV BSs in orbit are optimized to maximize the average energy efficiency with the user density distribution of the area. Moreover, we evaluate the performance of ANCOR via simulation experiments.

Optical circuit switching (OCS) is becoming used in some data center networks due to its low power consumption, low latency, and high bandwidth. Previous research introduced a design model for a twisted and folded Clos network (TF-Clos) as a data center network to maximize the switching network size, i.e., the number of connected terminals, while guaranteeing the admissible blocking probability. The previous model assumes that request active rates from all the terminals are identical. However, it is an overly conservative design when the active rates differ, resulting in a smaller switching network size than desired. This paper proposes a terminal-shuffling (TS) scheme for designing an OCS TF-Clos network with an admissible blocking probability guarantee, which supports different active rates. Each terminal can arbitrarily choose any leaf switch to connect, making the network design more adaptable to varying conditions. A patch panel or direct termination by operators can wire optical fibers between the terminals and the leaf switches. We formulate a TS-based TF-Clos design problem to maximize the switching network size. We develop an approximation approach to find a feasible solution to the optimization problem. Numerical results demonstrate that the switching network size of the proposed TS scheme is larger than that of baseline schemes.

Data center networks facilitate large-scale data processing by interconnecting multiple switching devices. Optical circuit switching (OCS) provides high transmission capacity and energy efficiency. It establishes dedicated paths for data transfer, ensuring reliable communication. A Clos network is widely used among multi-stage switching architectures due to its scalability and structured design. This paper investigates models for designing folded/unfolded Clos networks with an admissible blocking probability to maximize OCS network size. While previous studies have examined fundamental and stage-extended Clos networks, they have not addressed unfolded Clos network structures that maintain an admissible blocking probability across different configurations. To fill this gap, we introduce unfolded Clos network structures that ensure an admissible blocking probability for both fundamental and extended stages. We also discuss connection admission control mechanisms tailored to these network models. A key focus of this study is a comprehensive performance evaluation, including switching network size and computation time. Furthermore, we explore an alternative approach employing multiple network planes to enhance scalability and flexibility. The findings provide valuable insights into the design of large-scale OCS networks with controlled blocking probabilities.

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${N} \times {N}$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$1\times {M}$selector and an${M} \times 1$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${N} \times {N}$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${N} \times {N}$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.