# Design of Optical Tunnel Switching Networks for Big Data Applications
## 2 Torus Optical Tunnel Switch Network  
The structure of the wavelength selective switch based on LCoS technology is shown in Figure 1 (Provided by Acton Technology Corp.). The SDN technology is used to allocate a wavelength of the input port to the specific output port. For example, \(\lambda_{1}\), \(\lambda_{7}\), \(\lambda_{11}\) and \(\lambda_{20}\) of input port 1 are assigned to transfer to output port 3, and so on.  
Figure 2 shows a multi-plane Torus topology optical switching network. The X-axis has X nodes and the Y-axis has Y nodes, so there is a total of X \(\times\) Y nodes. In order to improve the throughput, Z planes are used.  
X-axis has X nodes that need X \(\times\) (X-1) different wavelengths (\(\lambda\)) if we need to establish full match tunnels. Similarly, Y-axis needs Y \(\times\) (Y-1) different wavelengths if we need to establish full match tunnels. Therefore, the total number of wavelengths named W is defined:  
Figure 1: Architecture of the wavelength selective switch.  
\[\mathrm{W}=\mathrm{X}\times\mathrm{(X\text{-}1)}+\mathrm{Y}\times\mathrm{(Y\text{-}1)}, \tag{1}\]  
Let \(\mathrm{Y}=\mathrm{X}\)  
\[\mathrm{W}=\mathrm{X}\times\mathrm{(X\text{-}1)}+\mathrm{X}\times\mathrm{(X\text {-}1)}=2\mathrm{X}^{2}\text{ - }2\mathrm{X}, \tag{2}\]  
After calculation, we can obtain  
\[\mathrm{X}=\frac{1+\sqrt{2\times W+1}}{2}\, \tag{3}\]  
Therefore, if \(\mathrm{W}=48\), \(\mathrm{X}=5.42\) takes its integer, and the maximum number of nodes is \(25\) (\(5\times 5\)). Similarly, if \(\mathrm{W}=96\), \(\mathrm{X}=7.3\) takes its integer, and the maximum number of nodes is \(49\) (\(7\times 7\)). If we use these wavelengths, we can create direct tunnels. For example, if \(\mathrm{X}=\mathrm{Y}=5\), the direct tunnels of each node to the other nodes are only \(8\) (\(4+4\)), but the tunnels of each node to the other nodes need \(24\), so the other \(16\) tunnels must be transferred through the relay nodes. The total number of tunnels needs \(600\) (\(24\times 25\)). Similarly, if \(\mathrm{X}=\mathrm{Y}=7\), the direct tunnels of each node to other nodes is only \(12\) (\(6+6\)), but the tunnels of each node to the other nodes need \(48\), so the other \(36\) tunnels must be transferred through the relay nodes. The total number of tunnels requires \(2352\) (\(48\times 49\)). These relay tunnels occupy the bandwidth of the direct tunnel, so multiple planes must be used to increase the network throughput. How many planes are needed depend on the number of nodes, and the required throughput that will be discussed in Sections 3 and 4.  
Each module is composed of N servers, Z MUXs (Multiplexer), Z CDMUXs (Cyclic De-Multiplexer), an SDN switch and Z nodes with a node in each plane as shown in Figure 3, where each node is a \(5\times 5\) WSS. This multi-plane architecture not only increases the throughput of the network, but also increases the stability of the network, and has fault tolerance capability. A module can be connected to N servers. These servers collect data and sort through an SDN switch to aggregate the data to the same module and then transfer it to the multiplexer. The \(\mathrm{(X+Y-2)}\) wavelengths are grouped into a DWDM signal and sent to a \(5\times 5\) wavelength selective switch (\(5\times 5\) WSS). Each node has a \(5\times 5\) WSS to set the different wavelengths to send to different nodes to establish a tunnel. Different wavelengths in the DWDM signal receiving from different nodes are decomposed into the SDN switch via a CDMUX, and then sent to their corresponding servers. Other planes have the same function to increase network throughput, and when a plane fails, traffic can be routed to another plane to increase network reliability and stability.  
Figure 2: Multi-plane Torus topology optical tunnel switching network.