# Optimization of Optical Networks Based on CDC-ROADM Technology
## 3 Results and Discussion  
Computational results were obtained for four optical networks with widely varying parameters. The first network was generated artificially and consists of five nodes only while the other networks, i.e., Polish, German and US, correspond to actual optical networks stemming from specified countries and were taken from [17]. Table 1 and Figure 3 provide the relevant parameters for all four selected networks and their topologies. Table 2 provides parameters characterizing the nodal equipment. In calculations three types of transponders (T1, T2 and T3) are considered, which vary in offered bit rates and incurred transponder costs. It was assumed that 100 G transponder (T3) is 6 times more expensive than 10 G transponder (T1), and at the same time 3 times more expensive than 40 G transponder (T2). Two types of multiplexers (M1 and M2) are also considered. It is assumed that multiplexers can handle any considered number \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Network** & **\# Nodes** & **\# Link** & **\# Demand** \\ \hline net5 & 5 & 14 & 10 \\ Polish & 12 & 18 & 66 \\ German & 17 & 26 & 136 \\ US & 26 & 84 & 325 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Analyzed network parameters. Figure 3: Analyzed network topologies: (**a**) artificial 5-node network; and (**b**) Polish, (**c**) German, (**d**) American (US) national transmission optical backbone network. of wavelengths while they differ in the offered functionality. C-ROADM multiplexer (M1) costs 1 unit while the CDC-ROADM multiplexer (M2) costs 3 cost units. M1 is conventional mux/demux with fixed ports and multiplexer M2 is tunable. Finally, it has been assumed that both C-ROADM and CDC-ROADM use the same wavelength selective switch (WSS), whose price is almost the same as 100 G transponder (T3). Additionally, cost intervention on sites was included and assumed equal 1 unit, in all considered cases. The demands, which allow for simulation of the traffic intensity, are given by demand matrix, which provides the values of traffic flow between selected nodes expressed in Gbps. An example demand matrix for the network from Figure 3b is presented in Table 3.  
The calculations were carried out using a linear solver engine of CPLEX 12.8.0.0 on a 2.1 GHz Xeon E7-4830 v.3 processor with 256 GB RAM running under Linux Debian operating system. The traffic in an analyzed DWDM network was increased by increasing the demands between initial and end nodes via demand matrix. It was assumed that all entries of the demand matrix were equal, i.e., all elements of the demand matrix were increased simultaneously. The sum of all demand matrix elements that correspond to allocated paths gives an estimate of the network capacity. In the simulations the elements of the demand matrix were increased until integer solution was not feasible. Thus, calculated maximum capacity of DWDM network depends also on the number of wavelengths admitted while searching for the optimum allocation of paths. The number of wavelengths \(s\) was set as an input variable and was different for different networks. Figures 4-7 show the calculated dependence of maximum capacity on the number of DWDM wavelengths and the dependence of network cost on the maximum capacity calculated for the largest number of DWDM wavelengths. For net 5 (Figure 4) results are obtained for 4 different \(s\) values equal to 4, 8, 12 and 16. The number of all non-zero elements of the demand matrix (upper triangular part) was 8 while the matrix element values were varied from 5 Gbps to 1 Tbps. Thus, totaling up to maximum network capacity of 8 Tbps. For the Polish network (Figure 5) the results are obtained for \(s\) values equal to 8, 16, 32, 64 and 96. 66 demands ranging from 5 Gbps to 1 Tbps were considered, totaling up to maximum network capacity of 66 Tbps. In the case of the German network (Figure 6), the results are obtained for \(s\) values equal to 8, 16, 32, 64 and 96. 136 demands were varied from