node i toward node j is proportional to the product of the degree of i and j. As an example, since the network has 18 nodes, there are N = 153 distinct couples of nodes. If it is stated that the overall number of wavelength paths routed through the network is Np = 24,000, the paths routed between nodes i and j are (10.31) where Ci is the degree of the ith node constant A is determined by the condition that the overall number of paths is Np, that becomes 300 km 300 km FIGURE 10.33 2400 km NSFNet network topology: A pan- 1600 km American network with 16 nodes. Next Generation Networking: Enabling Technologies, Architectures, and Performances Percentage of regenerators out of the number of crossing paths 7.00% 6.00% 5.00% 4.00% 3.00% 2.00% 1.00% 0.00% Node number FIGURE 10.34 Regenerators deployed per node as a percentage of the number of paths traveling through the node. (10.32) The result of the first dimensioning phase is reported in Figure 10.34 in terms of regenera- tors deployed per node as a percentage of the number of paths traveling through the node. With our assumption, this percentage remains almost constant varying the traffic load, due to the fact that all the elements of the traffic matrix increases of the same relative amount. It is evident that almost all the nodes host regenerators confirming the difficult transmis- sion situation of the network. Naturally, the number of regenerators is smaller, frequently much smaller, than the number of wavelength paths crossing the node. The consequence, we can derive from Figure 10.34, is that when the network is SO extended, transparency tends to fade due to the need of installing regenerators almost in all the nodes. 10.3.7 Summary: The Transparent Optical Network Status The idea of a transparent transport network has been around for more than 20 years, a suf- ficient period to develop all the tools (hardware and software) needed to implement such an innovative solution. The main advantages that were devised at the beginning, mainly the great sparing in energy