## 3 Network Model
To illustrate the considered B2B regeneration approach and the effect of transponder placement, we consider a simple example shown in Figure 2. We assume four modulation formats, namely, BPSK, QPSK, 8-QAM, and 16-QAM, with the bit rates transmitted by OCs and the transmission reaches of considered modulation formats based on data presented in [26] and [27] and shown in Table 1. A request (lightpath) is allocated on a routing path (\(a\), \(b\), \(c\), \(d\)) of an overall length 3800 km consisting of three links: (\(a\), \(b\)) 1000 km, (\(b\), \(c\)) 2300 km, and (\(c\), \(d\)) 500 km. Moreover, every link (i.e., (\(a\), \(b\)), (\(b\), \(c\)), (\(c\), \(d\))) has 12 free adjacent slices available that can be used to allocate the request. Twenty transponders are available in the network to be located in nodes \(a\), \(b\), \(c\), and \(d\) using various predeployment policies. We consider the following four scenarios of transponder location:  
* [5, 5, 5, 5], i.e., every node has 5 transponders, and the lightpath uses transponders in the following way <2, 5, 5, 2> (Figure 2a);
* [10, 0, 0, 10], i.e., 10 transponders are placed in nodes \(a\) and \(d\), and the lightpath uses transponders in the following way <4, 0, 0, 4> (Figure 2b);
* [8, 0, 8, 4], i.e., 8 transponders are placed in nodes \(a\) and \(c\), 4 transponders are placed in node \(d\), and the lightpath uses transponders in the following way <4, 0, 6, 2> (Figure 2c);
* [3, 7, 7, 3], i.e., 3 transponders are placed in nodes \(a\) and \(d\), 7 transponders are placed in nodes \(b\) and \(c\), and the lightpath uses transponders in the following way <3, 7, 7, 2> (Figure 2d). Note that the numbers in curly brackets \(\{\}\) represent the number of transponders located in each network node that can be used for establishing the considered lightpath. However, some of these transponders can remain non-allocated, and numbers in angle brackets < > and Figure 2 show only the transponders that are used to establish the considered lightpath, i.e., other spare transponders are not presented in the figure. For each of transponder placement scenarios, the request can be established using different regeneration options (configurations), where each option divides the transmission path into a number of transparent path segments. For each segment, we select the best allowable modulation format. The objective is to provision the request with the highest possible bit rate (throughput) accounting for limited resources of spectrum (12 adjacent slices) and transponders (20 devices located in various scenarios). We assume the flexible B2B regeneration approach. We can easily observe that the placement of transponders has a significant impact on the allowable bit rate of the considered request, since the following bit rates are achieved for the considered four scenarios: (a) 300 Gb/s, (b) 200 Gb/s, (c) 400 Gb/s, (d) 400 Gb/s. From the above example, we can notice that in spectrally flexible optical networks, such as EONs and SS-FONs with B2B regeneration, the placement of transponders is a key issue, since by \begin{table}
\begin{tabular}{c c c} \hline \hline
**Modulation Format** & **Reach (km)** & **Bit Rate Supported by One Transponder (Gb/s)** \\ \hline BPSK & 6300 & 50 \\ QPSK & 3500 & 100 \\
8-QAM & 1200 & 150 \\
16-QAM & 600 & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Transmission reaches (km) and supported bit rates (Gb/s) per one transponder for considered modulation formats. Figure 2: Example of different transponder placement scenarios for provisioning a request: a) placement of transponders in network nodes: [5, 5, 5, 5]; b) placement of transponders in network nodes: [10, 0, 0, 10]; c) placement of transponders in network nodes: [8, 0, 8, 4]; d) placement of transponders in network nodes: [3, 7, 7, 3]. proper predeployment of transponders one can allow to establish lightpaths with higher bit rate and thus serve more traffic without the need to deploy extra fibers.