## 3 Network Model  
To model the SS-FON, we used a graph \(G=(V,E)\), where \(V\) is a set of optical nodes, and \(E\) is a set of fiber links. Let set \(K\) include spatial modes available in each link \(e\in E\). In each spatial mode \(k\in K\), the available optical frequency spectrum is divided into frequency slices denoted as \(S=\{s_{1},s_{2},\,\ldots,\,s_{|S|}\}\). We assume that each slice is of 12.5 GHz width. The transmission of optical signals is provided by means of spectral super-channels (SChs). A SCH can contain a number of optical carriers (OCs), each using \(\Delta_{OC}\) frequency slices, where an OC is transmitted/received by one transponder. As proposed in [26] and [27], we assume that \(\Delta_{OC}=3\) slices, what is equivalent to 37.5 GHz. A set of modulation formats \(M=\{m_{1},\,\ldots,\,m_{|M|}\}\) is defined. Each modulation format \(m\in M\) is characterized by a certain transmission reach and spectral efficiency. Moreover, modulation format \(m\in M\) can support bit rate \(g(m)\) on a single optical carrier. In this paper, we considered a dynamic routing scenario assuming that a node-to-node dynamic traffic request \(d\) with a certain bit rate volume \(h(d)\) is to be served in the network using a provisioned lightpath connection. For each request \(d\), set \(P(d)\) contains candidate routing paths generated using the \(k\)-shortest path algorithm. Each path \(p\in P(d)\) connects the request source node and destination nodes and traverses intermediate nodes included in set \(V(p)\subseteq V\). Each of intermediate nodes included in \(V(p)\) can be selected as a regeneration point. As mentioned above, for regeneration we apply transponders operating in B2B configurations (i.e., with interconnections at the client side) [6; 7]. Figure 1 illustrates the general idea of the B2B regeneration. For more information on the SS-FON with B2B regeneration network model refer to Reference [11]. In our previous papers, we examined three B2B regeneration scenarios: minimal regeneration, regeneration without modulation conversion, and flexible regeneration allowing for modulation conversion. Since, according to the results presented in References [11; 25; 28], the flexible approach provides the best results in terms of blocking probability, in this paper we focused only on this scenario. In the flexible B2B regeneration, a full flexibility of the B2B regeneration was assumed [29]. In more detail, an extra regeneration of SChs with modulation conversion can be applied in any intermediate node of the routing path. The motivation behind full flexibility is to use more efficient modulation formats for shorter transparent path segments with the possibility to apply different modulation  
Figure 1: Provisioning of a 200 Gbit/s lightpath without back-to-back (B2B) regeneration (case A) and with B2B regeneration (case B). The following modulation formats are applied: BPSK (Binary Phase Shift Keying), QPSK (Quadrature Phase Shift Keying), and 16-QAM (Quadrature Amplitude Modulation). formats on different segments, i.e., modulation conversion and spectrum conversion is allowed in regeneration nodes. Nevertheless, the flexible regeneration, apart from switching the regenerated data units, may require to (dis)aggregate them in order to match the capacity of transponders operating with different modulation formats. It should be stressed that the presented model can be easily adapted to other assumptions that described above, e.g., different values of \(\Delta_{\text{OC}}\).