## 4 Algorithms  
In this section, we describe several algorithms developed for predeployment of transponders in SS-FONs with B2B regeneration. First, we present reference methods, mostly based on simple greedy algorithms. Next, we propose a new method scaled average used regenerators (SAUR) based on a data analytics approach. Let us assume that we are given \(T\) transponders to be located in network nodes in order to allow provisioning of the requests (lightpaths) with the possibility to use the B2B regeneration in some intermediate nodes of the routing path. Moreover, let \(t(v)\) denote the number of transponders predeployed in node \(v\in V\). The basic approach proposed in our previous paper [12] assumes that the transponders are located in the network nodes proportionally to a selected metric. The following versions of this approach are considered in this paper. Uniform location (UNI) assumes that each node is assigned with the same number of transponders [18]:  
\[t(v)^{\text{UNI}}=[T/|V|]. \tag{1}\]  
Nodal degree (ND) assumes that transponders are located proportionally to the degree of network node [18]:  
\[t(v)^{\text{ND}}=[T\cdot nd(v)/\sum_{w\in V}nd(w)], \tag{2}\]  
where \(nd(v)\) denotes the node degree of node \(v\). Routing only (RO) assumes that transponders are located proportionally to the number of times a particular node is included in the shortest path considering all node pairs [18]:  
\[t(v)^{\text{RO}}=[T\cdot nsp(v)/\sum_{w\in V}nsp(w)], \tag{3}\]  
where \(nsp(v)\) denotes the number of times node \(v\) is included in the shortest path between a node pair considering all node pairs. Configurations only (CONF) works similarly to RO; however, here, all the possible configurations (regeneration options) for the shortest path for each node pair are analyzed, and transponders are located proportionally to the number of times a particular node is included in the configuration considering all node pairs [12]:  
\[t(v)^{\text{CONF}}=[T\cdot nscp(v)/\sum_{w\in V}nscp(w)], \tag{4}\]  
where \(nscp(v)\) denotes the number of times node \(v\) is included in a configuration based on the shortest path between a node pair considering all node pairs [12]. Combined (COMB) assumes that transponders are located according to a metric that includes three elements: nodal degree (weight 40%, proportionally), number of transponders in the end nodes in the best configuration according to a metric showing usage of network resources (weight 40%, proportionally), and average distance to other nodes (weight 20%, inversely proportionally) [12]:  
\[t(v)^{\text{COMB}}=[0.4\cdot t^{\text{ND}}(v)+0.4\cdot t^{\text{ENC}}(v)+0.2 \cdot t^{\text{AD}}(v)], \tag{5}\]  
where \(t^{\text{ND}}(v)=[T\cdot nd(v)/\sum_{w\in V}nd(w)]\) denotes the number of transponders assigned to node \(v\) according to nodal degree, \(t^{\text{ENC}}(v)=[T\cdot enc(v)/\sum_{w\in V}enc(w)]\) denotes the number of transponders assigned to node \(v\) according to number of transponders in the end nodes in the best configuration, and \(t^{\text{AD}}(v)=[(T\cdot(1/ad(v))/\sum_{w\in V}(1/ad(w))]\) denotes the number of transponders assigned to node \(v\) according to number of transponders in the end nodes in the best configuration. It should be noted that the above presented algorithms do not account for additional knowledge that can be obtained by a data analytics approach which provides information on the network traffic profile observed in the near past or predicted for the future. Now, we present two traffic-based methods. In both proposed methods, for solving the dynamic RSSA problem we use the adaptive routing with back-to-back regeneration (ARBR) algorithm proposed in our previous paper [11]. Note that the results from Reference [11] clearly confirm that the ARBR method provides much better results in terms of bandwidth blocking probability when compared to other methods in the context of SS-FONs with B2B regeneration.