## 4 Algorithms
Since the traffic in the network is stochastic, therefore, to improve the quality of the obtained statistics of transponder usage, we perform data cleaning using the interquartile range method to remove outliers for each of analyzed nodes (Step 3). The interquartile range method is a measure of variability, based on dividing a rank-ordered data set into four equal parts (quartiles). The values that divide each part are denoted by Q1, Q2, and Q3. Interquartile range (IQR) is equal (Q3 - Q1), i.e., the difference between third and first quartiles. Outliers are defined as observations that fall below (Q1 - 1.5 IQR) or above (Q3 + 1.5 IQR). Next, for each node parameter, \(avt(v)\) is obtained (Step 4). In more detail, \(avt(v)\) denotes the average usage of transponders estimated over all time iterations. In particular, the time scale is divided into time slots (iterations) in which new requests arrive to the network and some other requests are finished according to the assumed average arrival rates and lifetimes. After each iteration, various statistics on the network usage are calculated, including usage of transponders at network nodes. To account for different traffic characteristics, in SAUR we use _scaled_ allocation, i.e., transponders are allocated proportionally to the average usage scaled by using the power function with exponent \(\beta\). To this end, in Step 5, parameter \(a(v)\) is calculated using the following formula:  
\[a(v)=power(avt(v),\beta), \tag{6}\]  
Finally, in Step 6, the number of transponders assigned to each node is computed using \(a(v)\):  
\[t(v)^{\text{SAUR}}=\lfloor a(v)\cdot T/\sum\limits_{w\in V}a(w)\rfloor, \tag{7}\]  
As mentioned above, MSU and SAUR are both traffic-based approaches that use data obtained by simulation of the routing algorithm for a selected network profile. However, when compared to MSU, SAUR provides the following key differences. First, SAUR addresses the fact that in our  
Figure 4: SAUR pseudocode. Figure 3: Workflow of the scaled average used regenerators (SAUR) method. network model, B2B regeneration is allowed, i.e., we predeploy transponders that are used not only for regeneration of the signal at some intermediate nodes (as in MSU) but also for transmitting/receiving (add/drop) of the signal at the source/destination. Second, in our previous research on performance of SS-FONs with B2B regeneration, we noticed that, according to the number of available transponders in the network (parameter \(T\)), the performance of the network changes (for instance, see the results in References [11; 12]). Therefore, we assume that every node has a limit of available transponders in the dynamic routing simulations, and thus there is the possibility of a lack of transponders at some network nodes which will affect the performance of the dynamic routing algorithm. In contrast, the MSU method assumes that during the simulations there are no limits on the number of regenerators available in the network nodes. Third, SAUR allocates transponders according to their average usage observed during the whole simulation, while MSU focuses on the maximum usage. This difference between both methods is motivated by the fact that, in our opinion, the average utilization observed over a longer period of time is more important than short-term dependencies that can occur due to the stochastic nature of the network traffic and dominate the final allocation of transponders. Finally, the proposed SAUR method can be tuned, i.e., transponders are allocated proportionally to the average usage scaled by using the power function with exponent \(\beta\). In this way, we can adjust the performance of SAUR to account for different traffic profiles that can occur in the network. It should be stressed that the two traffic-based methods described above (i.e., MSU and SAUR) strongly rely on the data analytics approach. Firstly, these methods depend on the knowledge on the network traffic obtained by analysis of historical data or traffic prediction methods.