# Traffic-Based Heuristics for Regenerator Placement in Translucent Dynamic Optical Networks
## 7 Conclusions  
In this paper, we propose two heuristic strategies to solve the regenerator placement problem (RPP) in translucent networks under dynamic traffic. The heuristics are based on both traffic forecasts and estimates of blocking probabilities in the network. The proposed heuristics are compared to other regenerator placement algorithms from the literature in two different typologies. We demonstrate the effectiveness of the new proposal under several different situations, such as uniform and non-uniform traffic, fixed and fixed alternative routing algorithms, different values of maximum transmission reach, as well as considering differences between forecast and actual network traffic. From the obtained results, we conclude that the proposed DLD algorithm finds translucent networks with significant lower BP values than the other investigated algorithms in the paper for the same number of installed regenerators; regardless of the topology, traffic pattern, or intensity considered, transmission reach assumed and whether the fixed of fixed alternate routing is used during the network operation. The superior performance of the DLD algorithm over FLD can be explained by the fact that the DLD uses a more precise node load estimate. On the other hand, the relative performance of the proposed FLD heuristic and the previously proposed RR, RO, ND, and UN heuristics are very dependent on the considered \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Topology** & \(T_{R}\) **(km)** & \
\begin{tabular}{c} **Number of** \\ **Essential Nodes** \\ \end{tabular} &
\begin{tabular}{c} **Index of the Essential Nodes** \\ \end{tabular} \\ \hline EuroNet & 1600 & 19 & 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 16, 17, 19, 20, 21, 23, 24, 26 \\ \hline EuroNet & 2000 & 13 & 2, 4, 8, 10, 11, 14, 15, 16, 17, 20, 21, 22, 26 \\ \hline EuroNet & 2400 & 4 & 9, 13, 16, 22 \\ \hline \multirow{3}{*}{CoreNet} & \multirow{3}{*}{1600} & \multirow{3}{*}{42} & 0, 2, 3, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 31, 32, 35, 36, 39, 41, 45, 46, 47, 52, 54, 56, 57, 60, 62, 63, 64, 65, 66, 67, 68} \\ \hline \multirow{3}{*}{CoreNet} & \multirow{3}{*}{2000} & \multirow{3}{*}{28} & 0, 2, 3, 7, 8, 9, 12, 14, 15, 18, 19, 21, 23, 26, 28, 31, 35, 46, 56, 57, 59, 60, 62, 64, 65, 66, 67, 68} \\ \cline{1-1} \cline{3-3}  & & & 0, 2, 3, 7, 9, 14, 18, 19, 21, 26, 28, 31, 32, 52, 56, 60, 65 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Total amount and node indexes of the essential nodes found for EuroNet and CoreNet topologies considering different transmission reaches of \(T_{R}\) = 1600 km, \(T_{R}\) = 2000 km, and \(T_{R}\) = 2400 km. Figure 11: Blocking probability as a function of the total number of regenerators in the EuroNet topology assuming transparent reaches of: (**a**) \(T_{R}\) = 1600 km; (**b**) \(T_{R}\) = 2400 km, each compared against the reach of \(T_{R}\) = 2000 km. scenario as the algorithm that achieves the lowest blocking probability values among them is strongly dependent on the topology, maximum transmission reach, number of regenerators deployed, and routing algorithm. We also believe that the proposed algorithms/methodology can be extended for multi-rate/flex-grid networks by considering, for each rate, it is respective offered load and transmission reach as proposed in Appendix A.  
Conceptualization, A.L.S.d.F. and D.A.R.C. ; Investigation, A.L.S.d.F. and D.A.R.C. ; Methodology, A.L.S.d.F. and D.A.R.C. ; Software, A.L.S.d.F. and D.A.R.C. ; Validation, A.L.S.d.F., R.C.A.J. and D.A.R.C. ; Writing--original draft, A.L.S.d.F., R.C.A.J. and D.A.R.C. ; Writing--review & editing, A.L.S.d.F., R.C.A.J. and D.A.R.C. All authors have read and agreed to the published version of the manuscript. This research was partially funded by Government Brazilian researching agencies National Council for Scientific and Technological Development (CNPq) and Fundacao de Amparo a Ciencia e Tecnologia de Pernambuco (Facepe).