# Comprehensive Comparison of VNE Solutions Based on Different Coordination Approaches
## 5 Mixed Coordination Algorithm Proposal  
The above results gave us the stimulus to propose a new and innovative algorithm that has not been proposed before in the known literature to our knowledge. The algorithm essentially creates a new category in the field of VNE coordination strategies. This mixed stage coordination solution combines the benefits of both the single and two stage candidates. The choice among the examined strategies was made according to their performance during the presented experimental procedure. The R-ViNE-PS was chosen as the two-stage representative because it performed equivalently to its deterministic counterpart regarding the AR and ANS metrics as Figures 11 and 12 illustrate, respectively, but with more competitive RTs (Figure 10). As far as the single stage solution is concerned, the AdvancedVNMFlib Algorithm 1 was chosen, due to the fact that it clearly outperformed the SimpleVNMFlib variant during the CR*MR index comparison (Figure 5), achieving embeddings of lower cost with relation to the respected mapped revenue ratio. The algorithm begins by initializing the substrate network SN with the sets of physical nodes \(N_{s}\) and links \(L_{s}\). By populating the VNR object, it is established that the number and specifications of the incoming VNRs, denoted as \(G_{j}^{V}(VN^{i})\), are predetermined and already known, creating an offline VNE environment. In this context, index \(j\) represents the number of the incoming VNRs, while index \(i\) indicates the scale of the VNs that constitute those  
Figure 12: ANs of the rounding techniques of R-ViNE-PS. VNRs. Afterward, each VNR is stored in the VNR_proc object and processed according to the following strategy. The initial VNRs are mapped by the embedding procedures of R-ViNE-PS, until the Relative Intensity Index (RII), calculated by the RII_calc() function, surpasses the value of 0.04. The RII is calculated for every scenario by Equations (14)-(17):  
\[RII_{i}=\frac{AAI_{i}}{\sum_{i=1}^{n}AAI_{i}} \tag{14}\]  
\[AAI_{i}=DI_{i}\times TD_{i} \tag{15}\]  
\[DI_{i}=\frac{\text{Nodes per VNR}}{\text{Number of VNRs}} \tag{16}\]  
\[TD_{i}=[\text{Number of nodes})\times\text{CPU}]+[(\text{Number of links}) \times BW)] \tag{17}\]  
where \(AAI\) is the Absolute Intensity Index of each scenario \(i\), \(DI\) is the Density Index of the respected trial, and \(TD\) represents the Total Demand of the incoming VNRs during an experimental iteration. According to our experimental results and as Tables 6 and 7 portray, the performance of the two-stage algorithm deteriorates after the RII passes the aforementioned threshold of 0.04. As the embedding process progresses, our algorithm begins to utilize the procedures of AdvancedVNMFlib for the realization of the embeddings. Finally, when all the VNRs have been successfully allocated or the SN resources have proven to be insufficient, the algorithm stops and returns the set of the successful embeddings SN\({}^{\prime}\). This novel solution produced promising results and performed satisfactorily under any circumstance of incoming VNRs, regardless of density and intensity. While the values of the RII index allow it, the algorithm incorporates the additional distance constraint (see Equation (2), Section 2.1.3 which thresholds the maximum permitted hops between virtual nodes and the respective physical mapping candidates. By doing so, shorter substrate paths are utilized, and less networking and computational resources are occupied; thus, lower costs are achieved. However, when the critical threshold is reached, the algorithm shifts to a more agile mapping strategy, adopting longer paths across the SN and maximizing the mapped revenue.