# A Heuristic Fuzzy Based 5G Network Orchestration Framework for Dynamic Virtual Network Embedding
## 4 Proposed Strategy for Dynamic Virtual Network Embedding (DVNE)
### Node Mapping for DVNE  
According to the literature, many strategies for node mapping have utilized the approach based on node ranking. Node rankings for the request and the physical infrastructure are prepared based on their respective node parameters. Because node parameters are different, recent techniques adopt multi-criteria decision making techniques for ranking. This proposed work employs the heuristic fuzzy ranking of request nodes and physical infrastructure for embedding. The membership functions for the respective node parameters are prepared using fuzzy, and the decision on the node's position in the ranking is made using the decision fuzzy set value of each node. In this work, the membership functions are developed for CPU capacity, degree, BW, and closeness centrality. * Membership function for CPU capacity: This membership function is used to determine how close a node's CPU capacity is to the maximum capacity of the cluster. The highest priority in the ranking is assigned to the member with the highest membership value. \(CPU_{min}\) and \(CPU_{max}\) are the ranges of CPU capacity that have been specified for the process. \[\mu_{CN,i}= \begin{cases}1&if(CN(i)\geq CPU_{max})\\ \frac{CPU_{max}-CN(i)}{CPU_{max}-CPU_{min}}&if(CPU_{min}\leq CN(i)<CPU_{max}) \\ 0&if(CN(i)<CPU_{min})\end{cases} \] (16)
* Membership function for node degree: This membership function determines how close a node's degree is to the node's maximum degree. The degree range is determined using network information. The maximum limit (\(DN_{max}\)) is determined by the node with the highest degree in the network, and the minimum limit (\(DN_{min}\)) is determined by the node with the lowest degree in the network. As a result, a node with the highest degree in the network has the membership value '1', while a node with the lowest degree in the network has the membership value '0'. The member with the highest membership value is given the highest priority in the ranking. Figure 2: Proposed strategy for dynamic network embedding. \[\mu_{DN,i}= \begin{cases}1&if(DN(i)\geq DN_{max})\\ \frac{DN_{max}-DN(i)}{DN_{max}-DN_{min}}&if(DN_{min}\leq DN(i)<DN_{max})\\ 0&if(DN(i)<DN_{min})\end{cases}  \tag{17}\]
* Membership function for bandwidth: the available bandwidth of any node can be compared to the maximum bandwidth of the node using this membership function. This is similar to the way a node's degree is determined by its location on the network. The maximum limit (\(BN_{max}\)) is taken from the node that has the most bandwidth available in the network, and the minimum limit (\(BN_{min}\)) is taken from the node that has the least bandwidth available. In this case, a node with the most bandwidth in the network is given the membership value of \"1\", while a node with the least bandwidth is given the membership value of \"0\". The member with the highest membership value is given the highest priority in the ranking. \[\mu_{BN,i}= \begin{cases}1&if(BN(i)\geq BN_{max})\\ \frac{BN_{max}-BN(i)}{BN_{max}-BN_{min}}&if(BN_{min}\leq BN(i)<BN_{max})\\ 0&if(BN(i)<BN_{min})\end{cases} \] (18)
* Membership function for closeness centrality: A node's closeness centrality can be calculated using this membership function by comparing it to the node in an associated network with the highest closeness centrality. The range for the closeness centrality is selected from the network information in the same way as the degree and bandwidth of a node. After calculating the closeness centrality of every node in a network, the upper and lower bounds ((\(LN_{max}\)) and (\(LN_{min}\))) are immediately determined. This means that the network's most central node receives the membership value '1', while the network node with the lowest closeness centrality receives the membership value '0'. Priority is given to the most valuable member in terms of membership value when ranking. \[\mu_{LN,i}= \begin{cases}1&if(LN(i)\geq LN_{max})\\ \frac{LN_{max}-LN(i)}{LN_{max}-LN_{min}}&if(LN_{min}\leq LN(i)<LN_{max})\\ 0&if(LN(i)<LN_{min})\end{cases}