# A Framework for the Joint Placement of Edge Service Infrastructure and User Plane Functions for 5G
## 4 Framework Proposal
### UPF Placement Stages
#### 4.2.2 Near-Optimal UPF Placement
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Service** & **Latency** & **Data Rate** & **Density** & **Reliability** & **m** \\  & **(ms)** & **(Mb/s)** & **(users/km\({}^{2}\))** & **(\%)** & \\ \hline Automated Factories & \(\leq\)1 & 1 & 10\({}^{4}\) (R), 0 (U) & 99.999 & 0 \\ mIoT & \(\leq\) 1 & 1 & 10\({}^{3}\) (R), 10\({}^{4}\) (U) & 99.999 & 0/1 \\ Cooperative Sensing & \(\leq\)1 & 5 & 10 (R), 100 (U) & 99.999 & 1 \\ Home \& Office & \(\leq\)10 & 50 (R), 300 (U) & 100 (R), 10\({}^{3}\) (U) & 90 & 0 \\ Traffic Efficiency & \(\leq\)5 & 25 & 5 (R), 50 (U) & 90 & 1 \\
50 Mb/s everywhere & \(\leq\)10 & 50 & 50 (R), 400 (U) & 90 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: 5G service requirements. Figure 3(a,b) both show the score, cost and number of ENs deployed by each placement strategy for all input TG values. To estimate the score, the procedure in [23] was followed. In summary, the Score plots (leftmost plots in Figure 4) demonstrate that HSA outperformed EA significantly (considering that a logarithmic scale was used to normalize the score estimation values). Namely, HSA achieved cost savings over 15% when compared to EA in every case, reaching around 20%-30% for more than 300 TGs. Similar values can be observed for the number of ENs deployed by each mechanism (rightmost plots in Figure 4), where the HSA reached a maximum of over 30% less ENs deployed. We strongly believe these results prove the complexity of the ENPP and the limitations to be considered in order to select an adequate solving heuristic. In this particular case, when applying EA to the ENPP, the coverage nature of the problem forces a high probability of occurrence for a \"dominoes effect\", where a continuous EN-TG re-arranging is caused after changing a previously selected EN-TG pairing solution. Since the node density is significantly high (as expected in future 5G networks), changing a valid EN-TG assignment, i.e., through the mutation and crossover techniques applied by evolutionary techniques, commonly results in a large chain of EN-TG reassignments throughout the complete service area. As a consequence, invalid solutions are typically generated and \"repair\" procedures have to be executed. This situation leads to a lower probability of a child solution enhancing a parent valid EN placement. The cost savings achieved by the placement strategies, in particular by the HSA, are directly linked to the EN network deployment costs. Nevertheless, our problem formulation and solving scheme ensure a significant reduction in the operating expenses as well due to the capacity assignment optimization and the reduction in the total number of ENs deployed. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Num. Generations & 100.00 \\ Num. Individuals & 100.00 \\ Mutation rate & 0.0100 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Input parameters for the Evolutionary Algorithm. Figure 4: Evaluation of the proposed heuristics to solve the ENPP. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Minimum Temperature & 0.0001 \\ Maximum Temperature & 1.0000 \\ Temperature Iterations & 10.000 \\ Fast Alpha & 0.8000 \\ Slow Alpha & 0.9500 \\ Num. Neighbors & 10.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Input parameters for the Hybrid Simulated Annealing. ### UPF Placement Results

For the UPF placement solutions, a scenario composed of 100 access nodes (TGs) and the set of EN locations obtained from the HSA were selected. To evaluate the performance of our solutions regarding user mobility considerations, similar placement conditions are mandatory. Hence, the use cases presented in Table 3 were classified by taking into account only latency and reliability requirements. Two service categories were obtained as a result of the placement analysis stage. The first group comprises services with the highest requirements, i.e., automated factories, mIoT and cooperative sensing, whereas the second one is formed by the remaining services.