# VNF Placement Optimization at the Edge and Cloud +
## 6 Results and Discussions
### Experiment 2: VNF-PEC Evaluation  
In this experiment, we evaluate the performance of the four algorithms under consideration. Figure 9 illustrates the average deployment cost per SC. As was expected, the MIP algorithm provides the lowest cost. Nonetheless, the TS approach manages to provide a very cost-efficient solution close to an optimal one. The reason is that TS adopts the same multi-objective function as the MIP algorithm. Hence, only solutions that lead to lower costs are produced at each step of the local search mechanism. On the other hand, the IC and Baseline algorithms present the worst performance. Even though both algorithms try to consolidate the VNFs on the same server or at the Edge, they fail to do it as efficiently as the other two algorithms. The rationale behind this behavior is that both algorithms do not consider any possible location constraint. Hence, they may not find neighbor servers that can host the rest of an SC, leading to using a higher number of links and thus a higher cost. This can be more evident for the Baseline algorithm, where VNFs constrained to be located at the cloud can lead to multiple crossings of the transport network, which significantly adds to the overall cost. To better understand the deployment solutions produced, we also evaluate the total number of servers and links used as illustrated in Figures 10 and 11. Our first observation is that, in the course of time, the number of nodes and links needed to facilitate the incoming users increases for all algorithms. This happens because even though we may consider 10 SCs, which is a typical number of a service portfolio by a SP, some of them need to be duplicated to serve all the incoming users. This can be validated by Figure 12, where we can see that initially only 10 SCs are deployed. However,  
Figure 8: Impact of the Termination Criterion in Tabu Search. Figure 9: Average deployment cost per service chain. VNFs are constrained to be located at the Edge or Cloud, efficient consolidation is not possible, leading to higher resource utilization. Similarly, for the Baseline algorithm, if the Edge resources are stressed or if there are VNFs with Cloud resource requirements, the resource allocation performance is significantly deteriorated. On the other hand, the MIP and TS algorithms utilize less physical resources and more efficiently. This validates the efficiency of a multi-objective approach, when considering both the Edge and Cloud infrastructures. The MIP algorithm as an optimal solution provides the lowest number of resources, while TS through the refinement mechanism applied by the Local Search can minimize the performance gap. Even though we would expect that the MIP and TS algorithms would present a higher total delay, since they utilize less resources than the other two algorithms, this is not the case. As illustrated in Figure 13, the MIP algorithm manages to succeed the least total delay per SC. This is because the MIP algorithm instantiates a higher number of SC and thus distributes more efficiently the load between the servers, while minimizing processing and queuing delays. At the same time, since it jointly tries to allocate the VNFs and interconnect them with the goal to minimize the deployment cost and overall delay, it performs a much more efficient link selection. On the other hand, the TS algorithm utilizes a simple shortest path algorithm similar to the other heuristics. Nevertheless, TS presents a lower delay since it takes into consideration the location constraints and thus can avoid long paths between the Edge and Cloud. The two heuristics once again show a poor performance. The Baseline algorithm, exactly due to the fact that does not take into consideration the latency overhead of using the transport network, presents a high propagation delay that significantly contributes to the overall delay.