# VNF Placement Optimization at the Edge and Cloud +
## 6 Results and Discussions  
In this section, a comparison of the two approaches is presented via simulation. However, it should be noted that the MIP algorithm is used as a benchmark since it is not implementable for large-scale systems (e.g., MIP needs 200 \(\times\) more execution time than TS). To better illustrate the efficiency of the proposed approaches, we compare them against the Instance Consolidation (IC) [38] and Baseline [40] heuristics. The IC algorithms try to consolidate as many adjacent VNFs of an SC as possible to a single instance that can be deployed on a server with the goal to minimize the resource idleness. This can be a very cost-effective solution since it can minimize the number of physical resources used for the placement of the VNFs. In the Baseline approach, the algorithm tries first to place the VNFs at the Edge. If there are not enough resources at the Edge, then it offloads the rest of the VNFs at the Cloud. The reason we selected this algorithm is to compare our approach with an algorithm that tries to benefit as much as possible from the presence of the Edge infrastructure. Our physical infrastructure consists of 50 nodes, with 60% cloud servers, 20% MEC servers, and 20% routers used only for forwarding purposes (e.g., for our transport network). Nodes are interconnected with 50% probability. The resource characteristics of the physical resources are provided in Table 1. Regarding the propagation delay, we assume we cover IoT applications on a smart city with a radius of 6 km. The edge servers are uniformly distributed in the vicinity of the IoT service area in a radius of 10 km. Finally, the core network lies in an area of 100 km away from our IoT devices. The infrastructure topology used to extract the propagation delay characteristics is illustrated in Figure 4.  
There are 10 SCs available consisting of a number of VNFs uniformly distributed in the range from 2 to 5 following the topological characteristics as in Figure 2. The resource demands are provided in Table 1. The demands of CPU and Memory are per VNF, while the demands of bandwidth are per IoT device. Regarding the requested bandwidth, we are using typical rate values generated per IoT device according to the IoT application it belongs (e.g., Virtual Reality [52], Retail [53], e-Health [54], Wearables [55], and Autonomous Vehicles [56]). To better illustrate the importance of an efficient resource allocation, we utilize high traffic rate IoT applications in order to stress the capabilities of our infrastructure. Each SC is assumed to handle a random number of devices according to the type of the service being processed. To this end, each SC is modeled with a different arrival rate between the range of 2-10 devices per hour, while the lifetime lies in the range of 1-24 h. The experiments last for a period of one day, while measurements are taken every half an hour. Based on this distribution, we can model a M/M/1 queue as described in Section 3. Furthermore, to model the transmission and processing delays, we assume that a server that is not fully loaded can process packets with a rate of 0.88 Mpps using packets of 1518 bytes. Moreover, we consider that each VNF may cause the traffic to be compressed, decompressed, or remain intact with an equal probability. For compression and decompression, a 20% change in the traffic is applied. Finally, we assume that 20% of the VNFs of an SC need to be deployed on the MEC layer, 30% on the Cloud, and the remaining 50% does not pose any location restrictions. To quantify the achieved performance, two experiments are carried out. In the first experiment, we evaluate the impact of each component of the TS algorithm in the allocation solution and we extract the optimal configuration. Following that, in the second experiment, we evaluate the various allocation algorithms in terms of the deployment cost. For modeling the deployment cost, we use the pricing model provided in [57].