## 5 Performance Evaluation
### Experimental Results
#### 5.2.2 Kafka Broker Virtual Network Function Experiment
It assumes a Poisson arrival process, and provides a useful relationship between the mean waiting time \(T_{w}\) and the service rate \(\mu\), as follows:  
\[T_{w}=\frac{\lambda\big{(}\sigma_{s}^{2}+(1/\mu)^{2})\big{)}}{2(1-\rho)}, \tag{3}\]  
where \(\sigma_{s}^{2}\) is the variance of the service time distribution. Since the Poisson approximation is acceptable for the arrival process when many low-rate and non-deterministic traffic sources combine together, this model can also be useful for predicting the response time of a VNF, once the distribution of the service time is known. However, when considering a real edge deployment, it is not enough to estimate the service time from a VNF or a cascade of them, but it is important to also take into account the latency to and from the edge location. In Ref. [51], the authors estimated the average downlink and uplink for a 4G network through a measurement campaign. It resulted in an average uplink latency of \(T_{uplink}=28.84\) ms, with a standard deviation of \(\sigma_{uplink}=18.64\) ms, an average value on the downlink side equal to \(T_{downlink}=18.63\) ms, and a standard deviation of \(\sigma_{downlink}=6.39\) ms. Therefore, the average round trip time was approximately 50 ms, which should be taken into account when compiling the latency budget, including any VNF startup time. All these values are definitely higher than the service time that is presented in Figure 11, which is lower than 10 ms. The situation becomes even trickier when vehicular devices are considered, as in C-V2X services. In this case, it is critically important to take into account not only the service time, any startup time and round-trip latency, but also the size of the service area and the travel speed. In fact, if a VNF must be transferred to another edge/MEC node due to the vehicle crossing the service area border, it is necessary to carefully evaluate the possible advance with which this operation has to be performed. If the service tolerates sub-second delays, like standard notification services that use CAM messages, it may be possible to avoid any early instantiation. In fact, from the moment a message is sent once the border of the service area is crossed, the overall time to load the information on the border would be equal to \(T_{up,max}=T_{uplink}+T_{RNIS}+T_{boot,F}+T_{s}\), where \(T_{RNIS}\) is the time needed by the Radio Network Information Service (RNIS) to detect the change in service area and to trigger the VNF instantiation. \(T_{RNIS}\) is estimated in the order of few ms and is assumed to be equal to approximately 4-5 ms [52]. Using the values mentioned above, we can estimate a \(T_{up,max}\) value of about 100-110 ms. Considering a vehicle speed of 120 km/h, typical of highways, we obtain the fact that, when the information was processed by the on-board C-V2X service, the vehicle could have moved less than 4 m. If the vehicle needs a response back, the overall round trip time has to also include \(T_{downlink}\), leading to about 120-130 ms, which corresponds to a vehicle movement of less than 4.5 m in the meantime. This value is acceptable for most services, with the exception of those that manage automatic maneuvers, which instead require uRLLC services with bounded times. Finally, we provide some comparative results, in terms of data plane KPIs, compared to the Kafka VNF broker implemented with VMs or containers in VMs. In order to compare VNFs that have quite different deployment models, we consider a normalized performance metric, defined as the CPU occupancy required by a Kafka VNF to handle 1 Mbps of traffic. Experimental results are shown in Table 4 for the following three deployments:  
* Kafka broker VNF, running inside a VM implemented with Ubuntu OS;
* Kafka broker VNF, running in a Docker container inside the same VM;
* Kafka broker VNF, running in a Kata container inside a Firecracker microVM. We emphasize that these three deployments all provide the same level of security and isolation.