# Stochastic Model Driven Performance and Availability Planning for a Mobile Edge Computing System
## 4 Evaluation of MEC Performance
### Basic SPN Model for MEC Architectures
#### 4.1.2 Numerical Analysis  
This section presents two numerical analyzes for MRT, discard, and utilization evaluations. In [40], the authors evaluated a MEC architecture with a single mobile device as a client and containers executing the services. Authors have evaluated a 3D game called Neverball, where the player must tilt the floor to control the ball to collect coins and reach an exit point before the time runs out. We have considered the system parameters in [40] as input parameters for our model. Therefore, our study evolves the work in [40] by performing numerical analysis to evaluate the scenarios considering multiple parameters. We have considered one of their scenarios with a game resolution of 800 \(\times\) 600 pixels. The adopted parameter value corresponding to the processing delay (PD) of a request is 24 ms. We adopted 5 ms as the time for distributing the requests in the system (DD transition). We established that the master server has a restriction regarding the maximum number of requests that may be simultaneously processed. This number corresponds  
mentioned above, we present the results considering MRT, discard, and utilization of the master server and slave servers. Figure 4 shows the results for the MRT. At first, it is expected that the larger the time interval between arrivals (AD), the smaller the MRT. The system will be more able to handle the incoming requests with the available processing resources. It is also expected that the higher the slave's capacity (SC), the lower the MRT because more processing capacity is available to handle the requests. These two behaviors are easily observed when the values of discards are minimal in the model (which can be observed in Figure 7). For minimal discards, the MRT decreases until the minimum time to perform requests without requests waiting in the queue. However, when the system discards incoming requests, we observe the increase of the MRT until a peak, decreasing after that. This behavior is due to the limiting value of resources in the system, where some of the incoming requests are discarded when there are no more resources available to process them. Thus, limiting the MRT variation to the time between arrivals. As can be deduced from [PERSON]'s law [39], the mean time between exits will increase along with the mean time between arrivals until to reach the peak. In our numeric results, the peaks were: for SC = 8 was in AD = 1.5 ms and for SC = 16 it was AD = 3.0 ms. At these points, the amount of work within the system begins to reduce, reducing MRT even when AD increases drastically. It is important to emphasize that in MRT, we consider the effective arrival rate, that is, adjusting its value by considering the discard probability. The MRT for SC = 32 is low, even for a time interval between arrivals of 1 ms. Comparing SC = 16 and SC = 32, and considering an arrival delay of 2.5 ms, the MRTs equalize. Considering an arrival delay of 5.5 ms, and the SC = 8, it also presents the same average result. Therefore, if the real context has had an AD = 5.5 ms, an 8-core server would achieve the same performance as more powerful servers. Therefore, our work may assist managers in the task of choosing servers and identifying the best performance and costs, considering the expected workload. Figure 5 shows the level of utilization of the master server. The master server is the first component that the request reaches upon entering the MEC layer. For the SC = 8 and SC = 16 configurations, the utilization level is around 100% in the lowest AD values; after that, utilization drops. For SC = 32, even with AD = 1.0 ms, the utilization value reaches only 20%. From AD = 5.5 ms, the three configurations have values similar to and  
Figure 4: MRT. close to 0%. The system administrator must consider the desire for high or low idle server levels. Figure 6 shows the level of utilization of the slave servers. The higher the number of resources, the lower the level of utilization of the slaves.