# Stochastic Model Driven Performance and Availability Planning for a Mobile Edge Computing System
## 4 Evaluation of MEC Performance
### Refined Model with Absorbing State
#### 4.2.3 Model Validation  
The validation of the proposed system SPN model is detailed in this section. We performed different experiments in practical scenarios to measure the system's MRT and then compare with the MRT computed by the proposed model for the sake of validation. An experimental laboratory test-bed (as shown in Figure 11) was developed to help validate the analysis results of the proposed model, which has the following configuration, (**i**) \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario** & **MASTERC** & **AD** & **SLAVEC** \\ \hline \#1 & 40 & 1 & 16 \\ \#2 & 40 & 2 & 16 \\ \#3 & 40 & 3 & 16 \\ \#4 & 40 & 4 & 16 \\ \#5 & 40 & 5 & 16 \\ \#6 & 40 & 6 & 16 \\ \#7 & 40 & 7 & 16 \\ \#8 & 40 & 8 & 16 \\ \#9 & 40 & 9 & 16 \\ \#10 & 40 & 10 & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Possible scenarios for case study 2. Figure 10: Cumulative Distribution Functions for Study 2.  
internet bandwidth at 40 Mbps, (ii) a computer for synthetic request generation with CPU of Intel Core i7 2.4 Ghz and RAM of 8 GB capacity. We adopted a well-known word processing algorithm (Word Count Algorithm [[https://tinyurl.com/y8](https://tinyurl.com/y8) hofs5x]([https://tinyurl.com/y8](https://tinyurl.com/y8) hofs5x), accessed on 10 November 2020) using MapReduce for big data processing. The algorithm can help compute the number of keywords in a text file upon their unique occurrences. The texts in the file are split into data blocks. The number of _splits_ determines the number of mapping steps for split jobs. Afterwards, all split tasks are allocated and distributed to slave nodes. This process generates key-value pairs in which a key is mapped to a specific word while the key's value is exactly the number \(1\). It is worth noting that, the mapping results do not imply the accumulated occurrences of words in a text file. The sorting process generates a list of all values by key, after that, the reducing process summarizes the occurrences of each key in the list to obtain the total number of each keywords. Finally, the reducing process creates a file consisting of the number of occurrences in the text file for each word. In experimental implementation, the execution of the mapping and reducing processes is allocated to each node. At the end, the processing time of a text file at 15 MB size is measured on a single node, and the measured output is used to feed to model parameters. We deployed the edge into four different machines--one master and three other slave nodes. The arrival rate of a new request is set to the value 230 s. Each request is to process three consecutive text files at 40 MB in size each. To comply with [PERSON]'s law, the processing tasks are allocated to machines in the way that each machine processes only one file at a time. In this way, the experiment can obtain the highest level of parallelism without stressing the computer system. The mean processing time of one file on a slave node (PD) is necessarily measured in order to feed to parameters in the proposed model. The values of parameters in the SPN model used for model validation are summarized as follows, (i) PD: 51.7 s, (ii) AD: 230 s, (iii) MC: 20 and (iv) SC: 3. Using stationary analysis for the SPN model, the calculated value of MRT was 86.74 s. Furthermore, the value of total resource utilization was 22.4%. The experiment is conducted by repeatedly dispatching a specific number of consecutive requests (_100 requests_) to the edge. The extracted sample showed a normal distribution with a mean of 86.906 s. The One-Sample _t_-Test (One Sample _t_-Test [[https://tinyurl.com/yanthw4e](https://tinyurl.com/yanthw4e)]([https://tinyurl.com/yanthw4e](https://tinyurl.com/yanthw4e)), accessed on 20 November 2020) is used to make inferences about a population mean, based on data from a random sample. One-Sample _t_-Test is adopted to compare the values of MRT which are generated by the model and by the sample mean, respectively. It should be pointed out that, the case which both means are equal falls in the null hypothesis.