# Performability Evaluation and Sensitivity Analysis of a Video Streaming on Demand Architecture
## 5 Numerical Analysis
### Design of Experiments (DoE)  
Design of Experiments (DoE) is a set of statistical techniques that help to increase the understanding of a product or process under study [25]. DoE can be used to evaluate the importance and interactions of input components in a particular process. Variations in input factors can be combined at different levels to produce a metric or response variable. Table 6 shows the factors and levels used in our approach. Two analyses were conducted, one for each metric being considered.  
The MTTF and MTTR of each component collected from the base model, along with the timed transitions from the Front-End and Back-End subnets, were used as the eight factors. Level 1 uses 50% less than the normal input value, while Level 2 uses 50% more. A set of combinations is created from these factors, consisting of the result of the equation of N factors minus 1, raised to the power of N levels. The number of combinations generated for this work was approximately 128. Figure 9 shows all of the DoE results.  
Figure 9a presents the Pareto chart, which indicates the impact of each factor. The factors with the greatest impact on availability were: Front_MTTR, Back_MTTR, Back_MTTF, and T_Process1. The components with the least relevance were T_Transmit1 and T_Transmit2, gateways that do not directly impact system availability.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Factors** & **Level 1** & **Level 2** \\ \hline Front_MTTR & 1.5 & 4.5 \\ Front_MTTF & 11,434.5 & 34,303.5 \\ Back_MTTR & 1.5 & 4.5 \\ Back_MTTF & 11,434.5 & 34,303.5 \\ T\_Process1 & 50 & 150 \\ T\_Process2 & 50 & 150 \\ T\_Transmit1 & 50 & 150 \\ T\_Transmit2 & 50 & 150 \\ \hline \hline \end{tabular}
\end{table}
Table 6: DoE factors and levels.  
Figure 8: Extended model using Hot-Standby redundancy.  
Figure 9e presents the interaction between the system factors. The average availability ranges from 0.9995 to 0.9997. When the lines are parallel, there is no interaction. The greater the interaction between the elements, the less parallel they are. As a result, we can observe that the most significant interactions occur when a component interacts with the system's Front-End, either with its MTTR or with its MTTF.  
Figure 9c shows the main effects graph. Each column presents a component. The effect of the difference in the set levels can be scaled based on the distance between the points and the slope of the line. In the Front_MTTF, T_Process1, and T_Transmit2 components, the impact of the levels was greater than the others.  
Figure 9b shows the impact of the combination of components on the MRT. The factor with the AC index (composed of Front_MTTR and Back_MTTR) was the most impactful combination on the entire system. Combining Front_MTTF and T_Transmit2 has a significant impact on the entire system. In addition, the least impactful components were T_Process2 and Back_MTTR.  
Figure 9f presents the interaction between the factors that impact the MRT. Some factors with a high level of interaction include: Front_MTTR x Back_MTTR and Front_MTTF  
Figure 9: DoE results. (**a**) Pareto chart of availability, demonstrating the impact of each factor on the system. (**b**) Pareto chart for MRT. (**c**) Main effect graph of system factors for availability. (**d**) Main effect graph for MRT. (**e**) Interaction between system factors for availability. (**f**) Interaction between system factors for the MRT.  
x T_Transmit2. In both cases, the evaluator must carefully consider the trade-off between these factors, because the consequences would be significantly different.  
Figure 9d shows the main effect for the metric MRT. In all cases, a steep slope of the lines significantly affects the MRT. The important thing here is to understand the alignment of the lines. For example, for Front_MTTR, the MRT decreases when this factor is increased.