# Assessing Database Contribution via Distributed Tracing for Microservice Systems
## 3 Methodology
### Determining the Importance Weight of Business Scenarios  
We determine the importance weight of the \(m\)-number business scenarios through analytical hierarchy process (AHP) [14,46]. AHP is a multicriteria decision-making approach, which was proposed by American operations research scientist [PERSON] in the 1970s. It has been widely used in enterprise management, engineering scheme determination, resource  
Figure 3: Framework of our method. Figure 2: An example of a general microservice system. The main practical influence of the calculated database contribution is to provide information for runtime deployment optimization. allocations, resolving conflict, etc. [47]. For determining the importance weight of business scenarios, the four steps are as follows:  
**Step 1. ** Structuring hierarchy of business scenarios. By combiningthe business scenarios of the microservice system, a hierarchical structure can be built, including the top layer, the middle layer (\(m\)-number business scenarios are divided into \(q\)-number different categories, and there are \(c_{i}\)-number business scenarios in the \(i\)-th category, i.e., \(c_{1}+c_{2}+\cdots+c_{q}=m\); in simple systems, this layer can be omitted), and the bottom layer (\(m\)-number business scenarios layer), as shown in Figure 4. It is important to note that the business scenarios cover at least all major business processes and functions. **Step 2. ** Constructing pairwise comparison matrices. Construct a set of pairwise comparison matrices for each of the lower levels with one matrix for each element in the level immediately above. For example, for the hierarchy model in Figure 4, a total of \(q+1\) pairwise comparison matrices need to be constructed. This step is usually achieved by inviting experts in related fields to use the relative scale measurement shown in Table 1[14; 46] for scoring. Denote the pairwise comparison matrix as \(\mathbf{C}\), and \(c_{ij}\) represents the comparison result of the \(i\)-th element relative to the \(j\)-th element (the orders of the \(q+1\) pairwise comparison matrices for the hierarchy model in Figure 4 are \(q,c_{1},c_{2},\ldots,c_{q}\), respectively). **Step 3. ** Hierarchical single sorting and consistency test. Hierarchical single ordering refers to calculating the importance weight of the elements in the lower layer to the corresponding element of the upper immediately layer. Correspondingly, for the hierarchy shown in Figure 4, we need to execute hierarchical single sorting and consistency test \(q+1\) times, and we illustrate this process using the middle layer (BS categories layer) as an example. Generally, hierarchical single sorting can be solved by the eigenvector method [48], as is shown in Equation (1). \[\mathbf{C_{MS}\hat{w}}=\lambda_{max}\hat{w} \tag{1}\] \begin{table}
\begin{tabular}{l l} \hline \hline
**Intensity of Importance** & **Description** \\ \hline
1 & Equal importance \\
3 & Moderate importance of one over another \\
5 & Essential or strong importance \\
7 & Very strong importance \\
9 & Extreme importance \\
2, 4, 6, 8 & Intermediate values between the two adjacent judgments \\ Reciprocals & Values for inverse comparison \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Pairwise comparison scale for AHP. Figure 4: Business scenarios hierarchy model. where \(C_{MS}\) is the corresponding \(q\)-order pairwise comparison matrix, \(\lambda_{max}\) is the largest eigenvalue of it, and \(\hat{\mathbf{w}}\) is the corresponding eigenvector of \(\lambda_{max}\). According to the properties of the pairwise comparison matrix [48], \(\lambda_{max}\) exists and is unique, the components of \(\hat{\mathbf{w}}\) are all positive components, and normalized \(\hat{\mathbf{w}}\) is the result of hierarchical single sorting. However, whether the calculated results are acceptable or not requires a consistency test, which requires the following two steps. * Calculating consistency index (\(CI\)). \(CI\) is determined by using the eigenvalue, as is illustrated in Equation (2).