## 3 Evaluation Approach
### Analytic Hierarchy Process : AHP  
The concept of weight involved in each method, is solved by the use of the AHP method. The authors of [18] proposed this process for decision-making in multi-criteria problems, they introduced AHP as a method of measurement with ratio scales, AHP allows comparison and a choice of preset options. It is based on the comparison of pairs of options and criteria.  
In our approach, AHP is used to calculate the weight vector \(w\), which represents the importance of each metric with respect to different QoS classes for use in SAW, MEW and TOPSIS methods. AHP provide as results \(w_{j}>0\), which represents the weight or importance of the \(j^{th}\) attribute, given that \(\sum_{j=1}^{j=M}w_{j}=1\).  
Weight computing needs answering to a sequence of comparisons between a pair metrics. The common way to ask a question is to consider two elements, and find out which one satisfies the criterion more. The answers are given by using the fundamental 1-9 AHP scale [18,19]. The values in the answers correspond to the scale in Table 1 below.  
Table 2 presents the answers of the questions asked about the relative importance between each pair, for example, in Conversational Class, the first comparison is (Ber, Jitter), the question is : How much more is Ber preferred over Jitter in conversational Class? Indeed, Jitter is 7 times more important than Ber, so the value in matrix is \(1/7\), and accordingly \(7\) is put in the opposite side (symmetrical to the diagonal). The other values can be obtained from Table 1.  
In [15] the authors explain that if \(C\) is defined as an AHP comparison matrix as in Table 1, then by solving the system : \(U.w=n_{max}\) (where \(n_{max}\) is the largest eigenvalue of \(U\) ), the priority or importance vector \(w\) can be obtained. Thus, the weights rely on the QoS prerequisite of the traffic classes. We use the eigenvector method used by the AHP to figure out the weights  
\begin{table}
\begin{tabular}{l l|c|c|c} \hline
**Conversational** & Ber & Jitter & Delay & Throughput \\ \hline Ber & 1 & 1/7 & 1/7 & 3 \\ Jitter & 7 & 1 & 3 & 7 \\ Delay & 7 & 1/3 & 1 & 7 \\ Throughput & 1/3 & 1/7 & 1/7 & 1 \\ \hline
**Streaming** & Ber & Jitter & Delay & Throughput \\ \hline Ber & 1 & 1/3 & 1/7 & 1/7 \\ Jitter & 3 & 1 & 1/3 & 1/3 \\ Delay & 7 & 3 & 1 & 1/3 \\ Throughput & 7 & 3 & 3 & 1 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c} \hline
**Interactive** & Ber & Jitter & Delay & Throughput \\ \hline Ber & 1 & 3 & 7 & 3 \\ Jitter & 1/3 & 1 & 5 & 3 \\ Delay & 1/7 & 1/5 & 1 & 1/7 \\ Throughput & 1/3 & 1/3 & 7 & 1 \\ \hline
**Background** & Ber & Jitter & Delay & Throughput \\ \hline Ber & 1 & 7 & 7 & 9 \\ Jitter & 1/7 & 1 & 3 & 5 \\ Delay & 1/7 & 1/3 & 1 & 5 \\ Throughput & 1/9 & 1/5 & 1/5 & 1 \\ \hline \end{tabular}
\end{table}
Table 2: Analytic Hierarchy Process (AHP) Matrices for Each Traffic Class.  
\begin{table}
\begin{tabular}{l l|c|c} \hline
**Importance** & **Definition** & **Explanation** \\ \hline
1 & _Equal importance_ & Two parameters contribute equally \\
3 & _Moderate importance_ & Experience favored 3 times one than another \\
5 & _Strong importance_ & Experience favored 5 times one than another \\
7 & _Very Strong importance_ & A parameters is favored and dominant in practice \\
9 & _Extreme importance_ & The evidence favoring one activity over another is of the highest possible order of affirmation \\
2,4,6,8 & _Intermediate values_ & When Compromise is needed \\ \hline \end{tabular}
\end{table}
Table 1: The scale of importance [18].