## 3 Results: Network Performance
### Delay
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Size (N)** & \begin{tabular}{c} **Offered Traffic** \\ \([\lambda_{2}\;\lambda_{3}\;\ldots\;\lambda_{N}]\) \\ \end{tabular} & \(\mathbf{W}^{ini}\) & \
\begin{tabular}{c} **Delay** \\ **(Av./Max.)** \\ \end{tabular} &
\begin{tabular}{c} **Packets Delivered** \\ \([\mathbf{P_{2}}\;\mathbf{P_{3}}\;\ldots\;\mathbf{P_{N}}]\) \\ \end{tabular} \\ \hline
4 & \(\left[\begin{array}{cc}\frac{1}{8}&\frac{1}{8}&\frac{1}{8}\\ \end{array}\right]\) & \begin{tabular}{c} \([2\;1\;0]\) \\ \([1\;2\;2]\) \\ \end{tabular} & \
\begin{tabular}{c} \(3.99/7\) \\ \(5.29/11\) \\ \end{tabular} &
\begin{tabular}{c} \([125\;124\;166]\) \\ \([125\;124\;166]\) \\ \end{tabular} \\ \hline
4 & \(\left[\begin{array}{cc}\frac{1}{8}&\frac{1}{8}&\frac{1}{8}\\ \end{array}\right]\) & \begin{tabular}{c} \([2\;0\;2]\) \\ \([1\;1\;3]\) \\ \end{tabular} & \
\begin{tabular}{c} \(3.69/7\) \\ \(4.99/11\) \\ \end{tabular} &
\begin{tabular}{c} \([125\;166\;124]\) \\ \([125\;166\;124]\) \\ \end{tabular} \\ \hline
4 & \(\left[\begin{array}{cc}\frac{1}{8}&\frac{1}{8}&\frac{1}{8}\\ \end{array}\right]\) & \begin{tabular}{c} \([2\;1\;0]\) \\ \([1\;2\;2]\) \\ \end{tabular} & \
\begin{tabular}{c} \(3.69/7\) \\ \(5.29/11\) \\ \end{tabular} &
\begin{tabular}{c} \([125\;124\;165]\) \\ \([125\;124\;166]\) \\ \end{tabular} \\ \hline
5 & \(\left[\begin{array}{cc}\frac{1}{8}&\frac{1}{8}&\frac{1}{8}\\ \end{array}\right]\) & \begin{tabular}{c} \([2\;1\;0\;0]\) \\ \([3\;0\;1\;3]\) \\ \end{tabular} & \
\begin{tabular}{c} \(3.29/7\) \\ \(4.69/11\) \\ \end{tabular} &
\begin{tabular}{c} \([125\;124\;165]\) \\ \([125\;124\;124]\) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Delay of the optimal scheduling (slots) using FIFO. Simulation time: 1000 time slots. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Size (N)** & \begin{tabular}{c} **Offered Traffic** \\ \([\lambda_{2}\;\lambda_{3}\;\ldots\;\lambda_{N}]\) \\ \end{tabular} & \(\mathbf{W}^{ini}\) & \
\begin{tabular}{c} **Delay** \\ **(Av./Max.)** \\ \end{tabular} &
\begin{tabular}{c} **Packets Delivered** \\ \([\mathbf{P_{2}}\;\mathbf{P_{3}}\;\ldots\;\mathbf{P_{N}}]\) \\ \end{tabular} \\ \hline
4 & \(\left[\begin{array}{cc}\frac{1}{8}&\frac{1}{8}&\frac{1}{8}\\ \end{array}\right]\) & \begin{tabular}{c} \([2\;1\;0]\) \\ \([1\;2\;2]\) \\ \end{tabular} & \
\begin{tabular}{c} \(3.99/8\) \\ \(5.29/11\) \\ \end{tabular} &
\begin{tabular}{c} \([125\;124\;165]\) \\ \([125\;124\;166]\) \\ \end{tabular} \\ \hline
4 & \(\left[\begin{array}{cc}\frac{1}{8}&\frac{1}{8}&\frac{1}{8}\\ \end{array}\right]\) & \begin{tabular}{c} \([2\;2\;2]\) \\ \([1\;0\;3]\) \\ \end{tabular} & \
\begin{tabular}{c} \(3.69/7\) \\ \(5.11\) \\ \end{tabular} &
\begin{tabular}{c} \([125\;166\;124]\) \\ \([124\;165\;124]\) \\ \end{tabular} \\ \hline
4 & \(\left[\begin{array}{cc}\frac{1}{6}&\frac{1}{8}&\frac{1}{8}\\ \end{array}\right]\) & \begin{tabular}{c} \([2\;1\;0]\) \\ \([1\;0\;1]\) \\ \end{tabular} & \
\begin{tabular}{c} \(3.29/6\) \\ \(4.69/8\) \\ \end{tabular} &
\begin{tabular}{c} \([167\;124\;124]\) \\ \([125\;124\;124]\) \\ \end{tabular} \\ \hline
5 & \(\left[\begin{array}{cc}\frac{1}{8}&\frac{1}{8}&\frac{1}{8}\\ \end{array}\right]\) & \begin{tabular}{c} \([2\;1\;0\;0]\) \\ \([3\;0\;1\;3]\) \\ \end{tabular} & \
\begin{tabular}{c} \(3.29/6\) \\ \(4.69/8\) \\ \end{tabular} &
\begin{tabular}{c} \([167\;124\;124]\) \\ \([166\;124\;124]\) \\ \end{tabular} \\ \hline
6 & \(\lambda_{j}=\frac{1}{10}\;(j=2,..,6)\) & \begin{tabular}{c} \([2\;1\;0\;0]\) \\ \([3\;0\;1\;3]\) \\ \end{tabular} & \
\begin{tabular}{c} \(3.99/8\) \\ \(5.29/11\) \\ \end{tabular} &
\begin{tabular}{c} \([125\;124\;165]\) \\ \([125\;124\;166]\) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Delay of the optimal scheduling (slots) using Round-Robin. Simulation time: 1000 time slots.