## 7 Performance Evaluation
### Numerical Results and Discussion
#### 7.2.1 Overlapping vs. WCD Evaluations  
In this section, we evaluate the effect of one-sided overlapping of lower- and higher-priority windows with \(Q_{4}^{h}\) windows. Both opening-edge and closing-edge overlapping are considered here in four different cases, as illustrated in Table 3. For lower priority, the fifth-priority queue is assigned to overlap with the fourth-priority queue with a variable OR, as shown in Table 3, and the third-priority queue for higher priority. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Priority**} & \multicolumn{2}{c}{**Open and Closed Edges for Window Intervals (\(\upmu\)s)**} \\ \cline{2-4}  & **(ES\({}_{1}\), SW\({}_{1}\))** & **(SW\({}_{1}\), SW\({}_{2}\))** & **(SW\({}_{2}\), ES\({}_{4}\))** \\ \hline
1 & (15, 35) & (20, 40) & Not assigned \\ \hline
2 & Not assigned & (40, 60) & (45, 65) \\ \hline
3 & (65, 85) & (70, 90) & (75, 95) \\ \hline
4 & (105, 125) & (125, 145) & (145, 165) \\ \hline
5 & (130, 150) & (155, 170) & (190, 210) \\ \hline
6 & Not assigned & (175, 190) & Not assigned \\ \hline
7 & (185, 200) & (200, 220) & Not assigned \\ \hline
8 & (205, 225) & (225, 240) & (235, 250) \\ \hline \hline \end{tabular} ES, end system; SW, switch.  
\end{table} 
Table 2: The initial GCL implementation. Cases 1 and 2: In these cases, the lower-priority overlapping is evaluated by varying the OR from 0 to 1, with different sizes of \(Q_{4}^{h}\). frames. Figure 14a,b shows the performance of the worst-case latency for \(Q_{4}^{h}\) traffic under opening-edge and closing-edge overlapping. As expected, the lowest WCD is obtained under full isolation between \(Q_{4}^{h}\) and \(Q_{5}^{h}\) windows (\(OR_{4,5}^{h}=0\)). In Figure 14a, the WCD increases with an increase in the OR at the opening side because the \(Q_{4}^{h}\) frame has to wait for the lower-priority frame, which is in the forwarding status. The increase continues until the time required to transmit the largest lower-priority frame is completed, which is assumed to be 200, 300, and 500 bytes, separately. These durations are equivalent to 8%, 12%, and 20% overlapping ratios. If the OR increases more than the largest frame size, the latency is fixed until the guard band interval, equal to 16% \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Link** & **Priority** & **Open\(-\)Window Interval (\(I_{m}^{h,m},I_{m}^{h,m}\)) (ss)** \\ \hline \multirow{4}{*}{1} & (ES\({}_{1}\), SW\({}_{1}\)) & 5 & \(\left(85+W_{4}^{1}OR_{4,5}^{1,E}\), \(105+W_{4}^{1}OR_{4,5}^{1,E}\right)\) \\ \cline{2-4}  & (SW\({}_{1}\), SW\({}_{2}\)) & 5 & \(\left(105+W_{4}^{2}OR_{4,5}^{2,B}\), \(125+W_{4}^{2}OR_{4,5}^{2,B}\right)\) \\ \cline{2-4}  & (SW\({}_{2}\), ES\({}_{4}\)) & 5 & \(\left(125+W_{4}^{2}OR_{4,5}^{1,B}\), \(145+W_{4}^{3}OR_{4,5}^{3,B}\right)\) \\ \hline \multirow{4}{*}{2} & (ES\({}_{1}\), SW\({}_{1}\)) & 5 & \(\left(125-W_{4}^{1}OR_{4,5}^{1,E}\), \(145-W_{4}^{1}OR_{4,5}^{1,E}\right)\) \\ \cline{2-4}  & (SW\({}_{1}\), SW\({}_{2}\)) & 5 & \(\left(145-W_{4}^{2}OR_{4,5}^{2,E}\), \(165-W_{4}^{2}OR_{4,5}^{2,E}\right)\) \\ \cline{2-4}  & (SW\({}_{2}\), ES\({}_{4}\)) & 5 & \(\left(165-W_{4}^{3}OR_{4,5}^{3,E}\), \(185-W_{4}^{3}OR_{4,5}^{3,E}\right)\) \\ \hline \multirow{4}{*}{3} & (ES\({}_{1}\), SW\({}_{1}\)) & 3 & \(\left(85+W_{4}^{1}OR_{4,3}^{1,B}\), \(105+W_{4}^{1}OR_{4,5}^{1,B}\right)\) \\ \cline{2-4}  & (SW\({}_{1}\), SW\({}_{2}\)) & 3 & \(\left(105+W_{4}^{2}OR_{4,3}^{2,B}\), \(125+W_{4}^{2}OR_{4,3}^{2,B}\right)\) \\ \cline{2-4}  & (SW\({}_{2}\), ES\({}_{4}\)) & 3 & \(\left(125+W_{4}^{3}OR_{4,3}^{3,B}\), \(145+W_{4}^{3}OR_{4,3}^{3,B}\right)\) \\ \hline \multirow{4}{*}{4} & (ES\({}_{1}\), SW\({}_{1}\)) & 3 & \(\left(125-W_{4}^{1}OR_{4,3}^{1,E}\), \(145-W_{4}^{1}OR_{4,3}^{1,E}\right)\) \\ \cline{2-4}  & (SW\({}_{1}\), SW\({}_{2}\)) & 3 & \(\left(145-W_{4}^{2}OR_{4,3}^{2,E}\), \(165-W_{4}^{2}OR_{4,3}^{2,E}\right)\) \\ \cline{1-1} \cline{2-4}  & (SW\({}_{2}\), ES\({}_{4}\)) & 3 & \(\left(165-W_{4}^{3}OR_{4,3}^{3,E}\), \(185-W_{4}^{3}OR_{4,3}^{3,E}\right)\) \\ \hline \hline \end{tabular}
\end{table}