# Mobility-Aware Hybrid Flow Rule Cache Scheme in Software-Defined Access Networks
## 5 Performance Evaluation
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Processing capacity of the controller (C) & 5000 messages/second \\ Flow rule capacity & 20,000 \\ Network topology & Abilene WAN [39] \\ Mobility model & Poisson–Voronoi tessellation [40] \\ The number of MNs & 10 \\ Packet-in message arrival rate per MN (\(\lambda\)) & 300 \\ Bandwidth of the control channel & 100 Mbps \\ Propagation delay & 1 ms \\ Mobility prediction error rate & 20\% \\ Ratio of delay sensitive flows & 50\% \\ Delay constraint of delay sensitive flows & 30 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Table 3 shows the time complexity according to the flow arrival rate. Since the computation complexity of the ILP problem (i.e., Pro(O)) depended on \(M^{2}\), the running time could increase quadratically according to the number of MNs. Consequently, due to its high computational complexity, the optimal solution for the ILP problem could be determined only with a small number of MNs [41]. On the other hand, because the computational complexity of the heuristic algorithm (i.e., Pro(H)) depended on \(M\)log\(M\), it could be practically considered in the real SDN environment [42]. Figure 5 displays the flow rules hit ratio according to the mobility prediction error per AD, which is the ratio of the hit flow rules to the total requested flows. The delay constraints for the proposed scheme were set to 50 ms and 30 ms (i.e., proposed (50 ms) and proposed (30 ms)). The flow rules hit ratio of the proposed scheme and MobiFlow became reduced according to the prediction error, because these schemes performed prediction-based proactive flow rule caches. Even though the prediction error existed, the proposed scheme had a higher hit ratio compared with MobiFlow because it utilized the proactive rule cache only when the response delay was not satisfied with the delay constraint. In addition, the flow rule hit ratio increased when the delay constraint of the flows increased. This was because the number of flows that did not need to be proac \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\lambda\) & **Pro(O)** & **Pro(H)** & **MobiFlow** & **Reactive** \\ \hline
300 & 29.65 & 30.82 & 31.21 & 41.52 \\
400 & 30.06 & 32.39 & 33.21 & 46.91 \\
500 & 33.68 & 36.77 & 39.79 & 57.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average response delay (ms) according to the flow arrival rate. Figure 4: Flow table utilization ratio according to the flow arrival rate of each mobile user. Note that the proposed scheme could have a lower risk of prediction error compared with MobiFlow because the proposed scheme utilizes the reactive flow rule cache method as much as possible based on the controller's response delay. However, if the prediction error became higher, the proposed scheme could also have a waste of resources due to the wrong prediction compared with the reactive flow rule cache method. Therefore, the operator should carefully determine whether to use the proactive rule cache method or not based on the prediction error, considering the trade-off between the perspectives of the resource efficiency and delay requirement support. Analysis of the trade-off according to the prediction error will be one of our future works.