# Mobility-Aware Hybrid Flow Rule Cache Scheme in Software-Defined Access Networks
## 5 Performance Evaluation  
We evaluated the performance of the proposed hybrid flow rule cache scheme compared with the basic reactive flow rule cache method [1] and MobiFlow [12]. The simulation parameters are presented in Table 1. We considered the Abilene WAN topology in Internet2 [39], including 12 switches which were connected to the SDN controller. We assumed that each switch had 20,000 flow rules [27]. This paper used the M/M/1 queuing model for the SDN controller as explained in Section 3, where the processing capacity of the controller was set to 5000. In addition, the propagation delay from the forwarding nodes to thecontroller through the dedicated control channel was set to 1 ms. Therefore, the response delay of the controller depended on the queuing delay. In addition, this paper adapted Poisson-Voronoi tessellation with the random way point mobility model [40]. According to the mobility model, there were 10 mobile users whose average packet-in message arrival rate was 300 based on the Poisson process. Evaluation results were drawn by generating 50,000 random numbers of the packet-in message arrival rate (with an average of 300), location, velocity (between 0 m/s to 50 m/s), and direction (between 0 to 360 degrees) in the Abilene WAN topology. In addition, the average delay constraint for the delay-sensitive flows was assumed to be 30 ms [18]. Moreover, to train the LSTM network, randomly generated packet-in messages according to the distribution at each time unit were utilized to calculate the response delay as the input data. Then, the LSTM network could predict the next response delay. This paper used 75% of the input data to train the network and 25% to test the network. For the training, the number of features, gradient threshold, and number of epochs were 1, and 30, respectively. Figure 4 shows the average flow table utilization ratio per AD according to the flow arrival rate of each mobile user. This is the average ratio of flow rule usage to the max capacity of flow entries. The reactive flow rule cache scheme had minimal flow rules because it did not include the proactively cached rules. Since the proposed scheme proactively cached rules only for flows which had a lower delay constraint than the controller's response delay, it could reduce the proactively cached rules compared with MobiFlow. For example, if the flow arrival rate was 300, the proposed scheme could save approximately 11 percent of the flow table space compared with MobiFlow. As the number of flows increased, the gap between the proposed scheme and MobiFlow decreased, because the controller's response delay became higher according to the number of flows. This means that the number of flows whose delay constraints were not satisfied also increased. Table 2 shows the average response delay according to the flow arrival rate. It can be noticed that the optimal solution of the proposed scheme (i.e., Pro(O)), which was derived through the above ILP problem, had lower values than those of the heuristic solution of the proposed scheme (i.e., Pro(H)), because the optimal solution estimated the response delay precisely per flow. When the flow arrival rate increased, the average response delay also increased for all schemes because of the maximum capacity constraint of the flow entries. However, the proposed scheme had lower values than MobiFlow, because the proposed scheme could retain more available space for the flow rules as described in Figure 4. In the case of the reactive flow cache scheme, since it always required the controller's interaction, it had the highest delay compared with the other schemes. Based on Figure 4 and Table 2, it can be noted that the proposed scheme could support the delay requirement of the flows (i.e., by using the proactive operation) while maintaining more available resources in the flow table (i.e., due to the reactive operation), which could be interpreted as the efficiency of the hybrid scheme.