5.3.2. TTC

Using RMVCA, we will analyze the impact of RMVCA on the efficiency of deploying intercept access points in whole hybrid SDN. In many experiments, we run three SDN interception models to deploy IAPs in three approaches during which the shortest paths need to be calculated, and thus the total times of calculating the shortest path (TTC) is different. In order to evaluate the performance of RMVCA, we employ TTC as its most important performance metric. We predict that RMVCA can improve the efficiency of deploying IAPs (i.e., reduce the total deployment time). The experimental results are shown in Figure 9.

**Figure 9.** The impact of three approaches in three SDN interception models on TTC under CRN topologies. TTC. The lower, the better.

From Figure 9, we can see that TTC of Fermat-point interception model is the highest whether in PA, RA or HA, namely, running Fermat-point model may take the longest time to deploy IAPs. In addition, TTC of T model and ECMP-T model is similar and is far lower than that of Fermat-point model. Therefore, in terms of the efficiency of deploying IAPs, T model and ECMP-T model are better than Fermat-point model.

Also, Figure 9 show the impact of three approaches in three SDN interception models on TTC under CRN topologies. From the figure, we can see that compared TTC in PA and RA, TTC in HA is the lowest, whether running T model, ECMP-T model or Fermatpoint model in hybrid SDN. Namely, HA is the best approach in terms of the efficiency of deploying IAPs based on thorough analysis and comparison.

Meanwhile, we also can see that TTC in PA is the highest and thus PA is the most undesirable approach. Considering that TTC is the most important performance metric of RMVCA, we can abandon PA. According to Figure 9, we can conclude by calculating that with the increasing number of N-SDN nodes (i.e., with the decreasing number of SDN nodes) in hybrid SDN, HA can significantly improve the deployment efficiency of intercept access points for the reason that compared with RA, HA can decrease TTC on average by 41.14%, 44.07%, 53.32% respectively in T model, ECMP-T model and Fermat-point model. In conclusion, PA is the most undesirable approach that should be abandoned. While HA is the best approach in terms of the deployment efficiency of IAPs.

#### 5.3.3. MILC, TOC and UQoS

After deploying the best intercept access point (IAP; I), the interception center (the law enforcement agencies; L) hopes to receive the data intercepted by the intercept access point with the minimum cost (i.e., the minimum cost or hop-count from the intercept access point (I) to the interception center (L); MILC). Therefore, MILC is one of the most important performance metrics of lawful interception system. In addition, the network operators are most concerned about the total cost of running intercept operation in global network (i.e., TOC) which is the prominent performance metrics of lawful interception system. Meanwhile, running different SDN interception models to deploy intercept access point may lead to the different selection of the best intercept access point (namely the placement location of IAP differs) and the different amount of calculation, thus affecting the quality of service of normal user's data stream (UQoS). Thus, UQoS is also one of the important performance metrics of lawful interception system. In a word, MILC, TOC and UQoS are of grea<sup>t</sup> significance for the Law Enforcement Agencies, the network operators and the users, respectively. Focused on three hybrid SDN topologies CRN, NSFNet and COST 239, we study and analyze the impact of running three different SDN interception models to deploy the best IAPs on MILC, TOC, and UQoS of whole lawful interception system under different number of SDN nodes. The experimental results of the three topologies are shown in Figure 10a–c.

**Figure 10.** The impact of three SDN interception models on MILC, TOC, UQoS under three topologies. Hop-count. The lower, the better.

From the figures, we can see that MILC, TOC in T model are relatively close to the ones in ECMP-T model. And MILC and TOC consumed by ECMP-T model are lower than that of T model, so ECMP-T model is better than T model. More importantly, compared with MILC and TOC in T model and ECMP-T model, MILC and TOC in Fermat-point model are the lowest in all number of SDN nodes. In other words, Fermat-point model can decrease MILC and TOC compared with T model and ECMP-T model. More specifically, compared with T model and ECMP-T model, Fermat-point model can decrease MILC on average by 13.41%, 11.11% in CRN topology, 14.91%, 8.73% in COST 239, and 19.72%, 16.04% in NSFNet, and TOC on average by 1.91%, 0.99% in CRN topology, 2.82%, 0.46% in COST 239, and 2.65%, 1.03% in NSFNet. These simulation results verify that the performance of Fermat-point model outperforms T model and ECMP-T model and thus Fermat-point model is the best SDN interception model in terms of MILC and TOC.

Meanwhile, from the figures, we can see that no matter in CRN, COST 239 or NSFNet, ECMP-T model and T model have the same UQoS. In other words, T model and ECMP-T model have little impact on the transmission quality of traffic normally accepted by users and on deployment efficiency of IAP. According to the principle of T model and ECMP-T model, we know the simulation results in three hybrid SDN topologies are consistent with the theory, so these results are true and reliable. In addition, we can also clearly observe from the figures that UQoS in Fermat-point model is higher than the one in T model and ECMP-T model, which means that Fermat-point model slightly affect UQoS. Thus, Fermat-point model has poor performance in terms of UQoS.
