# Enhancing Cache Robustness in Information-Centric Networks: Per-Face Popularity Approaches
## 5 Results
### PFP-\(\beta\) Results  
As discussed earlier, PFP-\(\beta\) (PFP-Beta) takes a \(\beta\) parameter, which acts as the exponent to the denominator for each of the contributions from faces during the overall popularity calculation. Equation (4) is repeated below and expanded to demonstrate the use of \(\beta\). \[P(C,\ \beta)=\sum_{ \begin{subarray}{c}i=1\\ 0\leq\beta\leq 1\end{subarray} }^{n}\frac{1}{r_{i}!^{\beta}}=\frac{1}{r_{1}!^{ \beta}}+\frac{1}{r_{2}!^{\beta}}+\ldots+\frac{1}{r_{n-1}!^{\beta}}+\frac{1}{r _{n}!^{\beta}}\]  
The lower the \(\beta\), the smaller the numeric difference between the per-face contribution for each item and the top item. This causes content objects that have interests received from multiple faces to be substantially favored. The mechanism for this behavior is described in more detail in Section 3.3. The motivation for this variation on PFP-DA is to see if we can further lower cache pollution and increase the hit rate. Through our initial tests, we have made some very interesting discoveries. Firstly, we can observe the effects (or lack thereof) of varying the attack speed of the single attacker. The pollution is 0%, which is impressive. The hit rates are substantially better than the single attacker scenarios we tested for PFP-DA (see Table 6). Of course, with PFP-DA, the regular Simple Topology was used, with 10 nodes attacking the router, whereas our PFP- \(\beta\) was tested with the Larger Simple Topology (LST), which has 20. However, we will find that even with two attackers (10%) against the LST, considering the coordination and the consistency of the percentage, the pollution will remain at 0%, with almost identical hit rates. Figure 8: ST with 100 cache size, 720 attacker frequency, and varying number of attackers—top 50 items hit %. Therefore, as shown in Table 10, we can conclude that if we consider the PFP-DA tests from earlier to be a special case of PFP- \(\beta\) where \(\beta\) = 1.0, that the smaller \(\beta\) = 0.05 for essentially the same variations performs approximately 16% better in terms of cache pollution, approximately 3.7% better for overall hit rate, about 25% better for the top 100 items (with Zipf-like distribution), and about 23% better for the top 50 items (98.83% vs. 75.53%, for a rate of 720). Astonishingly, the top 50 items experience just under a 99% hit rate with our \(\beta\) = 0.05. Although 75.53% was incredibly good and totally outperformed LFU-DA (50% top 50 hit rate), our \(\beta\) = 0.05 tests far surpass our previous PFP-DA tests in terms of small attacker percentage with varying attacker frequency. Secondly, we tested variations of the \(\beta\) value, keeping the number of attackers at 2 with attack frequencies of 720 each and a cache size of 100. As we see in Table 11, increasing the \(\beta\) value increases the pollution percentage and decreases the hit rates in these scenarios. _Ceteris paribus_, as \(\beta\) moves toward the regular PFP-DA (\(\beta\) = 1.0), the performance drops. Thirdly, we held the number of attackers at 2 with attack frequencies of 720 each, a constant \(\beta\) = 0.1, and varied the cache size. As more spaces become available, the pollution percentage increases extremely slightly, see Table 12. However, it is negligible, even for a cache size of 500 (5% of the content space), as only a few items, accounting for 0.4% of the entire cache, can make it into the content store's cache. The overall hit rate increases significantly, as would be expected since more items can reside in the cache overall. The top 100 and top 50 hit rates increase slightly, but they are so close to 100% already that there is little room for improvement. In Table 13, we see where PFP-\(\beta\) falls short. Although the performance of PFP-\(\beta\) is better than that of PFP-DA for small percentages of attackers, PFP-\(\beta\) performs worse than PFP-DA when the number of attackers increases.