## 6 Simulation Experiments
In addition, when \(\gamma\) and \(\alpha\) tend to infinity, the hit rate will approach the full hit rate, but the difference in probability distributions will become huge, no matter how small the cache size is, as long as one or more contents can be stored. In fact, with \(n=100\), \(m=50\), \(c=50\), \(k=20\), all \(d_{j}=0.3\), and \(\gamma=\alpha=30\), the LFU only achieves a hit rate of 17.929. After executing the algorithm in this paper, the hit rate can reach 45.317372, which is 90.63% of the limit full hit rate compared with the ideal full hit rate of 50 but at this time, the JSD is as high as 0.212237. That is to say, the hit rate is extremely high but the distortion of the user's preference is extremely large. The reason for this situation is that when \(\gamma\) and \(\alpha\) tend to infinity, the constraints on the recommendation score have actually failed. At this point, the algorithm in this paper will score the recommendation of some cached content as infinity, and then the recommendation score will completely sway the user's request, allowing the user to access only the cached content. This will result in a very poor user experience, because what the user can request is entirely up to the system. The experimentally relevant parameters for Figures 5 and 6 are \(n=100\), \(m=50\), \(c=100\), \(k=20\), \(\gamma=0\), and \(\alpha=0.2\). Figures 5 and 6 show how the hit rate and JSD vary with the upper limit of distortion \(d_{j}\), respectively. It can be seen that the hit rate does not always increase as \(d_{j}\) increases. But JSD increases all the time with \(d_{j}\). In fact, even if \(d_{j}\) tends to be close to the upper limit of 1, its hit rate will not be close to the full hit  
Figure 4: Jensen-Shannon Divergence varies with \(\gamma\) and \(\alpha\). Figure 3: Hit rate increments (compared with LFU) varies with \(\gamma\) and \(\alpha\). rate of 50 but up to 24.251540, while the JSD is as high as 0.001888. This shows that the upper limit of the degree of distortion can only determine the degree of \"honesty\" of the recommender system and cannot determine the degree of distortion of the system for the user's preferences. This shows that the upper limit of distortion can only determine the degree of \"honesty\" of the recommender system but cannot directly determine the degree of distortion of the system to the user's preferences. Figure 7 shows the relationship between cache hit rate and the number of caches \(n\) under different server capacities and different user preference distributions, with the following parameters: \(m=50\), \(k=20\), \(\gamma=0\), \(\alpha=0.2\), and \(d_{j}=0.3\). Here, the \"zipf\" suffix indicates that the data are experimental data whose user preferences conform to the zipf distribution; otherwise, the frequency of user preferences is completely random, i.e., conforms to the uniform distribution. We use the zipf distribution, i.e., content ranked \(x\), with user preference probability \(P(x)=\frac{1}{x\sum_{i=1}^{n}P(i)}\). The results show that in either case, the hit rate always decreases as the number of contents \(n\) increases, which can be explained by the fact that as the contents increase, there is a greater variation in preferences among users, making it more difficult to find contents that satisfy the majority of users who match. At the same time, the hit rate under the zipf distribution is always much higher than that under the uniform distribution. For example, with \(n=200\) and \(c=300\), the hit rate under the zipf distribution is 45.572, while the hit rate under the uniform distribution is 37.471, which is 21.62% higher for zipf. And this difference further expands as the number of contents \(n\) increases; when \(n=900\) and \(c=300\), the two hit rates are 42.65 and 20.97,  
Figure 5: Hit rate varies with distortion \(d_{j}\). Figure 6: [PERSON]–Shannon Divergence varies with distortion \(d_{j}\). respectively, the former being 103.39% higher than the latter.