## 6 Performance Evaluation and Results
### RSVTM Properties and Operation
Subsequently, a larger and more representative experiment was executed by considering 100 museum visitors (i.e., 25 visitors from each visiting style) with \(c_{A}=3.2\cdot 10^{-5}\), \(c_{B}=3.6\cdot 10^{-5}\), \(c_{C}=4\cdot 10^{-5}\)). Our aim is to better demonstrate the operation and behavior of the RSVTM algorithm in terms of several performance parameters and tradeoffs such as convergence, achieved QoE, visiting time, etc. Specifically, Figure 4 illustrates the convergence of the visitors to their selected recommendation, i.e., A, B, and C as a function of the time slots \(\tau\) of the recommendation selection part of the RSVTM algorithm. The results reveal that the RSVTM algorithm converges to a stable operation point where all visitors select their recommendation in an autonomous and distributed manner. The RSVTM algorithm converges to the stable point in less than 400 timeslots (and for practical purposes significantly less than 300 slots), which, in real time, is translated to less than 3.7 s. Furthermore, it is observed that the majority of visitors select the recommendation B and C, which are more enhanced when compared to the recommendation A, i.e., map of the museum provided to visitors at the entrance. It is noted that, if additional visitors were present and recommendations B and C were seriously populated, then recommendation A would become more attractive as the system and time evolves. Figure 5 depicts the number of visitors from each visiting style and the recommendation type they selected. It is shown that visitors' distribution in the recommendations follows similar trends for each visiting style. Thus, there is no case where visitors of a specific visiting style show preference for specific recommendations. Therefore, the behavior of visitors is homogeneous with respect to the recommendation selection even if they belong to different visiting styles and the choices are primarily influenced by the congestion factor and problem. With reference to the same setting and experiment, Figure 6 shows the average visitor QoE and the corresponding average visiting time of the four different visiting styles, i.e., ant, butterfly, fish, and grasshopper. The visitors who have greater flexibility and tolerance with respect to the museum  
Figure 4: Convergence of RSVTM algorithm to the recommendation selections as a function of the timeslots. Figure 5: Distribution of the visitors for the recommendations for all the visiting styles. congestion, i.e., smaller values of target relative visiting time, \(rt_{i}^{\text{target},b}<rt_{i}^{\text{target},a}<rt_{i}^{\text{target},f}<rt_{i }^{\text{target},g}\) are able to achieve greater QoE levels by spending less time to their museum visit. Therefore, combining our findings and observations from both Figures 2 and 6, we conclude that butterfly-style visitors are the most tolerant of congestion. Therefore, they achieve the highest QoE while spending the shortest visiting time on their museum tour. Ant, fish, and grasshopper visitors follow with decreasing QoE levels and corresponding increasing visiting times due to the fact that \(rt_{i}^{\text{target},b}<rt_{i}^{\text{target},a}<rt_{i}^{\text{target},f}< rt_{i}^{\text{target},g}\). Below, we study the convergence properties of the recommendation selection part of the RSVTM algorithm. Specifically, Figure 7a presents the running time (left vertical axis) of the RSVTM algorithm versus the learning rate \(b\) as well as the number of visitors deviating (right vertical axis) from their corresponding selection made with respect to the ground truth values achieved for \(b\) = 0.2. Similarly, Figure 7b presents the corresponding achieved average QoE (left vertical axis) and average visiting time (right vertical axis) as a function of the learning rate \(b\). Please note that, as ground truth values for this experiment, we considered the ones achieved for \(b\) = 0.2 since, for small values of the learning rate \(b\), visitors are able to better learn their available choices and make better decisions about themselves.