## 3 Results
The 95% quantile values are also close, as follows: from 33.09 (Stage 3) to 33.52 (full model), confirming good convergence of time characteristics despite differences in the structure of the models. Thus, the results of numerical modeling confirm that each of the models contributes characteristic features to the overall temporal structure of the process, and their combination within the full model leads to smoothed behavior with a slightly more pronounced delay and a lower initial probability of rapid completion. This is consistent with the logic of sequential request processing in systems where each subsequent stage depends on the completion of the previous one. From a practical standpoint, the obtained graphs and statistical characteristics represent valuable material for forecasting the performance and reliability of a future museum exhibit recommendation system. For example, the probability density of the processing time for each stage allows us to assess which components of the algorithm require additional optimization. If, for instance, Stage 2 shows a higher mean time and variance,  
Figure 10: Exceedance probability graphs of execution time for user request processing and the integrated model. this may indicate excessive complexity in the weight assignment procedure or insufficient adaptability in the filtering system. The exceedance function of execution time is especially important for tasks focused on ensuring user experience quality. If the probability that the system fails to generate a recommendation within 3 s exceeds 5%, this may be considered a critical threshold requiring intervention. Analysis of these graphs makes it possible to establish acceptable SLAs (Service Level Agreements) for each stage of the recommendation system's operation. It can also be noted that the obtained results provide a basis for adaptive load balancing. For example, if it is known that Stage 3 almost always completes faster than the others, it can be executed in parallel or used for preliminary candidate filtering, reducing the system's overall response time. More broadly, such a model can be used to evaluate and compare alternative system architectures, where stages can be redistributed, merged, or replaced. This is critically important for systems processing large volumes of heterogeneous user requests, including those with time constraints or limited exhibit availability. To validate the advantages of the GERT-based approach, we conducted a comparative experiment with a traditional Markov model using the same dataset and parameters. The Markov model was constructed by discretizing the processing stages into states with fixed transition probabilities, omitting feedback loops and time distributions. The results revealed that the GERT model provided more accurate estimates of processing times, especially in scenarios with iterative refinements. For instance, the Markov model underestimated the 95% quantile of total processing time by 15% compared to the GERT model, which accounted for feedback loops and probabilistic delays. A comparison between the GERT-based model and a Markov-based model using the same parameters is presented in Table 8.  
This demonstrates the superiority of GERT in capturing the complexity of real-world recommendation systems, particularly in domains like cultural heritage where iterative user interactions are common. In the context of personalized recommendation systems for cultural heritage platforms, temporal characteristics such as processing delay are crucial for maintaining acceptable user experience. Previous empirical studies [10; 34; 35] have demonstrated that user satisfaction with mobile museum applications drops significantly when response times exceed 4-5 s. In our study, we additionally conducted pilot interviews and observational feedback sessions within ongoing prototype deployments in Polish museum environments. The collected data indicate that most users consider 2-3 s as acceptable waiting time, while delays beyond 4.5 s begin to noticeably reduce perceived system responsiveness.