## 4 Discussion of Results  
The results of the numerical modeling, performed based on the developed GERT models, made it possible to comprehensively characterize the time parameters of user request processing in a recommendation system focused on the search for museum and cultural objects. The main attention was given to a step-by-step analysis of data processing logic and its probabilistic-temporal structure. It was shown that each stage has its own specific execution time distribution. The request categorization stage is characterized by moderate variance and average delay, reflecting the complexity of structural analysis and the possibility of returns due to classification errors. The weight assignment stage demonstrates greater variability and the highest average execution time, which may be associated with the logical complexity of correctness validation procedures and the potential for repeated iterations. The final stage, result generation, is distinguished by lower dispersion and a more compact distribution, due to a more deterministic computation structure. The integrated model exhibits averaged behavior, as follows: increased mean delay and the accumulation of a \"long tail\" in the distribution. This indicates the cumulative effect of uncertainties, especially in the presence of return cycles. The obtained values of mathematical expectation and standard deviation provide a quantitative basis for assessing the risks of exceeding critical time thresholds--both at individual stages and in the system as a whole. From a practical point of view, this means that even with high result quality, the system may encounter issues with timely response. For applied tasks, such as in a museum recommendation system, this requires additional optimization of the iterative processing logic, especially at the second stage, as well as the possible introduction of parallel processing or predictive filtering to reduce the load on critical nodes of the model. In addition, the use of the GERT approach made it possible not only to formalize the processing structure but also to propose a numerically stable analysis procedure applicable to systems of various architectures. This makes the developed methodology universal for evaluating the temporal characteristics of algorithms in other areas of personalized search. In the future, this approach can be expanded through modeling stochastic dependencies between stages, optimizing the network structure based on stability criteria, or implementing methods of adaptive modification of the processing structure depending on the complexity of the request. It also seems promising to use the obtained characteristics for dynamic SLA management (response time, acceptable delay levels, etc.) in intelligent user interaction systems. Thus, the results obtained in this work confirm the relevance of applying probabilistic-temporal modeling based on GERT networks as a tool for structural and quantitative analysis of algorithms in recommendation systems, particularly in the context of personalized search within museum collections. The comparative analysis with the Markov model highlighted the limitations of traditional approaches in handling feedback loops and probabilistic delays. While the Markov model provided simpler computations, it failed to account for the iterative nature of user interactions, leading to underestimations of processing times. The GERT model, with its ability to model cycles and time distributions, offered a more realistic representation of system behavior, making it better suited for recommendation systems in dynamic environments like cultural heritage. While the GERT approach provides significant advantages in modeling iterative processes, it has certain limitations. 1. Computational Complexity. The inversion of Laplace transforms and numerical analysis of transfer functions require non-trivial computational resources, especiallyfor large-scale systems with high concurrency. This may affect real-time performance in scenarios with thousands of simultaneous requests. 2. Scalability.