## 1 Introduction
ANNs, when optimized using PSO, provide a more robust and adaptive solution by enabling real-time predictions of queue congestion, patient waiting times and system load distribution [5]. A significant drawback of conventional ANN training techniques, like backpropagation (BP), is their dependence on gradient-based optimization. This method frequently leads to gradual convergence and vulnerability to the local minimum, which impairs the ANN's capacity to generalize efficiently. By contrast, PSO leverages a population-based search strategy that enables ANN models to continuously refine their weight parameters and improve predictive accuracy over multiple iterations. This hybrid ANN-PSO approach enhances queue estimation while facilitating dynamic decision-making in resource allocation, ensuring that telemedicine services can adapt to fluctuating patient demand [4]. This approach allows ANN-PSO models to optimize their weights iteratively, enabling them to make accurate queue predictions while dynamically adapting to changes in patient arrival patterns. Studies have demonstrated that ANN-PSO models outperform conventional ANN models trained using backpropagation in terms of both accuracy and computational efficiency. For example, [PERSON] [4] applied ANN-PSO in medical queue prediction, reporting a 24% reduction in prediction errors compared to traditional queuing models. Beyond improving queue prediction, the ANN-PSO framework also enhances decision-making in telemedicine by optimizing server allocation. Traditional queuing models often operate under fixed assumptions about the number of servers required for optimal performance, whereas ANN-PSO can dynamically allocate resources based on real-time demand. In this regard, by continuously monitoring patient influx and adjusting the number of active servers, ANN-PSO minimizes patient waiting times and ensures efficient resource utilization [5]. In support of this, [PERSON] et al. [7] proposed the integration of reinforcement learning with priority queuing algorithms for emergency healthcare services. Their model, tested in real hospital environments, demonstrated a 50% reduction in emergency waiting times and improved patient satisfaction, highlighting the viability of intelligent queue optimization in healthcare. Additionally, [PERSON] et al. [8] employed deep reinforcement learning with the RED algorithm for active queue management in networks, showing that dynamic adaptations could effectively stabilize queues and minimize delay--concepts applicable to telemedicine systems. Moreover, [PERSON] and [PERSON] [9] introduced a web-based queue system for non-tertiary hospitals in Nigeria, successfully reducing crowding and improving service delivery during the COVID-19 pandemic. Their model, based on Poisson distribution and Little's Law, validates the practical use of queuing theory in healthcare management. [PERSON] et al. [10] implemented a QR-code-based hospital check-in system to streamline queue verification and administration, which significantly improved operational efficiency. These examples reinforce the growing role of digital technologies in modern queue management systems. The combination of Markov Chains and ANNs has also been explored in traffic prediction models by [PERSON] et al. [11], who concluded that ANN outperformed Markov Chain models for predicting dynamic traffic flows--an analogy applicable to patient inflow in healthcare. In a follow-up study, [PERSON] et al. [12] applied ANN-PSO to traffic flow modeling, achieving over 98% accuracy. Their findings underscore the model's strength in dynamic, real-world environments and affirm its relevance for telemedicine queuing systems. [PERSON] et al. [13] further contributed by mathematically analyzing PSO convergence behaviors and demonstrating how constriction factors improve global search efficiency, supporting the theoretical soundness of PSO-enhanced ANN training.