## 1 Introduction  
The global telemedicine market is expanding rapidly due to the increasing demand for accessible and efficient healthcare services [1]. Telemedicine has played a crucial role in overcoming geographic and physical barriers to healthcare, particularly benefiting patients in rural and underserved areas. By facilitating remote consultations, it reduces the need for long-distance travel and minimizes in-person waiting times, while also improving healthcare access for vulnerable populations such as the elderly and people with disabilities. Additionally, telemedicine increases operational efficiency by allowing healthcare providers to serve more patients without the need for physical travel. Despite these advantages, the growing reliance on telemedicine platforms has introduced new operational challenges. Patient inflow is often highly variable, and traditional queuing models struggle to adapt to such fluctuations, leading to increased delays, system congestion, and inefficient resource utilization [2, 3]. This has created a pressing need for intelligent, data-driven systems capable of supporting real-time queue management and resource allocation. In response to this challenge, this study proposes a hybrid ANN-PSO model designed to improve telemedicine queuing system performance. ANN models offer robust predictive capabilities, while PSO enhances these models by optimizing their parameter configurations, resulting in better generalization and more accurate queue predictions. The ANN-PSO model dynamically adapts to variations in patient demand, helping administrators anticipate service bottlenecks and optimize resource utilization. The recent literature has demonstrated the effectiveness of ANN-PSO models in healthcare applications, outperforming traditional ANN models and classical queuing theory approaches in terms of prediction accuracy, adaptability, and computational efficiency [4; 5; 6]. By continuously updating its predictions using real-time data, the ANN-PSO model offers a scalable and flexible solution applicable to both small-scale and large-scale telemedicine systems. The novelty of this study lies not in the introduction of the ANN-PSO algorithm itself, but in its targeted application to the M/M/s/N queuing system for telemedicine environments. Specifically, the research contributes by (1) identifying optimal ANN-PSO configurations for multiple output performance metrics, (2) employing a queuing simulation-based data generation approach using Reveledu, and (3) applying the model to a complex telemedicine queuing framework that is underexplored in prior work. This research aims to enhance the performance of telemedicine queuing systems by reducing patient waiting times, optimizing server utilization, and improving the overall quality of virtual healthcare services. The proposed model serves as a valuable decision-support tool, empowering telemedicine administrators to manage patient flow effectively, adapt to fluctuating demand, and ensure timely and efficient service delivery. The objectives of the study are as follows:  
* To simulate telemedicine queuing scenarios and generate data for modeling system behavior. * To train an ANN model using simulated data to predict key performance indicators such as queue intensity, utilization, and delays. * To optimize the ANN model using PSO in order to identify the best parameter configurations for improving queuing system performance. In telemedicine, queue management presents a significant challenge as it directly influences service efficiency, resource utilization and patient satisfaction. The increasing reliance on telemedicine platforms has created a demand for efficient queuing mechanisms that can dynamically adapt to variations in patient inflow and service rates. Traditional queuing models, such as Markovian processes and queueing theory-based approaches, often operate on fixed assumptions regarding arrival rates and service times, which makes them ineffective in real-time applications.