Investigation of the Analytical Model of a Queue to Several Servers of Computer Networks with Priority Maintenance

BACKGROUND The performance of modern computer networks depends significantly on the number of nodes, available channels, and waiting slots. Efficient modeling of these factors is critical for optimizing resource allocation, reducing service delays, and maintaining high-quality metrics under dynamic loads. MATERIALS AND METHODS This study adopts a quantitative approach and aims to develop and validate an analytical model for multi-node, multi-server computer networks with finite queues and priority-based servicing. The model seeks to identify functional dependencies between nodes, channels, and waiting slots and to quantify their impact on key performance indicators, including waiting time, rejection probability, and server utilisation. An analytical model of a priority queueing system was constructed, incorporating finite queues, absolute priority for critical requests, and variable load conditions. Simulation experiments were performed under different network configurations to validate the theoretical dependencies. RESULTS Simulation results demonstrated that increasing the number of nodes from 10 to 100 raised average waiting time from 0.8s to 8s and rejection probability from 5% to 60%. Priority analysis revealed that under absolute priority at ρ = 0.99, critical requests were processed in 2.1s on average, while standard requests required 8s, with rejection rates staying within 16%. Additionally, increasing the number of servers from 2 to 5 at fixed load (ρ = 0.8) raised the average number of requests in the system from 4 to 6, but reduced service time variability, as the standard deviation-to-mean ratio decreased from 2.6 to 1.3. CONCLUSION The proposed model effectively captures the interplay between network nodes, channels, and waiting slots in determining quality of service under variable loads. The findings provide practical insights for optimizing network configurations to balance efficiency, fairness, and reliability in modern computer systems.