Abstract
<jats:p>The paper has developed an optimization formula to calculate service intensity and the number of active containers based on axiomatic analysis of queuing theory. The aim of the study is to analyse traffic intensity probabilities, calculate intensity under uncertain traffic conditions, optimize query distribution, and establish the relationship between optimization and efficiency. Modern distributed computing systems employing container virtualization encounter performance and cost challenges under uncertain traffic loads. The dynamism of request arrival speeds and interdependence among containers sharing common computational resources lead to difficulties maintaining system stability, low latency, and efficient resource utilization. Existing models often oversimplify these interconnections or ignore traffic fluctuations. Therefore, a formal model is needed to enable real-time calculation and adjustment of service intensity and container counts based on queueing theory, suitable for uncertain traffic conditions. A new formula derived from queuing theory allows computationally transforming service intensity within a specific timeframe and optimizing existing distributed computer systems with container virtualization. The results demonstrate the possibility of effectively distributing queries considering required resources and analysing the behaviour of distributed computer systems within a specific timeframe. Real-time experimental research observing traffic requests via Apache JMeter at a certain time of day, representing a cluster with container virtualization, illustrates stable query distribution by the load balancer and the applicability of the mathematical model for conducting optimization and efficiency computations in distributed computer systems.</jats:p>