This paper explores the application of queuing theory to assess the performance characteristics of the HaProxy load balancer, including response time, service waiting time, and the average number of busy servers. To approximate the load balancing process, we used MMAP/PH/M/N queuing analytical model type with a Marked Markovian input flow, the service time has PH - distribution, the system has a buffer of M capacity, the number of serving devices equals N. We use discrete event simulation (Monte Carlo method) to estimate the performance characteristics to simplify the process and save time instead of using the complex and time-consuming analytical calculations. In the paper, a numerical experiment was carried out to compare the performance values obtained through simulation with the metrics obtained from the test server. The effectiveness of the application of models was demonstrated.