In this paper, we propose a method for evaluating the key indicators of a multichannel queuing system with an unlimited queue and multiphase Erlang-type service. It is shown that the transition to the multichannel case leads to a sharp increase in the dimension of the state space and a complication of the system of Kolmogorov equations, which often makes direct analytical calculation unavailable. A meta-model based on machine learning methods, trained on discrete event simulation data, is proposed for an approximate forecast of the average waiting time, average queue length and the proportion of applications served. A comparison of basic regression and neural network models is performed and the stability of the approximation with a change in the load factor is considered.

Keywords: queuing system, queue, simulation modeling, meta-model, machine learning, neural network, multi-channel service, Erlang distribution, impatience, Kolmogorov equation, regression, gradient boosting, random forest, perceptron