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This article considers the mathematical model of queueing systems for the communication network with multiple access, which is used in the automated group of moving objects control systems. The dynamic communication model in the form of a single-line queuing model with the batch input claims was researched. The method of asymptotic analysis of the communication channel under a heavy load conditions was applied. As a result, the basic probabilistic characteristics of the system were obtained, including: the probability distribution of the waiting time values of the virtual claims, the average length of the queue claims at random time. It has been discovered that the characteristics of the communications models allow performing parametric optimization of communication networks, establishing the most appropriate values of the network parameters.