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A fundamental characteristic of the majority of communications networks is the mean message delay. In a packet-switching network, the mean packet and message delay may differ considerably from each other, and their distribution will often take different forms. The mean message delay depends both on the mean packet delay and on the dispersion of the packet delay. Obviously, by reducing the mean packet delay one can also reduce the message delay. However, it is not always possible to decrease the mean packet delay in the network. A proposed method of transmitting data in a network is based on the use of error-correcting coding, which reduces the dispersion of the packet delay with some increase in the mean packet delay. The conditions were obtained for which an increase in the mean packet delay with simultaneous reduction in the dispersion leads to an increase of the probability of message delivery during the limited time.