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The minimization of the total completion time for asynchronous transmission in distributed systems is discussed. Attention is focused on the problem of message scheduling on part of the sender. Messages to be sent form a queue, and the order in which they are to be sent has to be first established. The methods of scheduling messages, which minimize the factor of the total completion time, are presented herein. The message-scheduling problem becomes considerably complicated when the stream of data transmitted between the sender and the receiver is organized into packets ; A scheduling rule, according to which the shortest messages (SPT?Shortest Processing Time) are selected as the first to be sent, has been proven to be appropriate for the proposed model. A heuristic algorithm for scheduling messages with real-time constraints is proposed. The performance of the scheduling algorithm is experimentally evaluated. The results of the study show the possibility of improving the total completion time from a few to ten percent, depending on the characteristics of the sender. Thus, the practicability of the method has been proved.