The Model for the Formation of Time Intervals for Receiving Messages in Distributed Information Systems

The article discusses the transmission of groups of messages in modes that do not require delivery confirmation. It is expected that it can be used in messaging systems that involve a high percentage of messages transmitted with errors, such as sensor networks and Internet of Things networks. The message source transmits a sequence of messages, while the receiver forms a certain time window in which their delivery is expected. Increasing the time interval increases the number of messages arriving at the receiver from other sources operating as part of a distributed system, which increases the likelihood of message authentication code collisions. Reducing the size of the time interval increases the probability that at least one message from the group will not be included in it. The purpose of the work is to create a mathematical model based on the theory of random processes that allows to determine the appropriate boundaries of the time interval for receiving messages using the laws of distribution of the time of message delivery from the source to the receiver and the average intensity of message generation by the source. The relationship between the value of the time interval between the time of arrival of the first message of the group and the preceding beginning of the time window for receiving the message was determined. It has been established that the appropriate value of this interval is in the range of 0.3… 0.4 of the average time between receiving messages.