MODEL OF RANDOM MULTIPLE ACCESS IN A LOCAL COMPUTER NETWORK WITH FLOWS OF VARIOUS INTENSITY AND PRIORITIES
A mathematical model of data transmission in a common channel with random multiple access is considered. It allows one to estimate the average data transmission time in flows, the probability of data transmission in flows, the average queue length in data transmission devices with asymmetric operation. The access algorithm is based on competition using fixed priorities with a given number of repetitions over a fixed time interval. It is believed that the system transmits codograms (messages) of a fixed duration. The message flows in the system are Poisson. The presented model includes a mathematical description of three interconnected random processes - the process of transmitting a separate communication, the process of forming a queue in the memory of individual devices and the process of occupying-releasing a common data transmission channel. Interconnected analytical expressions and a system of differential equations are obtained that allow one to evaluate the probability-time characteristics of the exchange process. The results of calculations using the proposed model for assessing the probability-time characteristics of information exchange in a microprocessor system using the I2C interface are presented. In contrast to the simulation models traditionally used in solving this kind of problem, the proposed analytical model is much simpler to implement. The main purpose of the model is to evaluate the parameters of the transmission process in the design of data transmission systems with a common channel