Arbitrarily Accurate Approximation of Numerical Characteristics of Stationary ALOHA Channels

The development of the Internet of Things technology in cellular networks is considered within the framework of massive machine-type communications with the use of random multiple access algorithms such as ALOHA and its modifications. Despite the fact that this class of algorithms has been studied for a long time, there are no numerical methods for obtaining with a given accuracy such characteristics of the system as the average delay and the average number of transmissions per user. We propose a method for calculating upper and lower bounds for these characteristics, which converge to each other (and the exact value) as the computational complexity increases. The proposed method allows one to obtain these characteristics with an arbitrary accuracy.