Math model for estimating the probability of preambles collisions within random access in the mMTC scenario

Abstract

The mass machine-to-machine communication (mMTC) scenario is one of the key ones in 5G cellular communication system. Tens of thousands of devices can operate simultaneously in one mMTC cell, sending data asynchronously to the data collection point. This is the reason for the occurrence of unavoidable collisions of preamble in the random access procedure. Mathematical models of traffic generation from a large number of devices within a cell are used to reliably estimate the probability of collisions. Most existing models are based on the approach of generating aggregated traffic from all devices and do not allow taking into account the current state of each individual device, which reduces the reliability of model studies. To solve this problem, we propose a mathematical model for generating traffic (preambles) in a random access channel, taking into account the transition state matrix of a discrete Markov chain. This approach allows to describe more reliably the synchronous and asynchronous transmission of preambles within a cell. The developed model is designed to estimate the collision probability of the random access procedure in the mMTC scenario, taking into account the synchronous and asynchronous transmission of preambles.