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Machine-type communication (MTC) is a new service defined by the 3rd Generation Partnership Project (3GPP) to provide machines to interact to each other over future wireless networks. One of the main problems in LTE-advanced networks is the distribution of a limited number of radio resources among enormously increasing number of MTC devices with different traffic characteristics. The radio resources allocation scheme for MTC traffic transmission in LTE networks is also standardized by 3GPP and implements the Random Access Channel (RACH) mechanism for transmitting data units from a plurality of MTC devices. Until now, there is a number of problems with the congestion in radio access network, as evidenced by a series of articles calling attention to the fact that more research is required, and even modification of the RACH mechanism in order to address drawbacks, exhibiting for example when a large number of devices are trying to access simultaneously. However, not many results have been obtained for the analysis, which allows to explore a variety of performance metrics of RACH mechanism on a qualitative level. In this paper the mathematical model in a form of the discrete Markov chain is built taking into account the features of the access procedure under congestion conditions and collisions. This baseline model allows to obtain the solution for key performance measures of RACH mechanism, such as the access success probability and the average access delay, in an analytical closed-form. Based on the proposed baseline model it is possible to obtain new results for the analysis of some modifications of RACH mechanism such as ACB (Access Class Baring).

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