The growth of machine-to-machine (M2M) type interconnections in future mobile networks, such as 5G, LTE and LTE-Advanced, significantly increases both signaling and user data load on the network infrastructure of operators. The great influence on the radio access network has the transmission of massive Machine-type communications. To reduce the cost of servicing this type of traffic and to improve the performance measures, such as access success probability and access delay, the development of analytical methods for the analysis of the transmission of M2M traffic is actual. The paper contains the mathematical model in term of Markov chain, which consider session initiation procedure in random access radio channel and allows to estimate mentioned performance measures using obtained expressions. Given examples show the dependence of the obtained measures on the collision probability and possible retransmission of service messages. © 2018 ACM.