This paper focuses on the paradigm of Internet of Things (IoT), which gives rise to communications between a large number of different technological devices, e.g. sensors and controllers. The increasing demand for various services without human intervention motivates service providers to apply machine-tomachine (M2M) communications. In this paper, a LTE cellular system where M2M devices and human-to-human (H2H) users transmit their data into the wireless network is considered. In particular, a radio resource allocation scheme for M2M communications in IoT infrastructure is proposed and analyzed. The scheme is based on fixed transmission zones at which M2M traffic is served according to the Processor Sharing (PS) discipline. Also, the Markovian model to evaluate main performance measures, i.e. data transmission delays and blocking probabilities, is proposed. To carry out the numerical analysis the recursive algorithm for computing the stationary probability distribution is developed. © Springer International Publishing Switzerland 2015.