Several traffic models for the Internet of Things (IoT) have been proposed in the literature. However, they can be considered as heuristic models since they only reflect the stochastic characteristic of the generated traffic. In this paper, we propose a model to represent the communication of IoT devices. The model was used to obtain the traffic generated by the devices. Therefore, the proposed model is able to capture a wider understanding of device behaviour than existing, state-of-the-art traffic models. The proposed model illustrates the behaviour of Machine-to-Machine uplink communication in a network with multiple-access limited information capacity shared channels. In this paper, we analysed the number of transmitted packets using the traffic model extracted from our proposed communication model and compared it with the state-of-the-art traffic models using simulations. The simulation results show that the proposed model has significantly higher accuracy in estimating the number of transmitted packets compared with the current models in the literature. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.