Machine-to-machine (M2M) traffic is variegate and finding a traffic model which can cover a wide range of M2M sources is challenging. In this paper we address this challenge by proposing an extension of legacy renewal processes for modeling of M2M traffic sources. To this end, we first describe the model and derive some performance parameters, as the overall packet arrival distribution and its moments. We then discuss the packetgeneration process and consider the counting variable in atime interval, and give the mean and the Laplace transformof the z-transform for this variable. Successively, we present the asymptotic expansion for the variance and the Index of Dispersion of Counts (IDC). We derive the expression of the two first coefficients of this expansion in the general case, while more explicit expressions are provided for some special cases. More specifically, for the special case of a source model with two states, geometric distribution of the numbers of arrivals in each state, and exponential inter-arrival times, we solve for the modelparameters in terms of mean, variance and two IDCs. The model is then applied to real M2M traces obtained from an operational network. Albeit the match is not perfect, yet the proposed model captures the main features of the traces, in particular the large burstiness in the packet arrival process.