Providing LTE connectivity to emerging Machine-to-Machine (M2M) applications imposes several challenges to the operation and optimization of current and future 3GPP mobile broadband standard releases. Scheduling in an efficient way M2M traffic over the existing LTE MAC infrastructure is decisive for the smooth evolution towards an M2M-enabled LTE system. The large number of connecting devices compared to classical LTE terminals, and their vastly diverse quality-of-service requirements, call for the design of new packet scheduling schemes tailored to the M2M paradigm. To this end, we propose low complexity and signaling scheduling policies which periodically grant access to the M2M devices. In particular, we first propose an analytical model for predicting the QoS performance of M2M services when the fixed periodic scheduling algorithm is employed. Next we propose a modification to this scheme, which exploit queueing-dynamics and finally we examine QoS-differentiation issues when devices are grouped into clusters. Interesting performance-complexity trade-offs are exposed. The results of our study may aid the system designer in tuning and optimizing M2M traffic scheduling.