Future Internet is expected to sustain a huge number of devices, many orders of magnitude higher than state-of-the-art network architectures and handle larger and unconventional information flows. Machine Type communications (MTC) will play a critical role in this evolution and thus both architectural and algorithmic enhancements to existing converged mobile and fixed network infrastructures are needed. In this paper, we focus on resource management issues for combined Human-to-Human (H2H) and Machine-to-Machine (M2M) traffic. The proposed Context-Aware Backhaul Management (CABM) scheme is applicable for M2M gateways, which can provide the interconnection between cellular and capillary networks both via wired and wireless backhaul alternatives. CABM scheme adopts efficient QoS provisioning procedures, by taking into consideration the diverse QoS requirements of novel MTC services. Simulation results show that the proposed MTC Request Admission Control (MTCR-AC) algorithm is resilient regarding QoS-related metrics in overload-state situations, while its inherent prediction-based decision-making procedures can offer significant performance gains, too.