In recent years, the number of machine-to-machine (M2M) networks, which do not require direct human intervention, has been increasing at a rapid pace. Meanwhile, the need for a wireless platform to control and monitor these M2M networks, one with both a vast coverage area and a low network deployment cost, continues to be unmet. Mobile cellular networks (MCNs) and wireless sensor networks (WSNs) are emerging as two heterogeneous networks that can meet the challenges of M2M communication through network convergence. In this paper, a model for network convergence between a Long Term Evolution-Advance (LTE-A) cellular network and a WSN is proposed. Qualityof- Service (QoS) issues are assessed by a comparative study of the network delay in tight coupling and loose coupling LTE-A configurations. Simulation results indicate that the network delay in this proposed converged network is acceptable for various M2M applications. Additionally, it is demonstrated through simulation that the energy consumed by the implementation of the proposed protocol is suitable for resource-constrained devices.