Massive MTC over cellular networks is expected to be an integral part of wireless smart city applications. The LTE/LTE-A technology is a major candidate for provisioning of MTC applications. However, due to the diverse characteristics of payload size, transmission periodicity, power efficiency, and QoS requirement, MTC poses huge challenges to LTE/LTE-A technologies. In particular, efficient management of massive random access is one of the most critical challenges. In the case of massive random access attempts, the probability of preamble collision drastically increases, and thus the performance of LTE/LTE-A random access degrades sharply. In this context, this article reviews the current state-of-the-art proposals to control massive random access of MTC devices in LTE/LTE-A networks. The proposals are compared in terms of five major metrics: access delay, access success rate, power efficiency, QoS guarantee, and the effect on HTC. To this end, we propose a novel collision resolution random access model for massive MTC over LTE/LTE-A. Our proposed model basically resolves the preamble collisions instead of avoidance and targets the management of massive and bursty access attempts. Simulations of our proposed model show huge improvements in random access success rate compared to the standard slotted-Aloha- based models. The new model can also coexist with existing LTE/LTE-A MAC protocol and ensure high reliability and time-efficient network access.