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The vision for smart city imperiously appeals to the implementation of Internet-of-Things (IoT), some features of which, such as massive access and bursty short packet transmissions, require new methods to enable the cellular system to seamlessly support its integration. Rigorous theoretical analysis is indispensable to obtain constructive insight for the networking design of massive access. In this paper, we propose and define the notion of massive and sporadic access (MSA) to quantitatively describe the massive access of IoT devices. We evaluate the temporal correlation of interference and successful transmission events, and verify that such correlation is negligible in the scenario of MSA. In view of this, in order to resolve the difficulty in any precise spatio-temporal analysis where complex interactions persist among the queues, we propose an approximation that all nodes are moving so fast that their locations are independent at different time slots. Furthermore, we compare the original static network and the equivalent network with high mobility to demonstrate the effectiveness of the proposed approximation approach. The proposed approach is promising for providing a convenient and general solution to evaluate and design the IoT network with massive and sporadic access.