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Abstract-The Internet of things (IoT) will entail massive number of wireless connections with sporadic traffic patterns. To support the IoT traffic, several technologies are evolving to support low power wide area (LPWA) wireless communications. However, LPWA networks rely on variations of uncoordinated spectrum access, either for data transmissions or scheduling requests, thus imposing a scalability problem to the IoT. This paper presents a novel spatiotemporal model to study the scalability of the ALOHA medium access. In particular, the developed mathematical model relies on stochastic geometry and queueing theory to account for spatial and temporal attributes of the IoT. To this end, the scalability of the ALOHA is characterized by the percentile of IoT devices that can be served while keeping their queues stable. The results highlight the scalability problem of ALOHA and quantify the extend to which ALOHA can support in terms of number of devices, traffic requirement, and transmission rate.

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