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Massive connectivity and low latency are two important challenges for the Internet of Things (IoT) to achieve the Quality of Service (QoS) provisions required by the numerous devices it is designed to service. Motivated by these challenges, in the paper we introduce a new millimeter-wave non-orthogonal multiple access (mmWave-NOMA) transmission scheme designed for cellular machine-to-machine (M2M) communication systems for IoT applications. It consists of one base station (BS) and numerous multiple machine type communication (MTC) devices operating in a cellular communication environment. We consider its down-link performance and assume that multiple MTC devices share the same communication resources offered by the proposed mmWave-NOMA transmission scheme, which can support massive connectivity. For this system, a novel MTC pairing scheme is introduced the design of which is based upon the distance between the BS and the MTC devices aiming at reducing the system overall overhead for massive connectivity and latency. In particular, we consider three different MTC device pairing schemes, namely i) the random near and the random far MTC devices (RNRF); ii) the nearest near and the nearest far MTC devices (NNNF); and iii) the nearest near and the farthest far MTC device (NNFF). For all three pairing schemes, their performance is analyzed by deriving closed-form expressions of the outage probability and the sum rate. Furthermore, performance comparison studies of the three MTC device pairing schemes have been carried out., Comment: Accepted by IEEE Internet of Things Journal