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Being able to accommodate multiple simultaneous transmissions on a single channel, non-orthogonal multiple access (NOMA) appears as an attractive solution to support massive machine type communication (mMTC) that faces a massive number of devices competing to access the limited number of shared radio resources. In this paper, we first analytically study the throughput performance of NOMA-based random access (RA), namely NOMA-RA. We show that while increasing the number of power levels in NOMA-RA leads to a further gain in maximum throughput, the growth of throughput gain is slower than linear. This is due to the higher-power dominance characteristic in power-domain NOMA known in the literature. We explicitly quantify the throughput gain for the very first time in this paper. With our analytical model, we verify the performance advantage of the proposed NOMA-RA scheme by comparing with the baseline multi-channel slotted ALOHA (MS-ALOHA), with and without capture effect. Despite the higher-power dominance effect, the maximum throughput of NOMA-RA with four power levels achieves over three times that of the MS-ALOHA. However, our analytical results also reveal the sensitivity of load on the throughput of NOMA-RA. To cope with the potential bursty traffic in mMTC scenarios, we propose adaptive load regulation through a practical user barring algorithm. By estimating the current load based on the observable channel feedback, the algorithm adaptively controls user access to maintain the optimal loading of channels to achieve maximum throughput. When the proposed user barring algorithm is applied, simulations demonstrate that the instantaneous throughput of NOMA-RA always remains close to the maximum throughput confirming the effectiveness of our load regulation.