NB-IoT is a new radio access technology targeting a large set of use cases for massive machine-type communications standardized by the 3GPP. Compared to human-oriented technologies, NB-IoT has been enhanced in terms of coverage and power saving capabilities while reducing the complexity at the same time. These features allow connectivity of devices in challenging positions, enabling long battery life. This paper provides an overview of NB-IoT, together with a mathematical model of the network able to predict the maximum performance in a given scenario with a specific configuration of some design parameters. Finally, we present an analysis on how these parameters affect the overall performance and how the optimal configuration may be chosen according to arbitrary criteria.