Narrowband IoT (NB-IoT) is the latest IoT connectivity solution presented by the 3GPP. NB-IoT introduces coverage classes and introduces a significant link budget improvement by allowing repeated transmissions by nodes that experience high path loss. However, those repetitions necessarily increase the energy consumption and the latency in the whole NB-IoT system. The extent to which the whole system is affected depends on the scheduling of the uplink and downlink channels. We address this question, not treated previously, by developing a tractable model of NB-IoT access protocol operation, comprising message exchanges in random-access, control, and data channels, both in the uplink and downlink. The model is then used to analyze the impact of channel scheduling as well as the interaction of coexisting coverage classes, through derivation of the expected latency and battery lifetime for each coverage class. These results are subsequently employed in investigation of latency-energy tradeoff in NB-IoT channel scheduling as well as determining the optimized operation points. Simulations results show validity of the analysis and confirm that there is a significant impact of channel scheduling on latency and lifetime performance of NBIoT devices.