The increasing demand for power distribution systems in terms of control with nearly immediate response requires deploying a new type of user equipment (UE) that demands permanent connectivity. In NB-IoT systems, the traffic generated by such UEs may constitute a large part of the overall load. In this paper, we first propose a detailed two-dimensional Markov chain model to capture the system's behavior with the mixture of conventional stochastic and regular traffic types. To provide a computationally efficient solution, we then apply the state aggregation technique to reduce it to a one-dimensional model and develop approximations and associated numerical algorithms for assessing the mean delay when transmitting the considered traffic. Our results show that a single NB-IoT cell remains stable for up to 72x10^4 conventional UEs and 9x10^3 UEs demanding permanent connectivity. The presence of the latter UEs type has a linear effect on their delay, but affects conventional UEs more drastically. A delay bound of 10s specified in ITU-R M.2410 is met for the conventional UEs, even under a high number of permanently connected UEs 10^3. However, the delay on the side of the latter UEs is violated even for 100 permanently connected UEs requiring redesigning the NB-IoT channel access mechanism or expanding resources.