In the given paper a general analytical model for a queuing system with limited capacity buffer intended to control packets’ traffic in Internet of Things applications is proposed. This model is based on the following assumptions. There is a fixed number of packets’ classes. For each pair of these classes either preemptive or non-preemptive priority is set. Packets of each class arrive according to the Poisson process with the given arrival rate, and are transmitted without errors with the given transmission rate. The criterion on the structure of the set of priorities between the classes of packets avoiding unnecessary push-out of packets being in the transmission is proved. Continuous-Time Markov Chain associated with the proposed model has been defined and analyzed. Basic characteristics including blocking probability, push-out probability, delay, and utilization have been estimated for each class of packets. Basic measures for the proposed model, such as Grade of Service, cost function of operation, and performance are established.