Internet of Things (IoT) allows communication among human-to-things, things-to-human,and things-tothings that are incorporated into an information networks allowing automatic information interchange and the processing of data at real time. In this paper, we conducta performance analysis of a real application defined through four traffic classes withthe priorities present in smart cities using Continuous Time Markov Chains(CTMC). Based on a finite capacity queuing system, we propose a new cost-effective analytical model with a push-out management scheme in favor of the highest priority (emergency) traffic. Based on the analytical model, several performance measures for different traffic classes have been studiedextensively including blocking probability; push out probability, delay, channel utilization as well as overall system performance.