No / Abstract: Internet of Things (IoT) aims to enable the interconnection of a large number of smart devices (things) using a combination of networks and computing technologies. But an influx of interconnected things makes a greater demand on the underlying communication networks and affects the quality of service (QoS). This paper investigates into the QoS of delay sensitive things and the corresponding traffic they generate over the network. Things such as security alarms, cameras, etc, generate delay sensitive information that must be communicated in a real time. Such things have heterogeneous features with limited buffer capacity, storage and processing power. Thus the most commonly used Best Effort service model cannot be an attractive mechanism to treat delay sensitive traffic. This paper proposes a cost-effective analytical model for a finite capacity queueing system with pre-emptive resume service priority and push-out buffer management scheme. Based on the analytical model various simulation results are generated in order to analyse the mean queue length and the blocking probability of high and low priority traffic for system with various capacities.