Today, the Internet traffic is mostly dominated by an elastic data transfer. However, with the progressive development of the real time applications, it is anticipated that the streaming traffic will contribute a significant amount of traffic in the near future. By combining priority queuing with Class Based Weighted Fair Queueing (CBWFQ), The Low Latency Queueing (LLQ) is a very important router discipline that aims to provide the needed quality of service (QoS) for each traffic category. Priority queueing is used to guarantee delay constraints for real-time traffic, whereas CBWFQ is used to ensure acceptable throughput for traffic classes that are less sensitive to delay. In this paper, we focus on developing a fluid model to capture the relation between elastic traffic and the real time traffic in a LLQ system under a quasi-stationary assumption. Our analysis of the CBWFQ system is based on some numerical observations and relies on the conservation of the average total number of elastic flows carried by the elastic system. Detailed packet level simulations of TCP flows show the accuracy of our analysis. The results presented in this paper allows a rapid performance evaluation of TCP traffic circulating in the actual IP networks.