An Enhanced Low Latency Queue scheduling algorithm that categorizes and prioritizes the realtime traffic was developed. In this algorithm the high priority queues are introduced for scheduling the video applications separately along with the voice applications, with voice applications having a higher priority over video applications. The low priority queues are serviced using Class Based Weighted Fair Queueing. However, at high arrival rate of voice packets, the video packets may suffer resource starvation. To overcome this drawback, we propose an improved LLQ algorithm which delays voice packets that arrive while the video packets are already in the queue and services video packets found in the queue before servicing voice packets as long as the voice packets are not delayed beyond the maximum tolerable delay limit. MAT-LAB software is used to plot the graphs. This study discovers the possible ways of reducing the delay experienced by voice packets without over penalizing the video packets. This study will help researchers to uncover possible ways of providing the quality of service to various classes of traffic. Numerical results obtained from the derived models show that delaying voice packets leads to reduction in the average waiting time of video packets. Furthermore, voice packets can be delayed to serve video packets as long as the load and arrival rates of voice packets does not exceed 81% and 14 packets/second respectively and less dependent on the load and arrival rates of video packets.