Our research objective is to reduce the Average Waiting Time for patients in an Emergency Department of public sector hospital. We have based our model on M/M/s Queuing System, our study revealssignificant findings on arrival rate of patients. During this simulation, we have used a preemptive priority scheduling model. In our practice, the arrival rate followed a Poisson distribution, averaging 30 patients per hour, with the Mean Service time of1.5 hours and Average Waiting Time recorded around 12.13 minutes. This research offersvaluable help to achieve better time management in emergency departments of high-density medical facilities.