The Objective of the Study is to analyze the Queuing measures which help the Out-Patient Department in an hospital to function effectively Waiting on a Queue is not usually interesting, but reduction in this waiting time usually requires planning and extra investments. Queuing is a major challenge for Healthcare services all over the world, but particularly so in developing countries. Queuing theory is the branch of Operations Research in Applied Mathematics and deals with phenomenon of waiting lines. The Health Systems should have an ability to deliver safe, efficient and smooth services to the Patients. In this paper, we discuss about an Out-Patient Department in an Hospital and calculate the performance measures of the Queuing System based on the values of the parameters, for an Out-Patient Department in an hospital and we analyze how for the model under Study influence the behavior of the System.