Question: Most arrivals to a hospital emergency room are not considered emergencies in that the patients can wait to see a doctor until they complete the proper forms. At a county hospital, emergency patients arrive at a rate of 6 per hour. This process is, to no one's surprise, a Poisson arrival process. It takes the admission clerk approximately 10 min to fill out the patient's form.
The length of time is not exact and, in fact, follows an exponential distribution. As soon as the form is filled out, the patient is examined. The chief of staff is concerned with the quality of the operations and wants to know the expected performance of the current process. Use queuing theory to evaluate the performance of this process.