An outpatient clinic that is open two hundred days/year receives twelve thousand visits per year, or approximately sixty patients per day. These visits are divided over two wings, for thirty patients per wing. Appointments are made for two three - hour sessions per day. Thus, the patient arrival rate averages five patients per hour, ( λ ) = 5 patients/hour. By observing the check - in and checkout processes, the service rate can be determined. Each check - in requires that the patient be retrieved from the waiting area, contact and insurance information be reviewed, and possibly a copay collected.

This process takes approximately ten minutes, so the service rate for check - ins is six patients per hour. Thus, the service rate for check - ins is ( µ ) = 6 patients/hour. Checkout takes approximately twenty minutes per patient and involves scheduling follow - up appointments, ordering tests, and answering questions. Hence the service rate for check outs is ( λ ) = 3 patients/hour. Currently, three employees perform the administrative duties. One is assigned check - in duties, and the other two mostly check out patients. All are cross - trained on both roles, and in reality the staff varies from day to day in who performs which role.

To address the long wait times, the clinic administrator wants to evaluate hiring additional staff members. Assuming that both service rates approximate Poisson distribution, and using Excel queuing template, calculate the optimal staffing pattern for the clinic and the system performance measures.