An optometry practice routinely schedules patients to arrive every 15 minutes (8am, 8:15am, 8:30am…) Assume patients always arrive on time. Each patient needs to complete two steps: A computerized assessment where measurements and information are recorded directly as the patient looks through a device, and a doctor interview where the doctor collects information on the patient’s condition and performs further tests. The computerized assessment takes exactly 14 minutes to complete. The doctor visit takes 10 minutes on average and has an exponential distribution; it varies significantly depending on the needs of the particular patient.
a. What would be the average time in the system if the computerized assessment were always done first?
b. What would it be if the doctor interview were always done first?
c. Back in the original system with the computerized test being performed before the doctor visit, what would be the average wait for the doctor if on average after every hour of seeing patients the doctor, before moving on to the next patient, goes back to his office to check email, taking an exponentially distributed time with a mean of 15 minutes?