Mathematical relationship between waiting times and appointment interval for doctor and patients

Appointment systems try to achieve a balance between the time the doctor waits for patients to arrive and the time patients spend waiting to be seen. Mathematical analysis reveals that the time a patient can expect to wait increases exponentially as the appointment interval is reduced. An appointment interval that is less than the median consultation length can result in long waits for patients with no saving of time for the doctor. More frequent, shorter surgeries can save time for patients with no increase in the doctor's waiting time. Methods of improving the efficiency of use of surgery time are discussed.