"Ted Glickman, the administrator at D$.$C$.$ General Hospital emergency room, faces the problem of providing treatment for patients who arrive at different rates during the day. There are four doctors available to treat patients when needed. If not needed, they can be assigned other responsibilities $($such as doing lab tests, reports, X$-$ray diagnoses$)$ or else rescheduled to work at other hours.

It is important to provide quick and responsive treatment, and Ted thinks that, on the average,$$patients should not have to sit in the waiting area for more than $5$ minutes$$before being seen by a doctor. Patients are treated on a first$-$come, first$-$served basis and see the first available doctor after waiting in the queue. The arrival pattern for a typical day is as follows:"