The administration of the General Hospital in Calgary wants

to tackle issues with the emergency room service$-$

performance. There patients arriving at different rate times

during the day and there is a need to organize the

treatments. There are four doctors available for treat

patients when needed. If there is not need there are other

responsibilities, such as lab tests, reports, x$-$ray diagnoses, or

else reschedule $d$ to work at other hours. There is a need to

improve speed of treatment. There is an estimation that a

patient should not wait more than $5$ minutes before being

seen by a doctor. The emergency room services patient in

the order of arrival $($FIFO$).$ And the patient will see the

doctor available after the waiting time. A typical day is

describes in the table:

It is assumed that arrivals are Poisson distributed, and a

treatment time is about $12$ minutes on the average,

following an exponential pattern. How many doctors are

required in each period of time to keep the expected time of

patient care. What could happen if only one doctor is

between $9$ AM and $3$ PM