Time

Arrival Rate

$9$ A$.$M$\mathrm{.}3$ P$.$M$.$

$$patients$/$hour

$3$ P$.$M$\mathrm{.}8$ P$.$M$.$

$$patients$/$hour

$8$ P$.$M$.$midnight

$$patients$/$hour

Arrivals follow a Poisson$$ distribution, and treatment$$ times, minutes on the$$ average, follow the negative exponential pattern.

Part $2$

$$a$)$ How many doctors should be on duty during each period to maintain the level of patient care$$ expected?

The least number of doctors required during the $9$ A$.$M$\mathrm{.}3$ P$.$M$.$ shift to meet the set waiting time goal is

$$

$.$

Part $3$

The least number of doctors required during the $3$ P$.$M$\mathrm{.}8$ P$.$M$.$ shift to meet the set waiting time goal is

$$

$1$

$3$

$4$

$2$

$.$

Part $4$

The least number of doctors required during the $8$ P$.$M$.$Midnight shift to meet the set waiting time goal is

$$

$2$

$3$

$1$

$4$

$.$

Part $5$

$$b$)$ What condition would exist if only one doctor were on duty between and $?$

A$.$

Since $,$ the line would back up indefinitely.