Question

A clinic has one receptionist, one doctor and one nurse. The clinic opens at time zero and patients begin to arrive some time later. Patients arrive at the clinic according to the following probability distribution:

Time between arrivals (minutes)	Probability
5	0.06
10	0.10
15	0.23
20	0.29
25	0.18
30	0.14

A patient may need to see only the doctor, only the nurse, or both the doctor and the nurse together. If a patient needs to see both the doctor and nurse, the patient must wait until both the doctor and nurse are free. The attention needed by a patient who comes to the clinic is defined by the following probability distribution:

Patient Needs to See	Probability
Doctor only	0.50
Nurse only	0.20
Both Doctor and Nurse	0.30

The “service time” for a patient is the length of the time that the patient spends in consultation with the doctor/nurse/both, depending on the patient’s needs. The service time EXCLUDES the time that the patient spends waiting to see the doctor/nurse/both if they are busy. Based on whether the patient sees the doctor, the nurse, or both, the service time of each patient (in minutes) is defined by the following probability distributions.

Doctor	Probability		Nurse	Probability		Both	Probability
10	0.22		5	0.08		15	0.07
15	0.31		10	0.24		20	0.16
20	0.25		15	0.51		25	0.21
25	0.12		20	0.17		30	0.28
30	0.10					35	0.17
						40	0.11

Design a SIMULATION BY HAND of this clinic to simulate the arrival and departure of 8 patients using the following random numbers ranging 00 to 99 generated for each random variable:

• Time between arrivals

14        94        48        27        79        81        64        34

• The attention needed by the patient for each patient, in order of arrival 31        01    99    74    77    92    06 53

• The service time for the patient, in order of arrival

98        56        58        76        48        48        94        88

Part a

For each of the 8 patients, simulate the three random variables from above:

1. the length of time between their arrivals,
2. whom they need to see, and
3. the service time spent in consultation.

Answer 1