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	0.09
10	0.12
15	0.27
20	0.26
25	0.15
30	0.11

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	0.62
Nurse only	0.10
Both Doctor and Nurse	0.28

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 patients 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	0.12		5	0.21		15	0.16
15	0.21		10	0.56		20	0.25
20	0.32		15	0.15		25	0.36
25	0.18		20	0.08		30	0.17
30	0.17					35	0.05
						40	0.01

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

64 34 15 50 94 81 27 79

• The attention needed by the patient for each patient arriving in order 06 77 99 53 64 31 74 92

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

48 58 97 88 75 94 69 56

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.

Part b

Assume that the clinic opens at 9:00am and the first arrival occurs after the time between arrivals of the first patient (e.g. if the time between arrivals of patient 1 is 5 mins, then patient 1 arrives at 9:05am). Calculate each patients arrival time and departure time by completing the following table:

Patient	1	2	3	4	5	6	7	8
Arrival Time
Departure Time

Part c

From the results in (b), determine the following performance measures based on the 8 patients:

1. The average time that a patient must wait before service starts (i.e. before seeing the doctor/nurse/both)
2. The probability that the patient needs to wait for less than 30 minutes before service starts.