Probability Distribution Of Time Between Arrivals And Simulation Results

Probability Distribution of time between arrivals:

Time between arrivals (min)	Probability	Cumulative Probability
5 Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	0.1	0.1
10	0.15	0.25
15	0.22	0.47
20	0.25	0.72
25	0.18	0.9
30	0.1	1

Probability distribution of attention needed:

Patient needs to see	Probability	Cumulative Probability
Doctor	0.4	0.4
Nurse	0.35	0.75
Both	0.25	1

The length of the patient’s visit (in minute) is defined by the following probability distributions:

Doctor	Probability	Cumulative Probability
10	0.2	0.2
15	0.3	0.5
20	0.25	0.75
25	0.15	0.9
30	0.1	1

Nurse	Probability	Cumulative Probability
5	0.1	0.1
10	0.25	0.35
15	0.5	0.85
20	0.15	1

Simulation:

Simulation Results

Element	Element	Statistics	Overall
types	names		Means

Entrance(s)	Door	Objects entering process	45
		Objects unable to enter	0
		Service level	1

Work Station(s)	Clerk	Final status	NA
		Final inventory (int. buff.)	0
		Mean inventory (int. buff.)	0
		Mean cycle time (int. buff.)	0
		Work cycles started	45
		Fraction time working	0
		Fraction time blocked	0

	Sharon	Final status	NA
		Final inventory (int. buff.)	0
		Mean inventory (int. buff.)	0
		Mean cycle time (int. buff.)	2
		Work cycles started	10
		Fraction time working	0
		Fraction time blocked	0

	Peter	Final status	NA
		Final inventory (int. buff.)	0
		Mean inventory (int. buff.)	0
		Mean cycle time (int. buff.)	0
		Work cycles started	9
		Fraction time working	0
		Fraction time blocked	0

Buffer(s)	Line	Objects leaving	45
		Final inventory	0
		Minimum inventory	0
		Maximum inventory	2
		Mean inventory	0
		Mean cycle time	0

	License	Objects leaving	10
		Final inventory	10
		Minimum inventory	0
		Maximum inventory	11
		Mean inventory	5
		Mean cycle time	108

	Registration	Objects leaving	9
		Final inventory	4
		Minimum inventory	0
		Maximum inventory	5
		Mean inventory	2
		Mean cycle time	53

	Both	Objects leaving	10
		Final inventory	1
		Minimum inventory	0
		Maximum inventory	3
		Mean inventory	1
		Mean cycle time	15

	Served Customer	Objects leaving	0
		Final inventory	19
		Minimum inventory	0
		Maximum inventory	19
		Mean inventory	8
		Mean cycle time	18

Decision Point(s)	DP	Objects leaving	44
		Final inventory (int. buff.)	0
		Mean inventory (int. buff.)	0
		Mean cycle time (int. buff.)	0

Therefore, overall average waiting time in the process for customers = 18 minutes

The number of customers served during the 3-hour time peak period = 44

The number of customers who have already seen the clerk at the counter but waiting to be served at the end of the 3-hour peak period = 10+9+10 = 29

The utilisation of these three employees, i.e.

o The clerk at the counter = 45/45 = 100%

o Sharon = 10/45 = 22.22%

o Peter = 9/45 = 20%

Simulation result while one resource has been added:

Simulation Results

Element	Element	Statistics	Overall
types	names		Means

Entrance(s)	Door	Objects entering process	45.08
		Objects unable to enter	0.00
		Service level	1.00

Work Station(s)	Clerk	Final status	NA
		Final inventory (int. buff.)	0.00
		Mean inventory (int. buff.)	0.00
		Mean cycle time (int. buff.)	0.00
		Work cycles started	45.02
		Fraction time working	0.25
		Fraction time blocked	0.00

	Sharon	Final status	NA
		Final inventory (int. buff.)	0.29
		Mean inventory (int. buff.)	0.25
		Mean cycle time (int. buff.)	2.50
		Work cycles started	10.14
		Fraction time working	0.28
		Fraction time blocked	0.25

	Peter	Final status	NA
		Final inventory (int. buff.)	0.00
		Mean inventory (int. buff.)	0.00
		Mean cycle time (int. buff.)	0.00
		Work cycles started	9.54
		Fraction time working	0.34
		Fraction time blocked	0.00

Buffer(s)	Line	Objects leaving	45.02
		Final inventory	0.06
		Minimum inventory	0.00
		Maximum inventory	2.00
		Mean inventory	0.05
		Mean cycle time	0.21

	License	Objects leaving	10.14
		Final inventory	10.19
		Minimum inventory	0.00
		Maximum inventory	11.09
		Mean inventory	5.34
		Mean cycle time	108.36

	Registration	Objects leaving	9.54
		Final inventory	3.64
		Minimum inventory	0.00
		Maximum inventory	5.17
		Mean inventory	2.18
		Mean cycle time	45.34

	Both	Objects leaving	10.14
		Final inventory	1.11
		Minimum inventory	0.00
		Maximum inventory	2.78
		Mean inventory	0.79
		Mean cycle time	14.87

	Served Customer	Objects leaving	0.00
		Final inventory	19.00
		Minimum inventory	0.00
		Maximum inventory	19.00
		Mean inventory	8.49
		Mean cycle time	Infinite

Decision Point(s)	DP	Objects leaving	44.76
		Final inventory (int. buff.)	0.00
		Mean inventory (int. buff.)	0.00
		Mean cycle time (int. buff.)	0.00



	Resource(s)
	Mary	Mean number in use	11.12

Second order algebraic Model:

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