1. Discrete Event “Hand” Simulation of a GI/GI/1 Queue
Simulation with Arena
Chapter 2 – Fundamental Simulation Concepts

2. Chapter 2 – Fundamental Simulation Concepts
The System
Arriving
customers
Departing
(Server)
Queue (FIFO)
customer in Service 4 5 6 7
Simulation Objectives
Claimed objective: Estimate expected waiting time in queue, expected queue length, and proportion of time the server is busy.
Real objective: Introduce you to discrete event simulation
Simulation with Arena
Chapter 2 – Fundamental Simulation Concepts

3. Chapter 2 – Fundamental Simulation Concepts
Model Specifics
Initially (time 0) empty and idle
Base time units: minutes
Input data (assume given for now …), in minutes:
Customer Number Arrival Time Interarrival Time Service Time
Stop when 20 minutes of (simulated) time have passed
Simulation with Arena
Chapter 2 – Fundamental Simulation Concepts

4. Schematic System Representation
Simulation with Arena
Chapter 2 – Fundamental Simulation Concepts

5. Discrete Event Simulation by “Hand”: t = 0.00, Initialize
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Chapter 2 – Fundamental Simulation Concepts

6. Discrete Event Simulation by Hand: t = 0.00, Arrival of Customer 1
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Chapter 2 – Fundamental Simulation Concepts

7. Discrete Event Simulation by Hand: t = 1.73, Arrival of Customer 2
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Chapter 2 – Fundamental Simulation Concepts

8. Discrete Event Simulation by Hand: t = 2.90, Departure of Customer 1
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Chapter 2 – Fundamental Simulation Concepts

9. Discrete Event Simulation by Hand: t = 3.08, Arrival of Customer 32
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Chapter 2 – Fundamental Simulation Concepts

10. Discrete Event Simulation by Hand: t = 3.79, Arrival of Customer 42
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Chapter 2 – Fundamental Simulation Concepts

11. Discrete Event Simulation by Hand: t = 4.41, Arrival of Customer 53 2
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Chapter 2 – Fundamental Simulation Concepts

12. Discrete Event Simulation by Hand: t = 4.66, Departure of Customer 25 4 3
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Chapter 2 – Fundamental Simulation Concepts

13. Discrete Event Simulation by Hand: t = 8.05, Departure of Customer 34
Simulation with Arena
Chapter 2 – Fundamental Simulation Concepts

14. Discrete Event Simulation by Hand: t = 12.57, Departure of Customer 4
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Chapter 2 – Fundamental Simulation Concepts

15. Discrete Event Simulation by Hand: t = 17.03, Departure of Customer 5
Simulation with Arena
Chapter 2 – Fundamental Simulation Concepts

16. Discrete Event Simulation by Hand: t = 18.69, Arrival of Customer 6
Simulation with Arena
Chapter 2 – Fundamental Simulation Concepts

17. Discrete Event Simulation by Hand: t = 19.39, Arrival of Customer 76
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Chapter 2 – Fundamental Simulation Concepts

18. Discrete Event Simulation by Hand: t = 20.00, The End7 6
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Chapter 2 – Fundamental Simulation Concepts

19. Simulation by Hand: Finishing Up
Average waiting time in queue:
Time-average number in queue:
Server Utilization :
Simulation with Arena
Chapter 2 – Fundamental Simulation Concepts