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

2. Simulation with ArenaChapter 2 – Fundamental Simulation Concepts The System Arriving customers Departing customers (Server) Queue (FIFO) customer in Service 4567 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

3. Simulation with ArenaChapter 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 10.001.732.90 21.731.351.76 33.080.713.39 43.790.624.52 54.4114.284.46 618.690.704.36 719.3915.522.07 834.913.153.36 938.061.762.37 1039.821.005.38 11 40.82...... Stop when 20 minutes of (simulated) time have passed

4. Simulation with ArenaChapter 2 – Fundamental Simulation Concepts Schematic System Representation

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

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

7. Simulation with ArenaChapter 2 – Fundamental Simulation Concepts Discrete Event Simulation by Hand: t = 1.73, Arrival of Customer 2 12

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

9. Simulation with ArenaChapter 2 – Fundamental Simulation Concepts Discrete Event Simulation by Hand: t = 3.08, Arrival of Customer 3 23

10. Simulation with ArenaChapter 2 – Fundamental Simulation Concepts Discrete Event Simulation by Hand: t = 3.79, Arrival of Customer 4 234

11. Simulation with ArenaChapter 2 – Fundamental Simulation Concepts Discrete Event Simulation by Hand: t = 4.41, Arrival of Customer 5 2345

12. Simulation with ArenaChapter 2 – Fundamental Simulation Concepts Discrete Event Simulation by Hand: t = 4.66, Departure of Customer 2 345

13. Simulation with ArenaChapter 2 – Fundamental Simulation Concepts Discrete Event Simulation by Hand: t = 8.05, Departure of Customer 3 45

14. Simulation with ArenaChapter 2 – Fundamental Simulation Concepts Discrete Event Simulation by Hand: t = 12.57, Departure of Customer 4 5

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

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

17. Simulation with ArenaChapter 2 – Fundamental Simulation Concepts Discrete Event Simulation by Hand: t = 19.39, Arrival of Customer 7 67

18. Simulation with ArenaChapter 2 – Fundamental Simulation Concepts Discrete Event Simulation by Hand: t = 20.00, The End 67

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