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Discrete Event “Hand” Simulation of a GI/GI/1 Queue

Discrete Event “Hand” Simulation of a GI/GI/1 Queue . (Server). Arriving customers. Departing customers. 7. 6. 5. 4. Queue (FIFO). customer in Service. The System. Simulation Objectives

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Discrete Event “Hand” Simulation of a GI/GI/1 Queue

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

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

  3. 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 1 0.00 1.73 2.90 2 1.73 1.35 1.76 3 3.08 0.71 3.39 4 3.79 0.62 4.52 5 4.41 14.28 4.46 6 18.69 0.70 4.36 7 19.39 15.52 2.07 8 34.91 3.15 3.36 9 38.06 1.76 2.37 10 39.82 1.00 5.38 11 40.82 . . . . . . . . . . • Stop when 20 minutes of (simulated) time have passed Chapter 2 – Fundamental Simulation Concepts

  4. Schematic System Representation Chapter 2 – Fundamental Simulation Concepts

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

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

  7. Discrete Event Simulation by Hand:t = 1.73, Arrival of Customer 2 2 1 Chapter 2 – Fundamental Simulation Concepts

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

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

  10. Discrete Event Simulation by Hand:t = 3.79, Arrival of Customer 4 4 3 2 Chapter 2 – Fundamental Simulation Concepts

  11. Discrete Event Simulation by Hand:t = 4.41, Arrival of Customer 5 5 4 3 2 Chapter 2 – Fundamental Simulation Concepts

  12. Discrete Event Simulation by Hand:t = 4.66, Departure of Customer 2 5 4 3 Chapter 2 – Fundamental Simulation Concepts

  13. Discrete Event Simulation by Hand:t = 8.05, Departure of Customer 3 5 4 Chapter 2 – Fundamental Simulation Concepts

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

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

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

  17. Discrete Event Simulation by Hand:t = 19.39, Arrival of Customer 7 7 6 Chapter 2 – Fundamental Simulation Concepts

  18. Discrete Event Simulation by Hand:t = 20.00, The End 7 6 Chapter 2 – Fundamental Simulation Concepts

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

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