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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

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

Chapter 2 – Fundamental Simulation Concepts

the system

(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

model specifics
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

schematic system representation
Schematic System Representation

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 0 00 initialize
Discrete Event Simulation by “Hand”:t = 0.00, Initialize

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 0 00 arrival of customer 1
Discrete Event Simulation by Hand:t = 0.00, Arrival of Customer 1

1

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 1 73 arrival of customer 2
Discrete Event Simulation by Hand:t = 1.73, Arrival of Customer 2

2

1

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 2 90 departure of customer 1
Discrete Event Simulation by Hand:t = 2.90, Departure of Customer 1

2

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 3 08 arrival of customer 3
Discrete Event Simulation by Hand:t = 3.08, Arrival of Customer 3

3

2

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 3 79 arrival of customer 4
Discrete Event Simulation by Hand:t = 3.79, Arrival of Customer 4

4

3

2

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 4 41 arrival of customer 5
Discrete Event Simulation by Hand:t = 4.41, Arrival of Customer 5

5

4

3

2

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 4 66 departure of customer 2
Discrete Event Simulation by Hand:t = 4.66, Departure of Customer 2

5

4

3

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 8 05 departure of customer 3
Discrete Event Simulation by Hand:t = 8.05, Departure of Customer 3

5

4

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 12 57 departure of customer 4
Discrete Event Simulation by Hand:t = 12.57, Departure of Customer 4

5

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 17 03 departure of customer 5
Discrete Event Simulation by Hand:t = 17.03, Departure of Customer 5

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 18 69 arrival of customer 6
Discrete Event Simulation by Hand:t = 18.69, Arrival of Customer 6

6

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 19 39 arrival of customer 7
Discrete Event Simulation by Hand:t = 19.39, Arrival of Customer 7

7

6

Chapter 2 – Fundamental Simulation Concepts

discrete event simulation by hand t 20 00 the end
Discrete Event Simulation by Hand:t = 20.00, The End

7

6

Chapter 2 – Fundamental Simulation Concepts

simulation by hand finishing up
Simulation by Hand:Finishing Up
  • Average waiting time in queue:
  • Time-average number in queue:
  • Server Utilization :

Chapter 2 – Fundamental Simulation Concepts