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

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Presentation transcript:

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

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

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 Stop when 20 minutes of (simulated) time have passed

Simulation with ArenaChapter 2 – Fundamental Simulation Concepts Schematic System Representation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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