Chapter_02 - Fundamental Simulation Concepts Chapter 2 Last...

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Chapt. 2 -- Handout 1 Chapter 2 – Fundamental Simulation Concepts Slide 1 of 57 Simulation with Arena, 5th ed. Chapter 2 Fundamental Simulation Concepts Last revision June 21, 2009 Chapter 2 – Fundamental Simulation Concepts Slide 2 of 57 Simulation with Arena, 5th ed. What We’ll Do ... Underlying ideas, methods, and issues in simulation Software-independent (setting up for Arena) Example of a simple processing system square4 Decompose problem square4 Terminology square4 Simulation by hand square4 Some basic statistical issues Spreadsheet simulation square4 Simple static, dynamic models Overview of a simulation study
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Chapt. 2 -- Handout 2 Chapter 2 – Fundamental Simulation Concepts Slide 3 of 57 Simulation with Arena, 5th ed. The System: A Simple Processing System Arriving Blank Parts Departing Finished Parts Machine (Server) Queue (FIFO) Part in Service 4 5 6 7 General intent: square4 Estimate expected production square4 Waiting time in queue, queue length, proportion of time machine is busy Time units square4 Can use different units in different places … must declare square4 Be careful to check units when specifying inputs square4 Declare base time units for internal calculations, outputs square4 Be reasonable (interpretation, roundoff error) Chapter 2 – Fundamental Simulation Concepts Slide 4 of 57 Simulation with Arena, 5th ed. Model Specifics Initially (time 0) empty and idle Base time units: minutes Input data (assume given for now …), in minutes: Part 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
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Chapt. 2 -- Handout 3 Chapter 2 – Fundamental Simulation Concepts Slide 5 of 57 Simulation with Arena, 5th ed. Goals of Study: Output Performance Measures Total production of parts over run ( P ) Average waiting time of parts in queue: Maximum waiting time of parts in queue: N = no. of parts completing queue wait WQ i = waiting time in queue of i th part Know: WQ 1 = 0 (why?) N > 1 (why?) N WQ N i i = 1 i N i WQ max ,..., 1 = Chapter 2 – Fundamental Simulation Concepts Slide 6 of 57 Simulation with Arena, 5th ed. Goals of Study: Output Performance Measures (cont’d.) Time-average number of parts in queue : Maximum number of parts in queue : Average and maximum total time in system of parts (a.k.a. cycle time ): Q ( t ) = number of parts in queue at time t 20 ) ( 20 0 dt t Q ) ( max 20 0 t Q t i P i P i i TS P TS max ,..., 1 1 , = = TS i = time in system of part i
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Chapt. 2 -- Handout 4 Chapter 2 – Fundamental Simulation Concepts Slide 7 of 57 Simulation with Arena, 5th ed. Goals of Study: Output Performance Measures (cont’d.) Utilization of machine (proportion of time busy) Many others possible (information overload?) { 20 0 ( ) 1 if machine is busy at time , ( ) 0 if machine is idle at time 20 Bt dt t Bt t = Chapter 2 – Fundamental Simulation Concepts Slide 8 of 57 Simulation with Arena, 5th ed.
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