03.dasar simulasi
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The document discusses basic concepts in simulation including types of simulation models, random behavior, simulating random behavior using random number generators and generating random variates, and using spreadsheets to build simple stochastic simulation models. It provides examples of simulating customer arrivals and services at an ATM using random variables generated in a spreadsheet to model the dynamic and stochastic behavior of the system over time.
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03.dasar simulasi
- 1. Simulasi Komputer Chapter 03.Basic SImulation Dari buku Simulation with Promodel Harrell−Ghosh−Bowden Dipresentasikan Oleh Rio Aurachman, MT
- 2. INTRODUCTION CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman
- 3. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Introduction Sub chapter Sumber gambar: ctms.engin.umich.edu
- 4. TYPE OF SIMULATION CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman
- 5. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Tipe Simulasi • Static/Dynamic • Stochastic/Deterministic • Discrete event/Continuous Sub chapter Sumber gambar: en.wikipedia.org
- 6. RANDOM BEHAVIOUR CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman
- 7. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Perilaku Acak • Sistem Stokastik memiliki nilai yang berubah seiring waktu – Distribusi bisa normal – Eksponensial – Poisson – dll • Probabilitas bisa Diskrit atau Kontinyu • Probabilitas Diskrit memiliki nilai yang tertentu dengan probabilitas • Relationships among probability distributions - Wikipedia, the free encyclopedia Sub chapter Sumber gambar: en.wikipedia.org
- 8. SIMULATING RANDOM BEHAVIOUR CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman
- 9. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Simulasi Random behaviour • Kelebihan:Mampu Meniru perilaku yang acak • Bisa berdasarkan Distribusi Probabilitas Sub chapter 1.Generationg Random Number 2.Generating Random Variates Sumber gambar:
- 10. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Generate Random Number • Random Number generator • (0 ≤ x ≤ 1) • Tidak benar-benar Random • Pesudo Random Generator Sumber gambar: Sub chapter 1.Generationg Random Number 2.Generating Random Variates
- 11. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Linear Congurential generators Sumber gambar: Sub chapter 1.Generationg Random Number 2.Generating Random Variates slideplayer.info C
- 12. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Contoh LCG • a = 21, c = 3, and m = 16 Sumber gambar: Sub chapter 1.Generationg Random Number 2.Generating Random Variates
- 13. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman LCG • Bisa diulang • Di Promodel • Berulang sesuai M • Pemilihan M Sesuai (Pritsker,1995) Sumber gambar: Sub chapter 1.Generationg Random Number 2.Generating Random Variates reference.wolfram.com
- 14. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman LCG(2) • Stream – Satu sequence bisa dibagi menjadi banyak stream untuk banyak beberapa situasi random • Subdivide sequence • Dua tipe LCG – Mixed Cingruential generator (c>0) – Multiplicative Congruential Generator (c=0) • prime modulus multiplicative linear congruential generator • Promodel: (PMMLCG) dengan a =630,360,016, c = 0, and m = 2^31− 1 Sumber gambar: Sub chapter 1.Generationg Random Number 2.Generating Random Variates estadisticaccbas.uaa.mx
- 15. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Menguji random Number Generator • Pengetahuan kita akan random number sangat kecil • Random number kita harus – Independent – Uniformly distributed • Uji yang bisa dilakukan – Independent: Run test – Uniformly distributed: • Kolmogorov Smirnov • Chi Squared Sumber gambar: Sub chapter 1.Generationg Random Number 2.Generating Random Variates spin.atomicobject.com
- 16. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Generating random Variates • Mengubah uniform [0,1] hasil LCG menjadi distribusi lain • Terdapat beberapa metode – Inverse Transformation – Acceptance/rejection – Composition – Convolution Sumber gambar: Sub chapter 1.Generationg Random Number 2.Generating Random Variates a.Continuous b.discrete
- 17. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Continuous Distributrion • f (x) probability density function • cumula-tive distribution function of X • F(x) = P(X ≤ x) • U = F(x) • U is uniform(0,1) Sumber gambar: Sub chapter 1.Generationg Random Number 2.Generating Random Variates a.Continuous b.discrete
- 18. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Continuous Distribution (2) Sumber gambar: Sub chapter 1.Generationg Random Number 2.Generating Random Variates a.Continuous b.discrete
- 19. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Discrete Distribution • Mirip dengan continous Distribution • Misalkan punya 3 Kemungkinan Nilai • Dapat dijelaskan berikut – if 0≤ Ui ≤ 0.10, then Xi = 1; – if 0.10 < Ui ≤ 0.40, then Xi= 2; – if 0.40< Ui ≤ 1.00, then Xi = 3 • Dapat dibuat besar (tidak hanya 3 nilai) Sub chapter 1.Generationg Random Number 2.Generating Random Variates a.Continuous b.discrete
- 20. SIMPLE SPREADSHEET SIMULATION CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman
- 21. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Simulasi Spreadsheet Sederhana • Membuat stocastic dynamic simulation model • Objek Kajian ATM • System terminology • Tujuan • Bagaimana perilaku customer 17? Sumber gambar: Sub chapter 1.Simulationg Random variates 2.Simulating Dynamic, Stochastic Systems 3. Simulation replications and Output analysis
- 22. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Simulating random Variates • Nilai yang disimulasikan – Inter arrival – Service • Transformation equation Sumber gambar: Sub chapter 1.Simulationg Random variates 2.Simulating Dynamic, Stochastic Systems 3. Simulation replications and Output analysis
- 23. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Simulasi Dynamic and stochastic Model • Inti simulasi adalah meng generate random variates dan membuat kejadian stokastik di simulasi • See Excel Sumber gambar: Sub chapter 1.Simulationg Random variates 2.Simulating Dynamic, Stochastic Systems 3.Simulation replications and Output analysis
- 24. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman Simulation Replications and Output Analysis • Variasi yang besar menunjukkan dibutuhkan lebih banyak replication Sumber gambar: Sub chapter 1.Simulationg Random variates 2.Simulating Dynamic, Stochastic Systems 3.Simulation replications and Output analysis
- 25. SUMMARY CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman
- 26. CHAPTER 3 Basic Simulation 1.Introduction 2.Type of SImulation 3.Random Behaviour 4.Simulating Random Behaviour 5.Simple Spread Sheet Simulation 6.Rangkuman rangkuman Random Number Generator (Ui) Variates (dengan distribusi) (Xi) Performance dari Sistem Stokastik (contoh: Panjang antrian, waktu, dll) Sumber gambar: