Stochastic Simulation Introduction
Bo Friis Nielsen
Institute of Mathematical Modelling Technical University of Denmark 2800 Kgs. Lyngby – Denmark Email: bfn@imm.dtu.dk
Bo Friis Nielsen – 17/6-2001 C04245 2
Tentative course plan Tentative course plan
18 - 26/6 Monday Tuesday Wednesday Thursday Friday Monday Tuesday
9.00 - Introduction Sampling from Exercise 3 Simulation Exercise 5 Simulated Simulation
9.45 discrete continued software Continued annealing modelling
distributions
10.00 - Generating Exercise 2: Exercise 1,2,3 Exercise 4 Exercise 5 Exercise 7: Verification 10.45 random numbers sampling from continued continued continued Simulated validation
discrete Annealing
distributions
11.00 - Testing random Exercise 2 Discrete event Exercise 4 Markov chain Exercise 7 Presentation 11.45 number generators continued simulation continued monte carlo continued of projects 13.00 - Exercise 1: Sampling from Discrete event Arena Exercise 6 Bootstrap Selection of
13.45 generation of continuous simulation Markov Chain Projects
random numbers distributions Monte Carlo
14.00 - Exercise 1 Exercise 3: Exercise 4: Variance Exercise 6 Exercises in
17.00 continued sampling from discrete event reduction continued Bootstrap
continuous simulation methods
distributions Exercise 5
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Practicalities Practicalities
• Notes will be sold from Monday 18/6 in IMMs reception building 321, room 006 (1. floor). Price 100.00 kr.
Bo Friis Nielsen – 17/6-2001 C04245 3
Practicalities Practicalities
• Notes will be sold from Monday 18/6 in IMMs reception building 321, room 006 (1. floor). Price 100.00 kr.
• Course evaluation is: passed/not passed.
Bo Friis Nielsen – 17/6-2001 C04245 3
Practicalities Practicalities
• Notes will be sold from Monday 18/6 in IMMs reception building 321, room 006 (1. floor). Price 100.00 kr.
• Course evaluation is: passed/not passed.
• Teachers:
Bo Friis Nielsen – 17/6-2001 C04245 3
Practicalities Practicalities
• Notes will be sold from Monday 18/6 in IMMs reception building 321, room 006 (1. floor). Price 100.00 kr.
• Course evaluation is: passed/not passed.
• Teachers:
Bo Friis Nielsen, room 115, building 321 ext. 3397, e-mail bfn@imm.dtu.dk
Bo Friis Nielsen – 17/6-2001 C04245 3
Practicalities Practicalities
• Notes will be sold from Monday 18/6 in IMMs reception building 321, room 006 (1. floor). Price 100.00 kr.
• Course evaluation is: passed/not passed.
• Teachers:
Bo Friis Nielsen, room 115, building 321 ext. 3397, e-mail bfn@imm.dtu.dk
Lars Pedersen, room 215, building 321 ext. 3423, email lap@imm.dtu.dk
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Significance
Significance
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Significance Significance
• One of the most
Bo Friis Nielsen – 17/6-2001 C04245 4
Significance Significance
• One of the most (The most?)
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Significance Significance
• One of the most (The most?)important Operations Research techniques
Bo Friis Nielsen – 17/6-2001 C04245 4
Significance Significance
• One of the most (The most?)important Operations Research techniques
• Many modern statistical techniques rely on simulation
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What is simulation?
What is simulation?
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What is simulation?
What is simulation?
• Computer experiments with mathematical model
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What is simulation?
What is simulation?
• Computer experiments with mathematical model
• General engineering technique
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What is simulation?
What is simulation?
• Computer experiments with mathematical model
• General engineering technique
• Analytical/numerical solutions
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Why simulate?
Why simulate?
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Why simulate?
Why simulate?
• Real system expensive
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Why simulate?
Why simulate?
• Real system expensive
• Mathematical model to complex
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Why simulate?
Why simulate?
• Real system expensive
• Mathematical model to complex
• Get idea of dynamic behaviour
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Related areas
Related areas
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Related areas Related areas
• Statistics
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Related areas Related areas
• Statistics
• Computer science
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Related areas Related areas
• Statistics
• Computer science
• Operations research
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Target group
Target group
Bo Friis Nielsen – 17/6-2001 C04245 8
Target group Target group
• Methodology course of general interest
Bo Friis Nielsen – 17/6-2001 C04245 8
Target group Target group
• Methodology course of general interest
• Of special importance for students specialising in
Bo Friis Nielsen – 17/6-2001 C04245 8
Target group Target group
• Methodology course of general interest
• Of special importance for students specialising in Computer science
Bo Friis Nielsen – 17/6-2001 C04245 8
Target group Target group
• Methodology course of general interest
• Of special importance for students specialising in Computer science
Statistics
Bo Friis Nielsen – 17/6-2001 C04245 8
Target group Target group
• Methodology course of general interest
• Of special importance for students specialising in Computer science
Statistics
Operations Research
Bo Friis Nielsen – 17/6-2001 C04245 8
Target group Target group
• Methodology course of general interest
• Of special importance for students specialising in Computer science
Statistics
Operations Research
Planning and management
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Course goal
Course goal
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Course goal Course goal
• Topics related to scientific computer experimentation
Bo Friis Nielsen – 17/6-2001 C04245 9
Course goal Course goal
• Topics related to scientific computer experimentation
• Specialised techniques
Bo Friis Nielsen – 17/6-2001 C04245 9
Course goal Course goal
• Topics related to scientific computer experimentation
• Specialised techniques
Variance reduction methods
Bo Friis Nielsen – 17/6-2001 C04245 9
Course goal Course goal
• Topics related to scientific computer experimentation
• Specialised techniques
Variance reduction methods Random number generation
Bo Friis Nielsen – 17/6-2001 C04245 9
Course goal Course goal
• Topics related to scientific computer experimentation
• Specialised techniques
Variance reduction methods Random number generation Random variable generation
Bo Friis Nielsen – 17/6-2001 C04245 9
Course goal Course goal
• Topics related to scientific computer experimentation
• Specialised techniques
Variance reduction methods Random number generation Random variable generation The event-by-event principle
Bo Friis Nielsen – 17/6-2001 C04245 9
Course goal Course goal
• Topics related to scientific computer experimentation
• Specialised techniques
Variance reduction methods Random number generation Random variable generation The event-by-event principle
• Simulation based statistical techniques
Bo Friis Nielsen – 17/6-2001 C04245 9
Course goal Course goal
• Topics related to scientific computer experimentation
• Specialised techniques
Variance reduction methods Random number generation Random variable generation The event-by-event principle
• Simulation based statistical techniques Markov chain Monte Carlo
Bo Friis Nielsen – 17/6-2001 C04245 9
Course goal Course goal
• Topics related to scientific computer experimentation
• Specialised techniques
Variance reduction methods Random number generation Random variable generation The event-by-event principle
• Simulation based statistical techniques Markov chain Monte Carlo
Bootstrap
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Course goal Course goal
• Topics related to scientific computer experimentation
• Specialised techniques
Variance reduction methods Random number generation Random variable generation The event-by-event principle
• Simulation based statistical techniques Markov chain Monte Carlo
Bootstrap
• Validition and verification of models
Bo Friis Nielsen – 17/6-2001 C04245 9
Course goal Course goal
• Topics related to scientific computer experimentation
• Specialised techniques
Variance reduction methods Random number generation Random variable generation The event-by-event principle
• Simulation based statistical techniques Markov chain Monte Carlo
Bootstrap
• Validition and verification of models
• Model building
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Recommended reading Recommended reading
• Sheldon M. Ross: Simulation, second edition, Academic Press 1997,ISBN-0-12-598410-3
• Averill M. Law and W. David Kelton: Simulation Modeling and Analysis, McGraw-Hill 2000, ISBN 0-07-116537-1
• Jerry Banks, John S. Carson II, Barry L. Nelson, David M.
Nicol: Discrete-Event System Simulation, Prentice and Hall 1999, ISBN 0-13-088702-1
• Brian Ripley: Stochastic Simulation, John Wiley & Sons 1987, ISBN 0-471-818884-4.
• Reuven Y. Rubinstein and Benjamin Melamed: Modern Simulation and Modelling, John Wiley & Sons 1998, ISBN 0-471-17077-1
• Jack P. C. Kleijnen: Statistical Tools for Simulation
Practitioneers, Marcel Dekker 1987, ISBN 0-8247-7333-0
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Knowledge/science in simulation
Knowledge/science in simulation
Bo Friis Nielsen – 17/6-2001 C04245 11
Knowledge/science in simulation Knowledge/science in simulation
• Modelling skill
Bo Friis Nielsen – 17/6-2001 C04245 11
Knowledge/science in simulation Knowledge/science in simulation
• Modelling skill
• Statistical methods - it is necessary to understand statistical methodology
Bo Friis Nielsen – 17/6-2001 C04245 11
Knowledge/science in simulation Knowledge/science in simulation
• Modelling skill
• Statistical methods - it is necessary to understand statistical methodology
• OR - Stochastic Processes
Bo Friis Nielsen – 17/6-2001 C04245 11
Knowledge/science in simulation Knowledge/science in simulation
• Modelling skill
• Statistical methods - it is necessary to understand statistical methodology
• OR - Stochastic Processes
• Technical skills
Bo Friis Nielsen – 17/6-2001 C04245 11
Knowledge/science in simulation Knowledge/science in simulation
• Modelling skill
• Statistical methods - it is necessary to understand statistical methodology
• OR - Stochastic Processes
• Technical skills
Random number generations
Bo Friis Nielsen – 17/6-2001 C04245 11
Knowledge/science in simulation Knowledge/science in simulation
• Modelling skill
• Statistical methods - it is necessary to understand statistical methodology
• OR - Stochastic Processes
• Technical skills
Random number generations Sampling from distributions
Bo Friis Nielsen – 17/6-2001 C04245 11
Knowledge/science in simulation Knowledge/science in simulation
• Modelling skill
• Statistical methods - it is necessary to understand statistical methodology
• OR - Stochastic Processes
• Technical skills
Random number generations Sampling from distributions Variance reduction techniques
Bo Friis Nielsen – 17/6-2001 C04245 11
Knowledge/science in simulation Knowledge/science in simulation
• Modelling skill
• Statistical methods - it is necessary to understand statistical methodology
• OR - Stochastic Processes
• Technical skills
Random number generations Sampling from distributions Variance reduction techniques
Statistical techniques bootstrap/MCMC
Bo Friis Nielsen – 17/6-2001 C04245 11
Knowledge/science in simulation Knowledge/science in simulation
• Modelling skill
• Statistical methods - it is necessary to understand statistical methodology
• OR - Stochastic Processes
• Technical skills
Random number generations Sampling from distributions Variance reduction techniques
Statistical techniques bootstrap/MCMC
• General purpose/and specialised simulation software
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Discrete versus continuous
Discrete versus continuous
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Discrete versus continuous Discrete versus continuous
• Discrete event simulation
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Discrete versus continuous Discrete versus continuous
• Discrete event simulation
• as opposed to continuous simulation
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Discrete versus continuous Discrete versus continuous
• Discrete event simulation
• as opposed to continuous simulation
• mixed models
