IERG 3050 Week 8 Output Data Analysis and Variance ...ierg3050/Lectures/week8-lecture.pdf ·...
Transcript of IERG 3050 Week 8 Output Data Analysis and Variance ...ierg3050/Lectures/week8-lecture.pdf ·...
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IERG 3050 Week 8Output Data Analysis and Variance
Reduction Techniques
Bolei ZhouDepartment of Information Engineering
The Chinese University of Hong Kong
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Announcement
• Homework 3 is due tomorrow• Homework 4 will be out by the end of today. No need to hand in, but
very relevant to Quiz 2• Quiz 2 will be on Nov. 6• No lectures next week (Time for your course project)• End of Oct. 2019: a 4-page check-point report for course project
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Outline
• Output Data Analysis• Stochastic Processes• Ensemble Averages vs. Time Averages • Transient State and Steady State Behavior • Method of Replication• Transient Removal Methods• Terminating and Non-Terminating Simulations • Obtaining Specified Precision• Choosing Initial Conditions• Variance-Reduction Techniques: Common Random Numbers, Antithetic Variates, Control
Variates, Indirect Estimation, ConditioningReading: Chapters 9 and 11
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Output Data Analysis
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Output Data Analysis
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Output Data Analysis
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Review: Stochastic processes
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Review: Random Variables
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Review: Random Variables
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Review: Random Variables
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Review: Stochastic Processes
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Review: Stochastic Processes
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Some Simple Stochastic Processes
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Example 1: I.I.D. Process
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Example 2: “Fixed-Value” Process
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Example 3: Autoregressive Process
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Example 4: Hidden Markov Process
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Example 5: M/M/1/1 Queueing System
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Notations and Terms of Queueing Systems
Kendall notation: A/S/m/B/K/SD• A: interarrival time distribution• S: service time distribution• m: number of servers• B: system capacity: max number of users accommodated in the
system
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Interesting Quantities
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Interesting Quantities
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Interesting Quantities
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Ensemble Averages
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Example 1: I.I.D. Process
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Example 2: “Fixed-Value” Process
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Example 3: Autoregressive Process
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Estimating Ensemble Averages
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Estimating Time Averages
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Time Averages
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Example 1: I.I.D. Process
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Example 2: “Fixed-Value” Process
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Example 3: Autoregressive Process
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Time Averages
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Transient state and steady-state behavior
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Example 3: Autoregressive Process
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Example 3: Autoregressive Process
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Example 3: Autoregressive Process
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Example 3: Autoregressive Process
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Example 3: Autoregressive Process
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Transient vs. Steady State
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Method of Replication
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Method of Replication
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Method of Replication
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Method of Replication
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Transient Removal
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Some Transient Removal Methods
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Terminating and non-terminating simulations
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Terminating and Non-Terminating Simulations
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Terminating and Non-Terminating Simulations
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Obtaining a specified precision
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Obtaining a Specified Precision
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Choosing initial conditions
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Choosing Initial Conditions
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Variance reduction techniques
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Variance-Reduction Techniques
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Common Random Numbers
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Common Random Numbers
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Common Random Numbers
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Common Random Numbers
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Antithetic variates
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Antithetic Variates
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Antithetic Variates
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Antithetic Variates
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Control Variates
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Control Variates
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Control Variates
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Control Variates
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Indirect Estimation
![Page 69: IERG 3050 Week 8 Output Data Analysis and Variance ...ierg3050/Lectures/week8-lecture.pdf · •Homework 3 is due tomorrow •Homework 4 will be out by the end of today. No need to](https://reader033.fdocuments.in/reader033/viewer/2022060302/5f0897377e708231d422c388/html5/thumbnails/69.jpg)
Indirection Estimation
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Indirection Estimation
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Conditioning
![Page 72: IERG 3050 Week 8 Output Data Analysis and Variance ...ierg3050/Lectures/week8-lecture.pdf · •Homework 3 is due tomorrow •Homework 4 will be out by the end of today. No need to](https://reader033.fdocuments.in/reader033/viewer/2022060302/5f0897377e708231d422c388/html5/thumbnails/72.jpg)
Conditioning
![Page 73: IERG 3050 Week 8 Output Data Analysis and Variance ...ierg3050/Lectures/week8-lecture.pdf · •Homework 3 is due tomorrow •Homework 4 will be out by the end of today. No need to](https://reader033.fdocuments.in/reader033/viewer/2022060302/5f0897377e708231d422c388/html5/thumbnails/73.jpg)
Conditioning
![Page 74: IERG 3050 Week 8 Output Data Analysis and Variance ...ierg3050/Lectures/week8-lecture.pdf · •Homework 3 is due tomorrow •Homework 4 will be out by the end of today. No need to](https://reader033.fdocuments.in/reader033/viewer/2022060302/5f0897377e708231d422c388/html5/thumbnails/74.jpg)
Thank you!
• Homework 3 is due tomorrow• Homework 4 will be out by the end of today. No need to hand in, but
very relevant to Quiz 2• Quiz 2 will be on Nov. 6• No lectures next week (Time for your course project)• End of Oct. 2019: a 4-page check-point report for course project