Elements of Simulation Copyright by YuChi Ho 1
Elements of Simulation Copyright by Yu-Chi Ho 1
Simulation of DEDS One event delay x Enabled Event set G(x) state Lifetime Min of generator Cn(a) lifetimes a* event Lifetime of event a a State transition Described by the technique in LN #3. Clock system Event type (triggering) min lifetime event Minimal lifetime later Current state Next state Event happen time a 1 1: 00 2: 50 3: 10 … a 2 1: 20 1: 50 3: 00 … a 3 1: 05 2: 20 4: 00 … … … an 1: 35 3: 30 3: 55 … Copyright by Yu-Chi Ho 2
Menu • • Random number generation Random variable generation Inverse transform technique The composition technique The acceptance-rejection technique Estimate of mean and variance Order statistics Simulation language and GSMP model Copyright by Yu-Chi Ho 3
Random Number Generation • Linear Congruential Technique Copyright by Yu-Chi Ho 4
Random Variable Generation • • The Inverse Transform Technique The Composition Technique The Convolution Technique The Acceptance-Rejection Technique Copyright by Yu-Chi Ho 5
The Inverse Transform Technique Figure 10. 3: Illustrating the inverse transform technique. From CLB p 617 Copyright by Yu-Chi Ho 6
The Composition Technique The Convolution Technique Copyright by Yu-Chi Ho 7
The Acceptance-Rejection Technique If cu 1 less than this, accept. Copyright by Yu-Chi Ho 8
Estimates of mean and variances • Point estimation – Mean – Variance • Interval estimation – Mean – Variance Copyright by Yu-Chi Ho 9
Point Estimation Mean of x: Variance of mean: Sample variance: Copyright by Yu-Chi Ho 10
The n increases 1/2 1/(T) Limit n increases Figure 10. 9: Typical behavior of the pdf of the sample mean estimator as n increases. From CLB p 631. Copyright by Yu-Chi Ho 11
Interval Estimation Copyright by Yu-Chi Ho 12
Order Statistics 1. Take n i. i. d samples of an arbitrary random variable. 2. Order the sample by magnitude into 3. These order statistic on the average divide the population into n+1 parts with equal # of random variables. • Free in any statistical experiment including simulation Copyright by Yu-Chi Ho 13
Simulation Language and GSMP Model Event type 1 samples MIN Event type samples AUTOMATON CLOCK MECHANISM The TIMING and STRUCTURAL parts of the GSMP model Copyright by Yu-Chi Ho 14
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