IE 571 System Simulation
1. Review of Simulation
(Chapter 1)
1
Middle East Technical University
Department of Industrial Engineering
IE 571 - Nur Evin zdemirel
Ways to study a system
System
Experiment with
the actual system
Experiment with a
model of the
IE 571 System Simulation
Homework Assignment 3
Due Date: Tuesday, November 26th
1. Solve Problem 8.7 in Law (2007) with the additional part given below.
e) Show that if X ~ RT (0,1) then X = b (b a ) X ~ LT ( a, b) .
2. Consider the triangular(0, 1, m) di
IE 571 System Simulation
Homework Assignment 1
Due Date: Tuesday, November 5th
An electronic device contains two similar components (comp1 and comp2) that are connected
in parallel and operational simultaneously. That is, when one of the components fails,
IE 571 System Simulation
Homework Assignment 2
Due Date: Tuesday, November 19th
Empirically test the following random number generators for uniformity and independence.
1. LEcuyers (1999) combined multiple recursive generator mrand described in Appendix
7
IE 571 System Simulation
Homework Assignment 5
Due Date: Tuesday, December 24th
This assignment is related with the two examples given in Laws (2007) textbook, pages 496500.
Question 1: Consider M/M/1 queueing system with an arrival rate of = 1 per unit t
IE 571 System Simulation
Homework Assignment 6
Due Date: Tuesday, January 7th
Consider the following two processes.
Process 1: The output process of a simulation is autoregressive of order 1 (AR(1) as
follows: X i = + ( X i 1 ) + i where i are iid normal
IE 571 System Simulation
9. Experimental Design and Optimization
(Chapter 12)
Part 1
1
IE 571 - Nur Evin zdemirel
Middle East Technical University
Department of Industrial Engineering
Simulation optimization
Traditional objectives of simulation
Prediction
Banks, Carson, Nelson & Nicol
Discrete-Event System Simulation
Purpose & Overview
The goal of the validation process is:
To produce a model that represents true behavior closely enough for
decision-making purposes
To increase the models credibility to
IE 571 System Simulation
5. Generating Random Variates
(Chapter 8)
Part 2
1
IE 571 - Nur Evin zdemirel
Middle East Technical University
Department of Industrial Engineering
Acceptance-rejection
Inverse transform, composition and convolution are direct,
as
IE 571 System Simulation
5. Generating Random Variates
(Chapter 8)
Part 1
1
IE 571 - Nur Evin zdemirel
Middle East Technical University
Department of Industrial Engineering
Random variate (RV) generation
A random variate is a realization of (or an observa
IE 571 System Simulation
2. Review of Probability and Statistics
(Chapter 4)
1
IE 571 - Nur Evin zdemirel
Middle East Technical University
Department of Industrial Engineering
Basics you should know
Random variable
Probability mass or density function (pm
1
ARENA's Input Analyzer
ARENAs Input Analyzer offers the following capabilities for distribution fitting.
Tools
Input Analyzer opens the Input Analyzer window.
File
New (or Open) opens a new (or existing) distribution fitting environment.
File
Data File
IE 571 System Simulation
4. Random Number Generators
(Chapter 7)
1
IE 571 - Nur Evin zdemirel
Middle East Technical University
Department of Industrial Engineering
Random numbers
U(0,1) random variates (RVs) are called random numbers
(RNs)
In general, in
IE 571 System Simulation
3. Selecting Input Distributions
(Chapter 6)
1
IE 571 - Nur Evin zdemirel
Middle East Technical University
Department of Industrial Engineering
Input distributions
We need to specify distributions to generate realizations of
input
IE 571 System Simulation
7. Comparing Alternative Systems
(Chapter 10)
1
IE 571 - Nur Evin zdemirel
Middle East Technical University
Department of Industrial Engineering
Incorrect comparison
Example: M/M/1 versus M/M/2 with = 0.9
Expected average delay in
IE 571 System Simulation
8. Variance Reduction Techniques
(Chapter 11)
1
IE 571 - Nur Evin zdemirel
Middle East Technical University
Department of Industrial Engineering
Variance reduction
Idea: Reduce variance of an output random variable without
changin
IE 571 System Simulation
Law (2008) How to build valid and
credible simulation models
1
IE 571 - Nur Evin zdemirel
Middle East Technical University
Department of Industrial Engineering
Model validation
Validation is the process of determining whether a
si
IE 571 System Simulation
6. Output Analysis for a Single System
(Chapter 9)
1
IE 571 - Nur Evin zdemirel
Middle East Technical University
Department of Industrial Engineering
Simulation output
Randomness in simulation input (input probability
distribution
Banks, Carson, Nelson & Nicol
Discrete-Event System Simulation
Output Analysis For A Single Model
Output Analysis: Examination of data generated by
simulation
To predict performance, or
To compare performance of 2 or more designs (Chp 12).
2
Output Ana