introdução aos modelos temporizados · objective to study the fundaments of stochastic...
TRANSCRIPT
![Page 1: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/1.jpg)
Stochastic SimulationPerformance and Dependability
Paulo Maciel
Centro de Informática - UFPE
![Page 2: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/2.jpg)
Objective
To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability problems.
![Page 3: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/3.jpg)
Program
Introduction
Problems and Mistakes in Simulation
System and Model
Classification of Models
Types of Simulation
Discrete Event Simulation: an Overview
Random Number Generation
Random Variates Generation
Output Analysis – Steady State Simulation
Output Analysis – Transient Simulation
Verification and Validation
![Page 4: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/4.jpg)
Methodology
Expositive classes
Practical classes
![Page 5: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/5.jpg)
Evaluation
List resolutions
Write a draft paper
![Page 6: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/6.jpg)
Basic References
Art of Computer Systems Performance Analysis Techniques For Experimental Design Measurements Simulation And Modelingm, Raj Jain, Wiley Computer Publishing, John Wiley & Sons, Inc,1991.
Simulation modeling handbook : a practical approach, Christopher A. Chung. 2003.
Stochastic Simulation: Algorithms and Analysis, Søren Asmussen, Peter W. Glynn. Springer, 2007.
Introduction to Discrete Event Systems, Christos G. Cassandras, Stéphane Lafortune. Springer. 2008
![Page 7: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/7.jpg)
Introduction
Simulation
Analysis
Evaluation
![Page 8: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/8.jpg)
Introduction
When is simulation
an interesting option?
![Page 9: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/9.jpg)
Introduction
Common mistakes in simulation projects:
Not considering numerical or analytical methods as possible alternative
Inappropriate level of detail
Not taking into account the modeling and coding costs
Unverified and invalid models
Improperly handled initial conditions
Results without confidence level and error margin
Poor random-number generators
Poor interpretation of results
![Page 10: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/10.jpg)
System and Model
The Concept of System
An aggregation or assemblage of things so combined by nature or man as to form an integral or complex whole (Encyclopedia Americana).
An interacting or interdependent group of items forming a unified whole (Webster’s Dictionary)
A combination of components that act together to perform a function (IEEE Standard Dictionary).
There are two features in these definitions: 1. a system consists of interacting “components”, and
2. a system is associated with a “function”.
![Page 11: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/11.jpg)
System and Model
Model
Abstraction level
Perspective
![Page 12: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/12.jpg)
System and Model
Model
![Page 13: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/13.jpg)
System and Model
State and state variable
![Page 14: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/14.jpg)
System and Model
Event
An event may be identified with a specific action taken by a person or system or
It may be viewed as a spontaneous occurrence dictated by nature or
it may be the result of several conditions which are suddenly all met.
![Page 15: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/15.jpg)
System classification
![Page 16: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/16.jpg)
Types of Simulation
Static vs Dynamic Simulation
Static simulation is adopted for representing a system in which time does not play a role or to describe a system at a particular time.
Dynamic simulation is used for depicting a system that evolves over time.
![Page 17: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/17.jpg)
Types of Simulation
Deterministic vs Stochastic Simulation
Deterministic simulation considers models that do not contain any random variable, that is, the output is determined once the input quantities and the model relations are defined.
Stochastic simulation adopts models that have at least one random variable.
![Page 18: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/18.jpg)
Types of Simulation
Continuous vs Discrete Model Simulation
Continuous model simulation relies on continuous models for representing the system whereas discrete model simulation is supported by discrete models.
![Page 19: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/19.jpg)
Types of Simulation
Trace driven (Deterministic simulation)
Monte Carlo (Stochastic static model simulation)
Discrete event (Stochastic dynamic discrete model
simulation)
![Page 20: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/20.jpg)
Trace-Driven Simulation
Trace-driven simulation uses traces (time-ordered record of events on a real system) as its input applied to the simulation model which depicts the system behavior. This sort of simulation strategy has been applied for evaluating resource management algorithms, such as paging algorithms, cache analysis, CPU scheduling algorithms, and algorithms for dynamic allocation of storage.
![Page 21: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/21.jpg)
Monte Carlo Simulation
Monte Carlo simulations are used to model probabilistic phenomena that do not change characteristics over time.
Monte Carlo simulations are also used for evaluating non-probabilistic expressions using probabilistic methods.
![Page 22: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/22.jpg)
Monte Carlo Simulation
![Page 23: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/23.jpg)
Monte Carlo Simulation
Integration
Excel
Mathematica
![Page 24: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/24.jpg)
Monte Carlo Simulation
Estimating - Model
Minitab Mathematica
Model
Input parameters
Excel
0.2 0.4 0.6 0.8 1.0
0.2
0.4
0.6
0.8
1.0
Mathematica
V2
![Page 25: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/25.jpg)
Monte Carlo Simulation
Piston pump
![Page 26: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/26.jpg)
Monte Carlo Simulation
Cont.
![Page 27: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/27.jpg)
Model
Monte Carlo Simulation
![Page 28: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/28.jpg)
Monte Carlo Simulation
Input data parameters
![Page 29: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/29.jpg)
Monte Carlo Simulation
Create random input data
Apply the input data to the model
Analyze the output
Minitab Excel Mathematica
![Page 30: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/30.jpg)
Monte Carlo Simulation
Analyze the output
![Page 31: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/31.jpg)
Monte Carlo Simulation
Analyze the output
The average flow rate is pretty close to the specified value, but
the standard deviation far exceed 0.2 ml/min.
![Page 32: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/32.jpg)
Discrete Event Simulation: an Overview
![Page 33: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/33.jpg)
Discrete Event Simulation: an Overview
![Page 34: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/34.jpg)
Discrete Event Simulation: an Overview
![Page 35: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/35.jpg)
Discrete Event Simulation: an Overview
![Page 36: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/36.jpg)
Discrete Event Simulation: an Overview
![Page 37: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/37.jpg)
Discrete Event Simulation: an Overview
![Page 38: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/38.jpg)
Discrete Event Simulation: an Overview
![Page 39: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/39.jpg)
Discrete Event Simulation: an Overview
![Page 40: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/40.jpg)
Discrete Event Simulation: an Overview
![Page 41: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/41.jpg)
Discrete Event Simulation: an example
Excel
N/N/1
![Page 42: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/42.jpg)
Discrete Event Simulation: an example
C:\Users\Paulo Maciel\Dropbox\Models\Mercury\Mercury 4.4.3\Mercury 4.4.3.2\Examples
![Page 43: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/43.jpg)
Discrete Event Simulation: a SPN example
C:\Users\Paulo Maciel\Dropbox\Models\Mercury\Mercury 4.4.3\Mercury 4.4.3.2\Examples\StudyOnSimulation.xml
![Page 44: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/44.jpg)
Discrete Event Simulation: a SPN example
C:\Users\Paulo Maciel\Dropbox\Models\Mercury\Mercury 4.4.3\Mercury 4.4.3.2\Examples\StudyOnSimulation.xml
![Page 45: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/45.jpg)
Discrete Event Simulation: a SPN example
C:\Users\Paulo Maciel\Dropbox\Models\Mercury\Mercury 4.4.3\Mercury 4.4.3.2\Examples\StudyOnSimulation.xml
![Page 46: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/46.jpg)
Random Number Generator
![Page 47: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/47.jpg)
Random Number Generator
Generation of Uniform Random Numbers
Excel
![Page 48: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/48.jpg)
Random Number Generator
Generation of Uniform Random Numbers
Excel
![Page 49: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/49.jpg)
Random Number Generator
Generation of Uniform Random Numbers
Excel
![Page 50: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/50.jpg)
Random Number Generator
Generation of Uniform Random Numbers
Excel
![Page 51: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/51.jpg)
Random Number Generator
Generation of Uniform Random Numbers
Excel
![Page 52: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/52.jpg)
Random Number Generator
Generation of Uniform Random Numbers
Excel
![Page 53: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/53.jpg)
Random Variate Generator
A random variable is a function.
A random variate is an outcome provided by a random variable.
![Page 54: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/54.jpg)
Random Variate Generator
Basic methods
– Inversion transform
– Convolution
– Composition
– Characterization
– Acceptance-Rejection
![Page 55: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/55.jpg)
Random Variate GeneratorInversion transform
![Page 56: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/56.jpg)
Random Variate GeneratorInversion transform
Generation of Exponential Variate
The sequence of random numbers will not be identical,
but will be statistically equivalent.
Excel
Exponential
Mathematica
Exponential
![Page 57: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/57.jpg)
Random Variate GeneratorInversion transform
Generation of Exponential Variate
Excel
Exponential
Mathematica
Exponential
![Page 58: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/58.jpg)
Random Variate GeneratorInversion transform
Generation of Exponential Variate
Excel
Exponential
Mathematica
Exponential
![Page 59: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/59.jpg)
Random Variate GeneratorInversion transform
Excel
Discrete
Mathematica
Discrete
![Page 60: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/60.jpg)
Random Variate GeneratorInversion transform
Excel
Discrete
Mathematica
Discrete
![Page 61: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/61.jpg)
Random Variate GeneratorInversion transform
![Page 62: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/62.jpg)
Random Variate GeneratorConvolution
Excel
Erlang
Mathematica
Erlang
![Page 63: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/63.jpg)
Random Variate GeneratorConvolution
Excel Erlang
Mathematica
Erlang
![Page 64: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/64.jpg)
Random Variate GeneratorComposition
Excel Hyper-Exponential
MathematicaHyper-Exponential
![Page 65: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/65.jpg)
Random Variate GeneratorComposition
Excel Hyper-Exponential
MathematicaHyper-Exponential
![Page 66: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/66.jpg)
Random Variate GeneratorComposition
Excel Hyper-Exponential
MathematicaHyper-Exponential
![Page 67: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/67.jpg)
Random Variate GeneratorCharacterization
Excel Normal
MathematicaNormal
![Page 68: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/68.jpg)
Random Variate GeneratorCharacterization
Excel Normal
MathematicaNormal
![Page 69: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/69.jpg)
Random Variate GeneratorAcceptance-Rejection
Excel
![Page 70: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/70.jpg)
Random Variate GeneratorAcceptance-Rejection
Excel
![Page 71: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/71.jpg)
Random Variate GeneratorAcceptance-Rejection
Excel
![Page 72: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/72.jpg)
Random Variate GeneratorAcceptance-Rejection
Excel
![Page 73: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/73.jpg)
Random Variate GeneratorDeciding which method to adopt
Excel
![Page 74: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/74.jpg)
Output AnalysisExcel
![Page 75: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/75.jpg)
Output AnalysisExcel
![Page 76: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/76.jpg)
Output AnalysisExcel
![Page 77: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/77.jpg)
Output Analysis Excel
![Page 78: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/78.jpg)
Output Analysis Excel
![Page 79: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/79.jpg)
Output Analysis Excel
![Page 80: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/80.jpg)
Output Analysis
![Page 81: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/81.jpg)
Output Analysis
![Page 82: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/82.jpg)
Output Analysis
![Page 83: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/83.jpg)
Output AnalysisExcel
![Page 84: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/84.jpg)
Output AnalysisExcel
![Page 85: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/85.jpg)
Output AnalysisExcel
![Page 86: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/86.jpg)
Output AnalysisExcel
![Page 87: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/87.jpg)
Output AnalysisExcel
![Page 88: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/88.jpg)
Output Analysis
![Page 89: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/89.jpg)
Output Analysis
![Page 90: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/90.jpg)
Output Analysis
![Page 91: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/91.jpg)
Output Analysis
![Page 92: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/92.jpg)
Output Analysis
![Page 93: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/93.jpg)
Output Analysis Excel
![Page 94: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/94.jpg)
Output Analysis
<
Excel
![Page 95: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/95.jpg)
Output Analysis Excel
![Page 96: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/96.jpg)
Output AnalysisExcel
![Page 97: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/97.jpg)
Output AnalysisExcel
![Page 98: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/98.jpg)
Output Analysis Excel
Correlation
![Page 99: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/99.jpg)
Output Analysis Excel
Correlation
![Page 100: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/100.jpg)
Output Analysis Excel
Correlation
![Page 101: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/101.jpg)
Output Analysis Excel
Correlation
![Page 102: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/102.jpg)
Output Analysis Excel
Mathematica
Correlation
Minitab
Correlation
Excel
Correlation
![Page 103: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability](https://reader033.vdocuments.us/reader033/viewer/2022042311/5ed9a3688765f51e2e278da7/html5/thumbnails/103.jpg)
Output Analysis Excel
Mathematica
Correlation
Minitab
Correlation
Excel
Correlation