Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic...

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Stochastic Simulation Performance and Dependability Paulo Maciel Centro de Informática - UFPE

Transcript of Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic...

Page 1: Introdução aos Modelos Temporizados · Objective To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability

Stochastic SimulationPerformance and Dependability

Paulo Maciel

Centro de Informática - UFPE

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Objective

To study the fundaments of stochastic simulation, its methods, and applying simulation for solving performance and dependability problems.

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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

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Methodology

Expositive classes

Practical classes

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Evaluation

List resolutions

Write a draft paper

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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

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Introduction

Simulation

Analysis

Evaluation

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Introduction

When is simulation

an interesting option?

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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

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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”.

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System and Model

Model

Abstraction level

Perspective

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System and Model

Model

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System and Model

State and state variable

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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.

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System classification

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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.

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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.

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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.

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Types of Simulation

Trace driven (Deterministic simulation)

Monte Carlo (Stochastic static model simulation)

Discrete event (Stochastic dynamic discrete model

simulation)

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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.

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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.

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Monte Carlo Simulation

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Monte Carlo Simulation

Integration

Excel

Mathematica

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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

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Monte Carlo Simulation

Piston pump

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Monte Carlo Simulation

Cont.

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Model

Monte Carlo Simulation

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Monte Carlo Simulation

Input data parameters

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Monte Carlo Simulation

Create random input data

Apply the input data to the model

Analyze the output

Minitab Excel Mathematica

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Monte Carlo Simulation

Analyze the output

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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.

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Discrete Event Simulation: an Overview

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Discrete Event Simulation: an Overview

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Discrete Event Simulation: an Overview

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Discrete Event Simulation: an Overview

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Discrete Event Simulation: an Overview

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Discrete Event Simulation: an Overview

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Discrete Event Simulation: an Overview

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Discrete Event Simulation: an Overview

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Discrete Event Simulation: an Overview

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Discrete Event Simulation: an example

Excel

N/N/1

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Discrete Event Simulation: an example

C:\Users\Paulo Maciel\Dropbox\Models\Mercury\Mercury 4.4.3\Mercury 4.4.3.2\Examples

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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

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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

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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

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Random Number Generator

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Random Number Generator

Generation of Uniform Random Numbers

Excel

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Random Number Generator

Generation of Uniform Random Numbers

Excel

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Random Number Generator

Generation of Uniform Random Numbers

Excel

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Random Number Generator

Generation of Uniform Random Numbers

Excel

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Random Number Generator

Generation of Uniform Random Numbers

Excel

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Random Number Generator

Generation of Uniform Random Numbers

Excel

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Random Variate Generator

A random variable is a function.

A random variate is an outcome provided by a random variable.

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Random Variate Generator

Basic methods

– Inversion transform

– Convolution

– Composition

– Characterization

– Acceptance-Rejection

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Random Variate GeneratorInversion transform

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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

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Random Variate GeneratorInversion transform

Generation of Exponential Variate

Excel

Exponential

Mathematica

Exponential

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Random Variate GeneratorInversion transform

Generation of Exponential Variate

Excel

Exponential

Mathematica

Exponential

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Random Variate GeneratorInversion transform

Excel

Discrete

Mathematica

Discrete

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Random Variate GeneratorInversion transform

Excel

Discrete

Mathematica

Discrete

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Random Variate GeneratorInversion transform

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Random Variate GeneratorConvolution

Excel

Erlang

Mathematica

Erlang

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Random Variate GeneratorConvolution

Excel Erlang

Mathematica

Erlang

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Random Variate GeneratorComposition

Excel Hyper-Exponential

MathematicaHyper-Exponential

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Random Variate GeneratorComposition

Excel Hyper-Exponential

MathematicaHyper-Exponential

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Random Variate GeneratorComposition

Excel Hyper-Exponential

MathematicaHyper-Exponential

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Random Variate GeneratorCharacterization

Excel Normal

MathematicaNormal

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Random Variate GeneratorCharacterization

Excel Normal

MathematicaNormal

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Random Variate GeneratorAcceptance-Rejection

Excel

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Random Variate GeneratorAcceptance-Rejection

Excel

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Random Variate GeneratorAcceptance-Rejection

Excel

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Random Variate GeneratorAcceptance-Rejection

Excel

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Random Variate GeneratorDeciding which method to adopt

Excel

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Output AnalysisExcel

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Output AnalysisExcel

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Output AnalysisExcel

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Output Analysis Excel

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Output Analysis Excel

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Output Analysis Excel

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Output Analysis

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Output Analysis

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Output Analysis

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Output AnalysisExcel

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Output AnalysisExcel

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Output AnalysisExcel

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Output AnalysisExcel

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Output AnalysisExcel

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Output Analysis

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Output Analysis

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Output Analysis

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Output Analysis

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Output Analysis

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Output Analysis Excel

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Output Analysis

<

Excel

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Output Analysis Excel

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Output AnalysisExcel

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Output AnalysisExcel

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Output Analysis Excel

Correlation

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Output Analysis Excel

Correlation

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Output Analysis Excel

Correlation

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Output Analysis Excel

Correlation

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Output Analysis Excel

Mathematica

Correlation

Minitab

Correlation

Excel

Correlation

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Output Analysis Excel

Mathematica

Correlation

Minitab

Correlation

Excel

Correlation


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