Handout #2

Date:

Some definitions!� These definitions are taken from Discrete-Event System Simulation, by Jerry Banks and John S. Carson, II, or Modeling and Analysis:� An Introduction to System Performance Evaluation Methodology, by H. Kobayashi.

System:� A group of objects that are joined together in some regular interaction or independence toward accomplishment of some purpose.

Boundary:� A system has a boundary between the system and its environment.� Sometimes changes occurring outside the system environment can affect the system.

Components of a System:

Entity:� Object of interest in the system

Attribute:� Property of an entity

Activity: �Represents a time period of specified length

Example:

System:� Bank

Entities:� Customers

Attribute:� Balance in Customer's Checking Account

Activity:� Making deposits

A system can be modeled using state diagrams!

State of a system:� Collection of variables necessary to describe the system at any time, relative to the objectives of the study

Event: �An instantaneous occurrence that may change the state of the system

Endogenous:� Activities and events occurring within a system.

Exogenous:� Activities and events occurring within a system.

Discrete system:� A system where state variable(s) change only at a discrete system since the state variable changes only when a customer arrives or when the service provided a customer is completed.� (Ex.� Bank)

Continuous system:� A system where the state variable(s) change continuously over time.� (Ex. Dam)

Model: �A representation of a system for the purpose of studying the system.

Types of Models

Analytical:� Employ the deductive reasoning of mathematics to solve the model.� (Ex. Use differential equations to determine information.)� A solution is a functional relation between system parameters and a chosen performance criterion in terms of equations that are analytically solvable.� Queuing theory is important in analytical analysis.� An analytical model should be sought wherever possible, since it can evaluate the performance with minimal efforts and costs over a wide range of choices in the system parameters and configurations.

Simulation or Numerical:� Employ computational procedures to solve mathematical models.� (Ex.� Models are run rather than solved.)� When analytical models cannot be used due to intractable problems.� With simulation, a numerical technique for conducting an experiment of a system evolving in time.�

Empirical:� A statistical characterization of system performance based on data measured in a real system or simulator.

Hybrids are possible!

Simulation Models

Static:� Represents a system at a particular point in time.� Sometimes called a Monte Carlo simulation.

Dynamic:� Represents a system as they change over time.

Deterministic:� A simulation model that contains no random variables.� (Ex:� Dentist's office where all the appointments are scheduled.)

Stochastic:� A simulation model that has one or more variables as inputs.

Steps in a Simulation Study

Orientation Stage

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Model Building and Data Collection

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Running the Model

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Implementation

More of a Break-Down

Problem Formation

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Setting of Objectives and Overall Project Plan

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Model Building

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Data Collection

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Coding

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Verification

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Validation

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Experimental Design

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Production Runs and Analysis

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More Runs Needed?

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Document Program and Report Results

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Implementation