Extend sim 01

© Copyright 2010 Jeffrey Strickland, Ph.D.

Discrete Event Simulation with ExtendSim

Lesson 1

Missile Defense Agency

Directorate of Modeling and Simulation

Verification, Validation, and Accreditation

© Copyright 2007 Dr. Jeffrey Strickland

What we’ll do

Lesson 1: Introduce Simulation modeling and

Discrete Event Simulation

Lesson 2: Introduce ExtendSim modeling and explore

a single-server queue model (MM1)

Analytic solution

Simulation solution

Inherent problems and DOE

Lesson 3: Construct a bank lobby model (several

versions: basic, a variety of resourcing methods,

hierarchical, and with animation)

Lesson 4: Build a simple BMDS End-to-End model


Lesson 1 Learning Objectives

Learn about the specification of a Discrete Event Simulation

(DES)

Distinguish a DES from other simulations

Learn about basic queuing processes and problems associated

with simulating them

Learn how to use appropriate statistical method to validate a

simple queuing model

Learn how to model a simple queuing problem in Extend

Learn how to design a simulation experiment and analyze the

results

Learn how to build basic and complex hierarchical models

Learn how to construct basic model animation

Learn how to build customized Extend blocks


Extend Models

It would be nice to model people returning to the moon, from

and end-to-end perspective, but it would take us a few years to

do so.

Reality: we have three days to learn about DES and Extend

Our models will be simple enough to build in three days, yet

complex enough to demonstrate many of the modeling

constructs and methodologies of the former

Resource pools, queues, and resource controls

Multiple random variate inputs and input tables for arrival

processes and service processes

Mixed modeling blocks (DES, Generic, Utility, etc.)

Hierarchical modeling

User interfaces and Notebook utility

Customized block development


Bank Model

Hierarchical modeling

Statistics collection

Buttons

Notebooks

Ghost Connectors

Multiple random inputs


Circuit Card Assembly

Multiple queues

Multiple services

Parallel servises

Serial services

Conveyer belts

Batching


Transportation

Labor pools

Task completion delays

Transferring goods

Transporting goods


Different Kinds of Simulation

Monte Carlo SimulationEstimate stochastic, static model quantities that are difficult to

compute by exact computations. A scheme employing random

numbers which is used for solving certain stochastic problems

where the passage of time plays no substantive role.

1

Dynamic SimulationDynamic system simulations observe the behavior of the

system models over time. The time advance mechanism used

here include continuous, discrete time, and discrete event.

2

Differential Equation System Specification (DESS)2a

Discrete Time System Specification (DTSS)2b

Discrete Event System Specification (DEVS)2b


Discrete-Event Simulation

Estimate stochastic, dynamic, and discrete model outputs. A scheme for modeling a system as it evolves over time by a representation in which state variables change instantaneously at separate points in time.

In simple terms, DEVS describes how a system with discrete flow units or jobs evolves over time.

Technically, this means that a computer tracks how and when state variables, such as queue lengths and resource availability, change over time.

State variables change as the result of an event (or discrete event) occurring in the system.

A characteristic is that discrete-event models focus only on the time instances when these discrete events occur.

This feature allows for significant time compression because it makes possible to skip through all time segments between events when the state of the system remains unchanged.


Formalized by Bernard Zeigler, University of Arizona, 1976 & 1990, 2000 [see references]

Provides a means of specifying a mathematical model of a system

Fundamental components

States

Inputs

Outputs

Transform functions

Time base

Discrete Event Simulation


State Set

(attributes or variable)

Position Fuel Size

Weapons Health Strength

Percept Team Plans

S

Location Appear

YOutput

Events

Output

Event

Generators

Time Advance

ta

M Model

:03 :01

dintInternal

Transition

Function

Move Explode

XExternal

Imput

Events

:03 :01

Physical models

dextExternal

Transition

Function

DEVS formalism

Components of Discrete Event

Simulation


Basic System Specification

Formalisms

Discrete Event System Specification (DEVS)

DEVS = (X, Y, S, δext, δint, λ, ts)

X is the set of inputs

Y is the set of outputs

S is the set of sequential states

δext: Q X S is the set of external state transition function

δint: S S is the set of internal state transition function

λ: S Y is the output function that maps

ts: S o+ is the time advance function

Q = {(s,e)|sS, 0 < e < ta(s)} is the set of total states

Discrete Time System Specification (DTSS)

Differential Equation System Specification (DESS)


Basic Definitions

System State: a collection of variables containing all

information necessary to operate the model and record relevant

change in it over time.

Discrete-event dynamic system: system where the system

state change only at discrete points in time, which mark the

occurrence of an event.

Event: any occurrence that causes an instantaneous change in

the system state.

Arrival

Begin service

End service


Ordering Components

Event Scheduling

Events are generated and scheduled for the future

Event Queue Processing

Activity Scanning

Independent modules waiting to be executing

Sequential Model Execution

Process Interaction

Control each object through actions until delayed

Object List Processing


Event Scheduling

Need a mechanism to increment time by a variable amount between events.

Must be able to sequence events according to the time of occurrence and apply the associated transition function or event routine to make changes to the system state.

Accomplished by creating an event notice for each occurrence when its future time is determined.

Requires at least two items of information:

The actual time the event will occur

The type of event that is scheduled to occur

Event notices are stored in a list called the event list—ordered by time of occurrence.

The process of creating an event notice, recording the necessary information about the event, and placing it in the event list is called scheduling the event.


The System Clock

The system clock is a special system variable that holds the current system time.

The simulation progresses through time in the following way:

The first event notice on the event list is selected.

The system clock is set to the event time on this event notice.

Then the event routine for this type of event is executed to produce the appropriate changes in the system state for this type of event.

Finally, the event notice is discarded.

This process repeats until the event list is empty or some other signal is given to stop the simulation.

The routine that implements this process is called the timing routine—the heart of discrete-event simulation.


Model Development

The essence of modeling discrete-event simulation is to

determine:

1. what variables or components are needed to

adequately represent the systems state,

2. what events are needed to represent the system

changes, and

3. what state changes occur within each event,

including the details of which events are

schedules and when are they scheduled.

This is usually and iterative process.

There is no one unique model that represents a system.


Monte Carlo Theory

Random numbers are used to drive statistical models of processes and to make decisions.

The core of these algorithms is the uniformly distributed number between zero and one.

A series of independent and identically distributed numbers in the range from 0 to 1

Written as IID U(0,1)

Deterministic mathematical algorithms generate a series of numbers that appear random

X(n) = (ax(n-1) + c)mod(m)

U(0,1) = x(n)/MAX(m)

Random methods tend to generate very skewed sequences of numbers.


Random Variates

Uniform random numbers drive the selection values from other distributions (random variates)

Inverse Transform Methods assign the U(0,1) number as the Y-axis and traces it back to the X value through the desired cumulative distribution function.

Acceptance-Rejection Methods use an intermediate function to simplify the selection of numbers and maintain random selection.

Composition Methods decompose the distribution into a summed series of simpler distributions.


Characteristic Statistical Distributions

Statistical

Distribution

Potential Application

Uniform Source of random numbers between 0 and 1

Probability of Kill or Detection

Exponential Interarrival times of customers at a constant rate

Gamma Time to serve a customer

Weibull Time to failure for a piece of equipment

Normal Errors on the impact point of a bomb

Beta Proportion of defective items in a shipment

Bernoulli Success or failure of a specific experiment

Poisson Number of items in a batch of random size

Lognormal Task times with right-skewed distributions

Empirical Curves custom fitted to collected data


Output Analysis to Verify the Model

Finding the true distribution among events being generated of

time

Finite-Horizon Simulations start idle and execute to defined

terminating event

Eliminates the effects associated with starting the system

Steady-State Simulations run for long period of time until the

parameters achieve their steady-state

Eliminates bias in the starting values


Languages for Simulation

1950’s began seeking languages specifically designed for simulation problems

General Simulation Program (GSP) 1960The First Simulation-specific Programming Language

By K.D. Tocher and D.G. Owen, General Electric

Proceedings of the Second International Conference on Operations Research


Evolved Definition of Simulation

Language

Six key characteristics:

Generate Random Numbers

Transformation for Statistical Distributions

List Processing

Statistical Analysis

Report Generation

Timing Execution


Typical Simulation Program

Finished?

Start

Stop

0. Invoke Initialization

1. Invoke Timing

2. Invoke Event Handler

Main

0. Update state variables

1. Increment counters

2. Generate future events

Event Routines

1. Compute interest data

2. Write reports

Reports

1. Select next event

2. Advance sim clock

Timing

1. Statistical distributions

2. Mathematical operations

Mathematics

1. Set clock

2. Set state variables

3. Load event list

Initialization

NO

YES

Legend

Programmer’s

responsibility

Language’s

Responsibility


Activity

Scan

GSP

SIMPAC

CSL

ESP

ECSL

OPS-1,2

OPS-3

OPS-4

1960

1965

1970

1980

1990

GPSS V6000

Process

Interaction

GPSS

GPSS II

GPSS III

GPSS/360

GPSS IV

GPSS/H

GPSS 85GPSS PC

GPSS PL/I

SIMULA I

SIMULA 67

NGPSS

CONSUM

Event

Interaction

GASP

GASP II

GERTS

GASP IV

GASP PL/I

SLAM

SIMANSLAM II

GEMS

SPS-1

SIMSCRIPT

QUICKSCRIPT

SIMSCRIPT II

SIMSCRIPT II+

SIMSCRIPT II.5

SIMFACTORY II.5

MOSIM

NETWORK II.5

COMNET II


Sim Language Comparisons

GPSS/H

SIMULATE

GENERATE RVEXPO(1,1.0)

QUEUE SERVER

SEIZE SERVER

LVEQ DEPART SERVERQ

TEST L N$LVEQ, 1000, STOP

ADVANCE RVEXPO(2,0.5)

STOP RELEASE SERVER

TERMINATE 1

START 1000

END

SLAM II

GEN, 1,,,,,,72;

LIM,1,1,100;

NETWORK;

RESOURCE/SERVER(1),1

CREATE,EXPON(1.0,1),1,1;

AWAIT(1),SERVER;

COLCT,INT(1),DELAY IN QUEUE,,2;

ACTIVITY,EXPON(0.5,2),,DONE;

ACTIVITY,,,CNTTR;

DONE FREE,SERVER

TERM;

CNTR TERM,1000;

END;

;

INIT;

FIN;

SIMAN

BEGIN

CREATE,,EX(1,1):EX(1,1);

MARK(1);

QUEUE, 1;

SEIZE :SERVER;

TALLY :1, INT(1);

COUNT :1,1;

DELAY :EX(2,2);

RELEASE :SERVER;

DISPOSE;

END;


SIMSCRIPT II.5

DO

WAIT EXPONENTIAL.F(MEAN.INTERARRIVAL.TIME,1) MINUTES

ACTIVATE A CUSTOMER NOW

LOOP

…

LET TIME.OF.ARRIVALS=TIME.V

REQUEST 1 SERVER(1)

LET DELAY.IN.QUEUE=TIME.V-TIME.OF.ARRIVAL

IF NUM.DELAYS=TOT.DELAYS

ACTIVATE A REPORT NOW

ALWAYS

WORK EXPONENTIAL.F(MEAN.SERVICE.TIME,2) MINUTES

RELINQUISH 1 SERVER(1)


Visual Interactive Simulation (1)

Arena (SIMAN)SimProcess (SimScript II.5)


Visual Interactive Simulation (2)

ExtendOPNET


Alan Pritsker’s Seven Principles

1. Conceptualizing a model requires system knowledge, engineering judgment, and model-building tools.

2. The secret to being a good modeler is the ability to remodel

3. The modeling process is evolutionary because the act of modeling reveals important information piecemeal.

4. The problem or problem statement is the primary controlling element in model-base problem solving.

5. In modeling combined systems, the continuous aspects of the problem should be considered first. The discrete aspects of the problem should then be developed.

6. A model should be evaluated according to its usefulness. From an absolute perspective, a model is neither good or bad, nor is it neutral.

7. The purpose of simulation modeling is knowledge and understanding, not models.


References

Banks, J., Carson, J.S. II, Nelson, B., & Nicol, D.M. (2001). Discrete-Event System Simulation. Prentice Hall.

Cloud, D.J. & Rainey, L.B. (Eds.). (1998). Applied Modeling and Simulation: An integrated Approach to Development and Operation. McGraw-Hill.

Law, A.M. & Kelton, D.W. (1998). Simulation Modeling & Analysis, 2nd Ed., 234-266. McGraw-Hill.

Schriber, T.J. & Brunner, D.T. (1998). How discrete-event simulation software works. In Handbook of Simulation, 765-811. Wiley. Chapter 24.

Zeigler, B.P, Praehofer, H., & Kim, T.G. (2000). Theory of Modeling and Simulation, 2nd Ed., 75-96. Academic Press.

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Engineering

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