lecture 1 - random number generation

8/13/2019 Lecture 1 - random number generation

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bengu, c1/ 1

What is simulation?

Chapter 1?

Pr

Prof. Bengu


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bengu, c1/Simulation with Arena

Fundamental Simulation Concepts Bengu, C1/2

Simulation Is ...

u Very broad term, set of problems/approaches

u Generally, imitation of a system via computer

u Involves a model validity?

u Dont even aspire to analytic solution

Y Don t get exact results (bad)

Y Allows for complex, realistic models (good)

Y Approximate answer to exact problem is betterthan exact answer to approximate problem

u Consistently ranked as most useful, powerful

of mathematical-modeling approache


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Discrete-Event SystemSIMULATION

4 Most Widely used IE tool (OR)

Helps:

4 to evaluate performanceof asystembefore actuallyimplementing it.

4 to comparevarious operationalalternativeswithoutdisturbing the system.


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Who Uses it?

Although manufacturers have traditionally used

simulation technology, many other industries

have discovered the benefits of modeling a

process and seeing potential results beforeinvesting precious resources such as

time and money.

In fact, simulation software and consultingservices have been used by industries such as:


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Some Application Areas

u Manufacturing scheduling, inventory

u Staffing personal-service operationsBanks, fast food, theme parks, Post Office, ...

u Distribution and logistics

u Health care emergency, operating rooms

u Computer systems

u Telecommunications

u Military

u Public policy4 Emergency planning

4 Courts, prisons, probation/ parole


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Who Uses it?

vHealth care vPublishing

vCommunications vWaste management

vFast food vRailroads

vAerospace vGovernments

vTextiles vConsumer goods

vElectronics vPackage delivery


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b e n g u , c 1 / S i m u l a t i on w i t h A r e n a

F u n d a m e n t a l S i m u l a t i o n C o n c e p t s B e n g u , C 1 / 7

Systems

uPhysical facility/ process, actual or planned

uStudy its performance

YMeasure

Y ImproveY Design (if it doesn t exist)

YMaybe control in real time

uSometimes possible to play with the system

uBut sometimes impossible to do soY Doesn t exist

Y Disruptive, expensive


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A group of objects joined in some regular interaction

toward the accomplishment of some purpose.

i.e., Production systems: machines & workers

producing a vehicle.

SYSTEMObjects

Objects

SYSTEM

ENVIRONMENT

Boundaries: Market Size

Activity : ProductionAttr ibutes : Sport -Red

Production Time

S Y S T E M


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System State: Collection of variables describing the system

i.e., # of cars produced,Avg. # of cars in the system at any point in time (queue+service)

Avg. Production Time

12

Objects

0

1

2

3

Number of Cars Produced

DepartureEvent

SYSTEM STATE

Arrival Event


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Numerical Calculations in Computer Simulation

SimulationTime

EntityArrivalTime

DepatureTime

Time InSystem

InterDepartureTime

0.0 1 0 1 1-

1.0 2 1 3 2 2

2.0..

3..

2..

5..

3..

2

Total 6 4

Avg 2 4/2=2


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Numerical Calculations of Computer Simulation TIME

SimulationTime

EntityArrivalNumberof EntitiesEnteredNE+1

DepartureNumberof EntitiesDepartedNE-1

TimeInSystem

0.0 1 0 1 11.0 2 1 3 2

2.0. 3. 2. 5. 3

Total 6 4

Avg 2 4/3=1.3


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Avg. Number of Entities in the System

at any Given MomentNumber of

Entities

Simulation

TimeNE=NE+1 NE=NE-1

Avg. Number Area Under NE Curve

of Entities = Simulation Time

#/time # * time/ time


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Models

uAbstraction/ simplification of the system usedas a proxy for the system itself

uCan try wide-ranging ideas in the model

Y Make your mistakes on the computer where they don t count, ratherfor real where they docount

u Issue ofmodel validit y

uTwo types of models

YPhysical(iconic)

YLogical/ Mathematical-- quantitative and logical assumptions,approximations


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What Do You Do with a Logical Model?

u If model is simple enough, use traditionalmathematics (queueing theory, differential equations,linear programming) to get answers

Y Nice in the sense that you get exact answers to the model

Y But might involve many simplifying assumptions to make the model

analytically tractable -- validity??

uMany complex systemsrequire complex models forvalidity simulation needed


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Computer Simulation

uMethod for studying a wide variety of models ofreal-world systems

Y Use numerical evaluation on computer

Y Use software to imitate the system s operations and characteristics,

often over time

u In practice, is the process of designing andcreating computerized model of system anddoing numerical computer-based experiments

uReal power application to complex systemsuSimulation can tolerate complex models


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Simulation Software

k Simulation can be defined as:

Creating a computer model of a real or proposed system andconducting experiments on the model

to describe observed behavior and/or predict future behaviorbefore investing any time or money.

k Why Simulation?Because experimenting on a real system could be costly/ impractical,Simulation has become an extremely important toolfor designing and analyzing complex systems;it is a cost-effective way of pre-testing proposed systems,

plans, or policies before incurring the expense of prototypes,field tests, or actual implementations.In fact, many managers have come to view simulation as aninexpensive insurancepolicy.


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SIMULATION MODELING

ADVANTAGES:

Evaluates performance of a hypothesized system in a

compressed time due to the power of computers.

4 Easy to use (software+ hardware are getting better)

Pitfalls:4 Easily misused: Proper Data Analysis, Validation

Techniques, Design of Experiments are required.

Output

DATA

and Analysis

SimulationNumberCrunching

Input

DATA

and Rules


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Prerequisites

4Elementary Statistics and Probability: Mean, Variance,

Confidence Interval, Hypothesis Testing, Design of

Experiments

SIMULATION MODELING

OutputDATA

Simulation

NumberCrunching

InputDATA

REAL

SYSTEM

SIMULATED

SYSTEM

Valid

?


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REQUIREMENTS

Presentations(Projects):4Learning by Examples (ARENA, Power Point Slides)

Alternatives (C++, Java, Web pages)

4Literature Search

Content:4Concept of System, Simulation Model,

Simulation Experiment Results

4 Modeling Techniques: Event vs Process based

4 Examples:Queueing Models, Inventory SystemsC++, Java Programming


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CONTENT

4Input Data Analysis: Statistics,

Random Number Generation,Statistical Distribution and Fitting,

Goodness of Fit Tests

4Verification and Validation4Analysis of Simulation Output Data4Comparison of Simulated Model Results

4Optimization of Simulated Models4Simulation Applications via ARENA


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Popularity (contd.)

u (A)IIE, O.R. division members (1980)

Y First in utility and interest: Simulation

Y But first in familiarity: LP (simulation was second)

uLongitudinal study of corporate practice (1983, 1989, 1993)1. Statistical analysis

2. Simulation

uSurvey of such surveys (1989)

Y Consistent heavy use of simulation


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Popularity

uM.S. grads, CWRU O.R. Department (1978)

Y Asked about valueaftergraduation; rankings:

1. Statistical analysis, 2. Forecasting, 3. Systems analysis,

4. Information systems,5. Simulation

u137 large firms (1979)

1. Statistical analysis (93% used it)

2. Simulation(84%)

Y Followed by LP, PERT/CPM, inventory, NLP


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Discrete SystemsPRODUCTION SYSTEMS,

BANK, HOSPITALS

0

1

23

Number of Entities in System

0

5

10

1st Qtr 2nd Qtr 3rd Qtr

Gas Level in Tank

State variables change at discrete

points in time. These occurrenceschanging system status are called

events.

State variables change continuously

over time. These changes are function

of time.

TYPE OF SYSTEMS

Continuous SystemsWATER FLOWS INTO DAM


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Different Kinds of Simulation

uStatic vs.Dynamic P1V1= P2V2 ?Does time have a role in the model?

uContinuous-change vs.D iscrete-change

Can the state change continuously or only at discrete points in time?

uDeterministic vs.Stochastic m= 5

Is everything for sure or is there uncertainty?m= N orm(5,4)

m= Ex(5)

uMost operational models:

Dynamic,Discrete-change,Stochastic


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Advantages of Simulation

uEliminate Blunders: Flexibility to model things as they are(even if messy and complicated)

Avoid looking where the light is (a morality play):

u Allows uncertainty,nonstationarityin modelingYThe only thing that s for sure: nothing is for sureY Danger of ignoring system variabilityY Model validity

You re walking along in the dark and see someone on hands and knees searching the groundunder a street light.

You: What s wrong? Can I help you?Other person: I dropped my car keys and can t find them.

You: Oh, so you dropped them around here, huh?

Other person: No, I dropped them over there. (Points into the darkness.)

You: Then why are you looking here?

Other person: Because this is where the light is.


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Advantages of Simulation(contd.)

uAdvances in computing/ cost ratiosY Estimated that 75% of computing power is used for various kinds of

simulations

Y Dedicated machines (e.g., real-time shop-floor control)

uAdvances in simulation softwareY Far easier to use (GUIs)

Y No longer as restrictive in modeling constructs (hierarchical, down to C)

Y Statistical design & analysis capabilities


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Benefits

Introduction to Simulation Using SIMAN (McGraw Hill, 1995) lists the following benefits associated with simulation.

k New policies, operating procedures, decision rules,organizational structures, information flows, etc., can be

explored without disrupting ongoing operations.

k New hardware designs, physical layouts, software

programs, transportation systems, etc., can be testedbefore committing resources to their acquisition and/or

implementation.

k Hypotheses about how or why certain phenomena occur

can be tested for feasibility.


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Benefits (cont)

k Time can be controlled: it can be compressed,

expanded, etc., allowing us to speed up or slow

down a phenomenon for study

k Insight can be gained about which variables are

most important to performance and how these

variables interact.

k Bottlenecks in material, information, and productflow can be identified.


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Benefits (cont)

k A simulation study can prove invaluable to

understanding how the system really operates as

opposed to how everyone thinks it operates.

k In new situations, about which we have limitedknowledge and experience, can be manipulated

in order to prepare for theoretical future events.

k Simulation s great strength lies in its abilityto let us explore what if questions.


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The Bad News

uDont get exact answers, only approximations,estimates

Y Also true of many other modern methods

YCan bound errors by machine roundoff

uGet random output(RIRO)from stochasticsimulations

Y Statistical design, analysis of simulation experiments

Y Exploit: noise control, replicability, sequential sampling,variance-reduction techniques

YCatch: standard statistical methods seldom work


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Simulation by Hand:The Buffon Needle Problem

uEstimatep (George Louis Leclerc, c. 1733)

uToss needle of lengthlonto table with stripesd(>l)apart

uP (needle crosses a line) =

uRepeat; tally = proportion of times a line is crossed

uEstimatep by

d

l

p

2

$p

2l

pd$


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Why Toss Needles?

Buffon needle problem seems silly now, but it hasimportant simulation features:

Y Experiment to estimatesomething hard to compute exactly (in 1733)

YRandomness, so estimate will not be exact; estimate the error in the

estimate

YReplication(the more the better) to reduce error

YSequential samplingto control error -- keep tossing until probable error

in estimate is small enoughYV ariance reduction(Buffon Cross)


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Using Computers to Simulate

uGeneral-purpose languages(C++. C, FORTRAN, JAVA )

YTedious, low-level,time consumingto develop,error-prone

Y But, almost completeflexibilityand computation speed

uSupport packagesY Subroutines for list processing, bookkeeping, time advance

Y Widely distributed, widely modified

uSpreadsheets

Y Usually static modelsY Financial scenarios, distribution sampling, SQC


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Using Computers to Simulate(contd.)

uSimulation languages

Y GPSS, SIMSCRIPT, SLAM, SIMAN,ARENA,

SIMFACTORY, PROMODEL, AUTOMOD, WITNESS,..

Y Popular, in wide use todayY Learning curve for features, effective use, syntax

uHigh-level simulators

Y Very easy, graphical interface

Y Domain-restricted (manufacturing, communications)

Y Limited flexibility model validity?


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Where Arena Fits In

ArenaTemplate

StandardEdition P

rofessionalEdition

A singlegraphical userinterfaceconsistent atany level ofmodeling

Higher

Level ofModeling

Lower

SIMAN

Template

VerticalSolutions

User-Created TemplatesCommonly used constructsCompany-specific processesCompany-specific templatesetc.

Application Solution TemplatesCall$imBP$imetc.

Common Panel

Many common modeling constructsVery accessible, easy to useReasonable flexibility

Support, Transfer PanelsAccess to more detailed modeling for greater

flexibility

Blocks, Elements PanelsAll the flexibility of the SIMAN simulation

language

User-Written Visual Basic, C/C++, FORTRANCode

The ultimate in flexibilityC/C++/FORTRAN requires compiler

u Hierarchical structure

Y Multiple levels ofmodeling

Y Can mix differentmodeling levels togetherin the same model

Y Often, start high then golower as needed

u Get ease-of-useadvantage of simulatorswithout sacrificingmodeling flexibility


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When Simulations are Used

uUses of simulation have evolved with hardware,software

uThe early years (1950s-1960s)

Y Very expensive, specialized tool to useY Required big computers, special training

Y Mostly in FORTRAN (or even Assembler)

Y Processing cost as high as $1000/ hour for a sub-286 level machine


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When Simulations are Used (contd.)

uThe formative years (1970s-early 1980s)

Y Computers got faster, cheaper

Y Value of simulation more widely recognized

Y Simulation software improved, but they were still languages to be

learned, typed, batch processed

Y Often used to clean up disasters in auto, aerospace industries

4Car plant; heavy demand for certain model

4 Lineunderperforming

4 Simulated, problem identified

4 But demand had dried up simulation was too late


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The recent past (late 1980s)

YMicrocomputer power

Y Software expanded into GUIs, animation

YWider acceptance across more areas4Traditional manufacturing applications

4 Services

4Health care

4 Business processes

Y Still mostly in large firms

YOften a simulation is part of the specs


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uThe present

Y Proliferating into smaller firms

Y Becoming a standard tool

Y Being used earlier in design phaseY Real-time control

uThe future

Y Exploiting interoperability of operating systems

Y Specialized templates for industries, firms

Y Automated statistical design, analysis


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SYSTEM STATE

VARIABLES

EVENTS ENTITIES ATTRIBUT

ES

ACTIVITIE

S

Banking # busy tellers# customers

waiting

1.Arrival of Customer

2.Departure of Customer

Customers ServiceTime

Makingdeposit

and

withdrawal

Inventory Level of

inventoryBacklogged

demands

1. Demand for

Inventory2. Review of

Inventory

3. Arrival of

Inventory

Inventoried

Items

Capacity

Mfg

Examples

lecture 1 - random number generation

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