chapter six process simulation using arena mcgraw-hill/irwin © 2005 the mcgraw-hill companies, inc....
TRANSCRIPT
Chapter Six
Process Simulation
Using Arena
McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Six Learning Objectives
Analyze queuing processes using Excel and Arena
Develop and utilize Arena simulation models for a simple queuing process
Use Arena to compare alternative queuing processes
Develop new Arena modeling techniques by using Arena Example and Smart models
Chapter Six Worksheet MenuChapter 6 Exhibits
Use Ctrl-Shift-R to return to
this worksheet
Process Analysis and Improvement: Tools and Techniques Copyright ©2005 by The McGraw-Hill Companies, Inc.
Filename Sheet / Page NameExhibit Number Application / Caption
Drawings.vsd MM1 1 M/M/1 Queueing Process Diagram
Worksheets.xls Exponential 2 Exponential Probability Density Function
Worksheets.xls MM1 3 M/M/1 Queue Calculations
Worksheets.xls MM1 Calculations 4 M/M/1 Queue Calculations
Worksheets.xls MM1 5 M/M/1 Queue Measures of Performance versus Traffic Intensity
Drawings.vsd MM3 6 M/M/3 Queueing Process Diagram
Worksheets.xls Manual Simulation 7 F/F/1 Queue Simulation Calculations
Worksheets.xls Manual Simulation 8 F/F/1 Queue Simulation Chart
Worksheets.xls Manual Simulation 9 M/F/1 Queue Simulation Calculations
Worksheets.xls Manual Simulation 10 M/F/1 Queue Simulation Chart
Worksheets.xls Manual Simulation 11 M/M/1 Queue Simulation Calculations
Worksheets.xls Manual Simulation 12 M/M/1 Queue Simulation Chart
Drawings.vsd Simulation Tasks 13 Process Simulation Tasks
Worksheets.xls Arena Components 15 Arena Simulation Model Development Environment Components
Drawings.vsd Arena File Structure 16 Arena File Structure
Worksheets.xls MM1 Comparison 20 M/M/1 Queue Comparison: Theorical versus Simulated
Worksheets.xls Arena Components 21 Arena Template Panel Modules
Worksheets.xls Arena Modules 22 Arena Basic Process Panel Modules
Worksheets.xls Arena Components 33 Arena Simulation Engine
Worksheets.xls Items Ordered Data 35 D&E Order Size
Drawings.vsd Comparison 46 Two Queueing Process Analysis Diagram
Worksheets.xls Arena Components 59 Arena Stand Alone Programs
Worksheets.xls Examples 60 Arena Examples
Worksheets.xls Smarts 61 Arena Smart Files
Worksheets.xls HSmart Arena Packaging Edition Smart File Examples
Worksheets.xls FSmart Arena Factory Analyzer Edition Smart File Examples
Related Files
Filename Source Application
Comparison.doe Text CD-ROM M/M/3 Queue Comparison Simulation Model
MM1 Statistics.doe Text CD-ROM M/M/1 Queue Simulation Model
MM1.doe Text CD-ROM M/M/1 Queue Simulation Model
MM3.doe Text CD-ROM M/M/3 Queue Simulation Model
MV1.doe Text CD-ROM M/Various/1 Queue Simulation Model
QueueStencil.vss Text CD-ROM Queue Visio Stencil
View Selected Worksheet or Drawing
Chapter Six Files
CD File Description
Chapter 6 Drawings.vsd Chapter 6 Drawings
Chapter 6 Presentation.ppt Chapter 6 PowerPoint Presentation
Chapter 6 Worksheets.xls Chapter 6 Worksheets
Comparison.doe M/M/3 Queue Comparison Simulation Model
MM1 Statistics.doe M/M/1 Queue Simulation Model
MM1.doe M/M/1 Queue Simulation Model
MM3.doe M/M/3 Queue Simulation Model
MV1.doe M/Various/1 Queue Simulation Model
QueueStencil.vss Queue Visio Stencil
Chapter Six Outline
Analyze queuing processes using Excel and Arena
Arena Simulation Environment Other Queueing Process Models Other Arena Programs and Examples
Analysis and Simulation of Queuing Processes
Queuing Process Analysis Using Excel M/M/1 Queue M/M/3 Queue
Manual Simulation Using Excel Process Simulation Tasks Why Use Arena for Process Analysis
and Improvement?
Queuing Process Analysis Using Excel
Process Boundary Defines process limits Arrival Source Supplies process customers Queue Allows customers to wait for service Server Provides customer service
Departure
Process Boundary
ArrivalSource
QueueSingle
Server
Exhibit 6-1 p. 155Page: MM1
M/M/1 Queue
M The time between arrivals follows the exponential distribution
M The time for service follows the exponential distribution
1 The process has 1 server
Exponential Probability Density Functions
f(x) = λe-λx, for 0 ≤ x < ∞
0.0
0.5
1.0
1.5
2.0
2.5
0.0 1.0 2.0 3.0 4.0 5.0 6.0
x
f(x
)
λ =1.0
λ =1.5
λ =2.0
Exhibit 6-2 p. 156Sheet: Exponential
Exponential Distributionf (x) = λe-λx, for 0 ≤ x < ∞E (X) = 1/λ V(X) = 1/λ2
F (x) = 1-e-λx, for 0 ≤ x < ∞
M/M/1 Queue Calculations
Column Customers / Minute Formula Units Source
B Mean Inter Arrival Time 1 / λ Seconds Input
C Mean Arrival Rate λ Customers / Minute 60 / Column B
D Mean Service Time 1 / μ Seconds Input
E Mean Service Rate μ Customers / Minute 60 / Column D
F Traffic Intensity ρ = λ / μ Dimensionless Column C / Column E
G Expected Number in Process Lp = ρ / (1 - ρ) Customers Column F / (1 - Column E)
H Expected Number in Queue Lq = Lp - ρ = ρ2 / (1 - ρ) Customers Column G - Column F
I Expected Time in Process Wp = Lp / λ =1 / (μ - λ) Minutes Column G / Column C
J Expected Time in Queue Wq = Lq / λ =ρ / (μ - λ) Minutes Column H / Column C
Exhibit 6-3 p. 156Sheet: MM1
Exhibit 6-4 p. 156Sheet: MM1 Calculations
M/M/1 Queue Calculations
Traffic Intensity = ρ = Mean Arrival Rate / Mean Service Rate =Mean Service Time / Mean Inter Arrival Time
λ = 1 / 60 = 0.0167 Customers per Seconds = 0.0167 * 60 = 1.00 Customers per Minute
μ = 1 / 55 = 0.0182 Customers per Seconds = 0.0182 * 60 = 1.09 Customers per Minute
ρ = 1.00 / 1.09 = 0.917 Expected Number in Process = Lp
= ρ / (1 - ρ) Expected Number in Queue = Lq
= Lp - ρ = ρ2 / (1 - ρ)
Exhibit 6-5 p. 167Sheet: MM1
M/M/3 Queue
ArrivalSource
Queue
Three
Servers
Process Boundary
Departure
Exhibit 6-6 p. 157Sheet: MM3
Manual Simulation Using Excel
Mean Inter Arrival Time in Seconds, 60 Mean Service Time in Seconds, 50 Arrival Option, 0 = Fixed or 1 = Exponential Service Option, 0 = Fixed or 1 =
Exponential F(60) / F(50) / 1 Exhibits 6-7 & 6-8 M(60) / F(50) / 1 Exhibits 6-9 & 6-10 M(60) / M(50) / 1 Exhibits 6-11 & 6-12
Manual Simulation F(60) / F(50) / 1
Exhibit 6-8 p. 158Sheet: Manual SimulationExhibit 6-7 p. 158
Sheet: Manual Simulation
Manual Simulation M(60) / F(50) / 1
Exhibit 6-10 p. 159 Sheet: Manual SimulationExhibit 6-9 p. 159
Sheet: Manual Simulation
Manual Simulation M(60) / M(50) / 1
Exhibit 6-12 p. 160Sheet: Manual Simulation
Exhibit 6-11 p. 160Sheet: Manual Simulation
Process Simulation Tasks
Exhibit 6-13 p. 160Page: Simulation Tasks
Why Use Arena for Process Analysis and Improvement?
Simulation History 1961 GPSS (Gordon – IBM) 1982 SIMAN (Pegden – Penn State) 1992 Arena (Systems Modeling Corp.) 2002 Arena Factory Analyzer (Rockwell Software)
Other Simulation Products AutoMod Flexsim ProModel Simul8 Witness
Arena Simulation Environment
Arena Modeling Environment Arena Template Panel Modules Arena Simulation Engine
Arena Modeling Environment
Modeling Environment Exhibit 6-14 Template Panel Modules Exhibit 6-21 Simulation Engine Exhibit 6-33 VBA Interface Chapter 8 Stand Alone Programs Exhibit 6-59
Arena Modeling Environment
Exhibit 6-14 p. 161Model: MM1.doe
Tool Bar
FlowchartWindow
SpreadsheetWindow
ProjectBar
StatusBar
Arena Modeling Environment
Exhibit 6-15 p. 162Sheet: Arena Components
Arena Modeling Environment
Exhibit 6-16 p. 163Page: Arena File Structure
Queueing Process Models
MM1.doeMM3.doeComparison.doeMV1.doe
MM1.doe @ 60 Minutes
Exhibit 6-17 p. 163TNOW = 60 Minutes
MM1.doe
Exhibit 6-18 p. 164Run Setup Dialog
Exhibit 6-19 p. 164Category Overview Report (Queue)
M/M/1 Queue Comparison: Theoretical versus Simulated
Exhibit 6-20 p. 165Sheet: MM1 Comparison
Arena Template Panel Modules
Create Module Process Module Dispose Module Entity Spreadsheet Queue Spreadsheet Resource Spreadsheet Variable Spreadsheet
Arena Template Panel Modules
Exhibit 6-21 p. 165Sheet: Arena Components
Arena Basic Process Template
Panel Module Type Module Reference
Basic Process Data Entity Entity
Basic Process Data Queue Queue
Basic Process Data Resource Resource
Basic Process Data Schedule Resource
Basic Process Data Set System
Basic Process Data Variable System
Basic Process Flowchart Assign Entity
Basic Process Flowchart Batch Entity
Basic Process Flowchart Create Entity
Basic Process Flowchart Decide Entity
Basic Process Flowchart Dispose Entity
Basic Process Flowchart Process Resource
Basic Process Flowchart Record Entity
Basic Process Flowchart Separate Entity
Exhibit 6-22 p. 166Sheet: Arena Modules
Exhibit 6-23 p. 166Arena Basic Process Panel Module Icons
Create Module
Exhibit 6-24 p. 166MM1.doe Create Module Dialog Box
Process Module
Exhibit 6-25 p. 167MM1.doe Process Module Dialog Box
Resource Detail
Exhibit 6-26 p. 168MM1.doe Process Module Resource Detail Dialog Box
Exhibit 6-27 p. 168 Arena Resource Picture Placement Window
Dispose Module
Exhibit 6-28 p. 168MM1.doe Dispose Module Dialog Box
Entity Spreadsheet
Exhibit 6-29 p. 169MM1.doe Entity Spreadsheet
Queue Spreadsheet
Exhibit 6-30 p. 169MM1.doe Queue Spreadsheet
Resource Spreadsheet
Exhibit 6-31 p. 169 MM1.doe Resource Spreadsheet
Variable Spreadsheet
Exhibit 6-32 p. 169 MM1.doe Variable Spreadsheet
Arena Simulation Engine
Entity Simulation Clock and Event Calendar Random Number Generator Statistic Collection Tools Crystal Reports Statistic Output
Arena Simulation Engine
Exhibit 6-33 p. 170Sheet: Arena Components
Entity
Entities are the dynamic elements in the Arena model Entities enter the model via a Create module and exit via a
Dispose module While a large arena model may contain thousands of entities at
any one point in time, or one entity is active. The active entity attempts to move as far as possible through the
logic modules of the model. In model MM1.doe, the only point at which an entity can be
delayed is the process module. When an entity enters the Service Process module, either the service
function is started immediately or the entity is held in the Service.Queue.
If Resource Server is available, the duration of the service is determined based on the random expression illustrated previously. The Arena simulation engine schedules an End-Of-Service event on the Event Calendar to take place at a future point in time.
If Resource Server is not available, the duration of the time in queue cannot be determined. The entity will be released from the queue only after the server has processed all previously waiting entities.
Simulation Clock and Event Calendar
The Simulation Clock control the advance of simulation time
When the active entity is halted The movement of another entity may
be started or The clock advances to the next
scheduled event, starting the associated entity
Simulation Clock and Event Calendar
Exhibit 6-34 p. 171MM1.doe Trace Report Extract
Random Number Generators
Statistical Distributions BETA (Alpha1, Alpha2) EXPOnential (Mean) GAMMa (Beta, Alpha) JOHNson (gamma, delta, lambda, xi) ERLAng (Mean, k) LOGNormal (LogMean, LogStd) NORMal (Mean, SD) POISson (Mean) TRIAngular (Min, Mode, Max) UNIForm (Min, Max) WEIBull (Beta, Alpha)
Empirical Data CONTinuous (Prob1, Value1, Prob2, Value2, ... ) DISCrete (Prob1, Value1, Prob2, Value2, ... )
Random Number Generator Example
Items Ordered FrequencyCumulative Frequency Cumulative %
1 11 11 11.0%2 17 28 28.0%3 18 46 46.0%4 23 69 69.0%5 21 90 90.0%6 10 100 100.0%
Discrete Distribution
0.0%
25.0%
50.0%
75.0%
100.0%
0 1 2 3 4 5 6
Item s OrderedC
um
ula
tive
%
Disc (0.11, 1, 0.28, 2, 0.46, 3, 0.69, 4, 0.90, 5, 1, 6)
Exhibit 6-35 p. 172Sheet: D&E Order Size
Statistic Collection Tools
CounterTally Time PersistentOutputFrequency
Counter
Exhibit 6-36 p. 173MM1.doe Record Number Served
Crystal Reports Statistic Output
Exhibit 6-37 p. 173MM1.doe Advanced Process Statistics Module
Exhibit 6-42 p. 176MM1.doe User Specified Report
Tally
Exhibit 6-38 p. 173MM1.doe Record Time Between
Time Persistent
Exhibit 6-39 p. 174Arena Expression Builder, Current Number in Queue
Output
Exhibit 6-40 p. 174Arena Expression Builder, Number In Entity
Frequency Report
Exhibit 6-42 p. 176MM1.doe Frequencies Report
MM3.doe
Exhibit 6-43 p. 177MM3.doe Network Logic Flow
MM3.doe @ 60 Minutes
Exhibit 6-44 p. 177MM3.doe at TNOW = 60 Minutes
MM3.doe Report
Exhibit 6-45 p. 177MM3.doe Category Overview Report (Queue)
Comparison.doe
Separate Module Assign Module
Variables Attributes
• Entity Type• Entity Picture
Other Entity Icon Simulation Results
Comparison.doe
Process Boundary
ArrivalSource
QueueSingle
Server
ArrivalSource
QueueSingle
Server
ArrivalSource
QueueSingle
Server
Departure
Departure
Queue
Triple
Servers
Process Boundary
Departure
Departure
Exhibit 6-46 p. 178Page: Comparison
Comparison.doe
Exhibit 6-47 p. 178Comparison.doe Network Logic Flow
Separate Module
Exhibit 6-48 p. 179Comparison.doe Module Separate 1
Assign Module
Exhibit 6-49 p. 179Comparison.doe Module Assign as Parallel
Exhibit 6-50 p. 179Comparison.doe Assignments Dialog
Assign Module Types
Variables (Available throughout model) Attributes (Available for each entity)
Entity Type Entity Picture User Defined
Other J (Only Arena Integer) M (Station)
Default Arena Entity Attributes
Entity.HoldCostRateEntity.JobStepEntity.PictureEntity.SequenceEntity.StationEntity.Type
Entity Icon or Picture
Exhibit 6-51 p. 180Entity Pictures Dialog Window
Exhibit 6-52 p. 180Arena Picture Editor
Comparison.doe @ 60 Minutes
Exhibit 6-53 p. 181Comparison.doe at TNOW = 60 Minutes
Comparison.doe Report
Exhibit 6-54 p. 181Comparison.doe Number in Queues Report
MV1.doe
Exhibit 6-55 p. 182MV1.doe Network Logic Flow
Branch Block
Exhibit 6-56 p. 182MV1.doe Branch Block
MV1.doe @ 60 Minutes
Exhibit 6-57 p. 182MV1.doe at TNOW = 60 Minutes
MV1.doe Report
Exhibit 6-58 p. 183MV1.doe Number in Queues Report
Arena Stand Alone Programs
Exhibit 6-59 p. 183Sheet: Arena Components
Arena Examples
Exhibit 6-60 p. 184Sheet: Examples
Model Name (*.DOE) DescriptionACME Medical Equipment
Example of how Arena can be used to model a complete business process. The following concepts are illustrated: Process module, Decide module, animation of several different resources, changing entity picture in mid-model to represent current status, generating a job number automatically in Arena, attaching the job number to an entity (Assign module), and permanent batching.
Bank Kiosk Analysis This study examines alternatives for utilizing automatic ("self-serve") kiosks in a bank lobby. The optimization problem is to minimize the total resource cost (of tellers and kiosks), while providing acceptable customer service. Options include how many tellers to assign to customer transactions, how many kiosks to place in the bank, and what proportion of customers will use tellers.
Banking Transactions Demonstrates the various transactions and activities at a bank, including ATM, teller, and drive-thru transactions.
Billing Department Complex model of a standard billing center. The following concepts are illustrated: Process module, assigning an attribute (Assign module), different processing by attribute (Decide module by condition), resource animation, modeling an error checking scenario, entity duplication for parallel processing, and modeling resource cost.
Arena Smart Files
Exhibit 6-61 p. 184Sheet: Smarts
\Program Files\Rockwell Software\Arena\Smarts 258 Number of Smart models
Category
Model Name Smarts*.DOE Application
VBA and Visual Basic® 001 VBA—VariableArray ValueModules 002 Batch and Separate ModulesBatching 002 Batch and Separate ModulesModules 003 Assign Module ExampleResources 004 Defining a Resource CapacityDecision Logic 005 Decide Module ExampleModules 005 Decide Module ExampleNamed Views 006 Using Named ViewsBasic Concepts 007 Basic ModelingHierarchical Submodels 008 Hierarchical ModelingHierarchical Submodels 009 Nested Submodel ExampleAnimation 010 Animating Resource Status
Arena SMART files, a collection of small example models that demonstrate a variety of modeling techniques and situations commonly encountered using Arena.Smart files have been specifically designed for use as a training or reference tool.
Each SMART File is listed in one or more of the categories below.
Summary
Process Simulation Using Arena Analysis and Simulation of Queuing
Processes Arena Simulation Environment Other Queueing Process Models Other Arena Programs and Examples
Next: Arena Applications