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# Chapter Six Process Simulation Using Arena McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc. All rights reserved.

## Presentation on theme: "Chapter Six Process Simulation Using Arena McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc. All rights reserved."— Presentation 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 Menu

Chapter Six Files

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 BoundaryDefines process limits Arrival SourceSupplies process customers QueueAllows customers to wait for service ServerProvides customer service Exhibit 6-1 p. 155 Page: MM1

M/M/1 Queue MThe time between arrivals follows the exponential distribution MThe time for service follows the exponential distribution 1The process has 1 server Exhibit 6-2 p. 156 Sheet: Exponential Exponential Distribution f (x) = λe -λx, for 0 ≤ x < ∞ E (X) = 1/λ V(X) = 1/λ 2 F (x) = 1-e -λx, for 0 ≤ x < ∞

M/M/1 Queue Calculations Exhibit 6-3 p. 156 Sheet: MM1 Exhibit 6-4 p. 156 Sheet: 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. 167 Sheet: MM1

M/M/3 Queue Exhibit 6-6 p. 157 Sheet: 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) / 1Exhibits 6-7 & 6-8 M (60) / F (50) / 1Exhibits 6-9 & 6-10 M (60) / M (50) / 1Exhibits 6-11 & 6-12

Manual Simulation F (60) / F (50) / 1 Exhibit 6-8 p. 158 Sheet: Manual Simulation Exhibit 6-7 p. 158 Sheet: Manual Simulation

Manual Simulation M (60) / F (50) / 1 Exhibit 6-10 p. 159 Sheet: Manual Simulation Exhibit 6-9 p. 159 Sheet: Manual Simulation

Manual Simulation M (60) / M (50) / 1 Exhibit 6-12 p. 160 Sheet: Manual Simulation Exhibit 6-11 p. 160 Sheet: Manual Simulation

Process Simulation Tasks Exhibit 6-13 p. 160 Page: 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. 161 Model: MM1.doe Tool BarFlowchart Window Spreadsheet Window Project Bar Status Bar

Arena Modeling Environment Exhibit 6-15 p. 162 Sheet: Arena Components

Arena Modeling Environment Exhibit 6-16 p. 163 Page: Arena File Structure

Queueing Process Models MM1.doe MM3.doe Comparison.doe MV1.doe

MM1.doe @ 60 Minutes Exhibit 6-17 p. 163 TNOW = 60 Minutes

MM1.doe Exhibit 6-18 p. 164 Run Setup Dialog Exhibit 6-19 p. 164 Category Overview Report (Queue)

M/M/1 Queue Comparison: Theoretical versus Simulated Exhibit 6-20 p. 165 Sheet: 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. 165 Sheet: Arena Components

Arena Basic Process Template Exhibit 6-22 p. 166 Sheet: Arena Modules Exhibit 6-23 p. 166 Arena Basic Process Panel Module Icons

Create Module Exhibit 6-24 p. 166 MM1.doe Create Module Dialog Box

Process Module Exhibit 6-25 p. 167 MM1.doe Process Module Dialog Box

Resource Detail Exhibit 6-26 p. 168 MM1.doe Process Module Resource Detail Dialog Box Exhibit 6-27 p. 168 Arena Resource Picture Placement Window

Dispose Module Exhibit 6-28 p. 168 MM1.doe Dispose Module Dialog Box

Entity Spreadsheet Exhibit 6-29 p. 169 MM1.doe Entity Spreadsheet

Queue Spreadsheet Exhibit 6-30 p. 169 MM1.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. 170 Sheet: 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. 171 MM1.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 Disc (0.11, 1, 0.28, 2, 0.46, 3, 0.69, 4, 0.90, 5, 1, 6) Exhibit 6-35 p. 172 Sheet: D&E Order Size

Statistic Collection Tools Counter Tally Time Persistent Output Frequency

Counter Exhibit 6-36 p. 173 MM1.doe Record Number Served

Crystal Reports Statistic Output Exhibit 6-37 p. 173 MM1.doe Advanced Process Statistics Module Exhibit 6-42 p. 176 MM1.doe User Specified Report

Tally Exhibit 6-38 p. 173 MM1.doe Record Time Between

Time Persistent Exhibit 6-39 p. 174 Arena Expression Builder, Current Number in Queue

Output Exhibit 6-40 p. 174 Arena Expression Builder, Number In Entity

Frequency Report Exhibit 6-42 p. 176 MM1.doe Frequencies Report

MM3.doe Exhibit 6-43 p. 177 MM3.doe Network Logic Flow

MM3.doe @ 60 Minutes Exhibit 6-44 p. 177 MM3.doe at TNOW = 60 Minutes

MM3.doe Report Exhibit 6-45 p. 177 MM3.doe Category Overview Report (Queue)

Comparison.doe Separate Module Assign Module Variables Attributes Entity Type Entity Picture Other Entity Icon Simulation Results

Comparison.doe Exhibit 6-46 p. 178 Page: Comparison

Comparison.doe Exhibit 6-47 p. 178 Comparison.doe Network Logic Flow

Separate Module Exhibit 6-48 p. 179 Comparison.doe Module Separate 1

Assign Module Exhibit 6-49 p. 179 Comparison.doe Module Assign as Parallel Exhibit 6-50 p. 179 Comparison.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.HoldCostRate Entity.JobStep Entity.Picture Entity.Sequence Entity.Station Entity.Type

Entity Icon or Picture Exhibit 6-51 p. 180 Entity Pictures Dialog Window Exhibit 6-52 p. 180 Arena Picture Editor

Comparison.doe @ 60 Minutes Exhibit 6-53 p. 181 Comparison.doe at TNOW = 60 Minutes

Comparison.doe Report Exhibit 6-54 p. 181 Comparison.doe Number in Queues Report

MV1.doe Exhibit 6-55 p. 182 MV1.doe Network Logic Flow

Branch Block Exhibit 6-56 p. 182 MV1.doe Branch Block

MV1.doe @ 60 Minutes Exhibit 6-57 p. 182 MV1.doe at TNOW = 60 Minutes

MV1.doe Report Exhibit 6-58 p. 183 MV1.doe Number in Queues Report

Arena Stand Alone Programs Exhibit 6-59 p. 183 Sheet: Arena Components

Arena Examples Exhibit 6-60 p. 184 Sheet: Examples

Arena Smart Files Exhibit 6-61 p. 184 Sheet: Smarts

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

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