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Course: INDE 6370, Fall 2008
School: U. Houston
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Word Count: 457

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Analysis Continuous AGENDA Non-terminating and combined event modeling TYPES OF NON-TERMINATINGSYSTEMS Most manufacturing systems Service systems that do not close Service systems where the customer leaves something to be picked up at another time Examples Automobile plant Repair facilities Hospitals NON-TERMINATINGSYSTEM TIME TACTICAL CONSIDERATIONS Starting conditions Determining steady state...

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Analysis Continuous AGENDA Non-terminating and combined event modeling TYPES OF NON-TERMINATINGSYSTEMS Most manufacturing systems Service systems that do not close Service systems where the customer leaves something to be picked up at another time Examples Automobile plant Repair facilities Hospitals NON-TERMINATINGSYSTEM TIME TACTICAL CONSIDERATIONS Starting conditions Determining steady state Autocorrelation Length of replication Batch method STARTING CONDITIONS Begin with the system empty Preferred Begin with the system loaded How many to load with? DETERMIING STEADY STATE Must eliminate initial transient Graphical approach Linear regression approach GRAPHICAL APPROACH Visually determine when the slope of the initial transient approaches 0 Highly subjective and influenced by individual interpretation Not recommended LINEAR REGRESSION Uses the least squares method to determine where the initial transient ends If the observations slope is not zero, advance the range to a later set of observations Eventually the range of data will have an insignificant slope coefficient Steady state behavior has been reached AUTOCORRELATION Correlation between performance measure observations in the system Possible issue with non-terminating systems Problem if not addressed Practitioner may underestimate variance Results in the possibility of concluding that there is a difference when this actual is not Methods to address Can be accounted for by complex calculations Can be avoided by special techniques BATCH METHOD Identify the non-significant correlation lag size Make a batch 10 times the size of the lag Make the steady state replication run length 10 batches long EXAMPLE Run replication single for 10,000 minutes Observe 4000 entities Initial transient requires 2000 minutes Steady state for 8000 minutes EXAMPLE DETERMINE RUN LENGTH Non-significant lag occurs at 200 observations Batch size 200 x 10 = 2000 observations to remove autocorrelation 2000 x 10 batches = 20000 total observations Time for each observation 10000 / 4000 = 2.5 minutes per observation Total simulation length must be 2000 + 20000 x 2.5 = 52000 minutes FINAL ANALYSIS Remove initial transients Split remainder into 10 batches / replications Process just like terminating simulations CONTINUOUS AND COMBINED MODELING What is continuous event modeling Continuous event related blocks Continuous event related elements Animating continuous event models WHAT IS CONTINUOUS EVENT MODELING All previous modeling has involved discrete events Hopping between events on the event list Continuous models Contain one or more continuously changing variable values Differential equations Model fluids or fluid like entities May...

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U. Houston - INDE - 6370
11.1010.9610.3211.8410.3710.5510.1311.1210.5810.319.3311.0710.068.979.0111.679.569.1611.049.858.588.8611.1610.028.2310.989.738.5810.609.9911.0711.519.6910.7210.8710.5810.0710.2710.2510.388.568.6610.239.128.
U. Houston - INDE - 6370
AGENDATerminating systemsThree or more model comparisonsTHREE OR MORE ALTERNATIVE COMPARISONSANOVAONE WAYANALYSIS OF VARIANCEDetermines if one or more alternatives is different than the othersBased on a ratio of the variance between and with
U. Houston - INDE - 6370
AGENDAAnalyzing Input DataData collection exerciseHomework assignmentTHE USE OF INPUT DATA IN SIMULATIONObserve input dataFit to theoretical distributionGenerate data from theoretical distributionANALYZING INPUT DATADetermining underlying t
U. Houston - INDE - 6370
AGENDABalkingRenegingJockeyingBALKINGQueue is too full when entity arrivesEntity does not enter the queueEntity goes elsewhereModeled within QUEUE blockCapacity - deterministic or probabilisticBalk label RENEGINGEntities enters a queue
U. Houston - INDE - 6370
AGENDAContinuous and combined event modelingEnd term reviewCONTINUOUS AND COMBINED MODELINGWhat is continuous event modelingContinuous event related blocksContinuous event related elementsAnimating continuous event modelsWHAT IS CONTINUOUS
U. Houston - INDE - 6370
AGENDAData collection updateReviewDATA COLLECTION UPDATECollectionAnalysisREVIEWBasic simulation issuesInput data analysisRandom number generationModelingBASIC ISSUES.Simulation processManual event listPerformance measures BASIC SIM
U. Houston - INDE - 6370
AGENDAProject progress reportsArrivals elementResource related elementsSystem statusARRIVALS ELEMENTForce entities to appearModeling customers waiting before opening timeMake entities appear for demonstration purposes.ARRIVALS ELEMENTGen
U. Houston - INDE - 6370
AGENDAEnd term review for exam on 17 APR 08REVIEWValidationReplication analysisExperimental DesignOutput analysis of two systemsOutput analysis of more than two systemsNon-terminating system analysisVALIDATIONFaceStatisticalData collec
U. Houston - INDE - 6370
AGENDAConveyorsAdditional Modeling StructuresTYPES OF CONVEYORSNon-AccumulatingAccumulating CONVEYOR RELATEDSTRUCTURESBlocksAccessConveyExitElementsConveyorsSegmentsAnimationACCESS BLOCKHolds the entity in a queue until sufficient
U. Houston - INDE - 6370
AGENDAIntroduction to ARENABasic model blocksBasic experiment elements INTRODUCTION TO ARENAGraphically oriented simulation packageToolbarsProject barModel WindowFlow chart viewSpreadsheet viewMODULESBuilding blocks for modelsFlowchart
U. Houston - INDE - 6370
AGENDAEntity related Resource and queue relatedStatistics relatedHomeworkReviewBRANCH BLOCKUsed to control flow of entities through the modelPrimary entitySecondary entities may be clonedMore than one branch may be takenTypesProbabilisti
U. Houston - INDE - 6370
AGENDABasic Simulation Study ProcessCourse ProjectsAn example projectBASIC SIMULATION PROCESSProblem DefinitionProject PlanningSystem Definition / Model FormulationInput Data Collection and AnalysisModel TranslationVerificationValidation
U. Houston - INDE - 6370
AGENDAQueues relatedResource relatedSystem statusQUEUE RELATEDDuplicateMatchArrivals elementDUPLICATEUsed to generate additional entities from original entitiesAll duplicates inherit attribute valuesIf to be later rejoined, must have ide
U. Houston - INDE - 6370
AGENDATransportersReviewTRANSPORTER USESMaterial handling equipmentForkliftsDollysWorkers that process orders for later pickupValetStarbucks coffee makerSonic fast food carhopTYPES OF TRANSPORTERSFree pathFork liftCan go between any a
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Definition and Example 1Monday, March 03, 2008 1:13 PMMethods for combining functions: 1. Sum 2.(f + g )(x ) = f ( x ) + g( x ) Difference (f - g )(x ) = f ( x ) - g( x )(fg )(x) = f ( x)g( x) 4. Quotient f ( x ) = f ( x ) g( x ) provided
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U. Houston - MATH - 4377
U. Houston - MATH - 6397
Stochastic Processes - Spring 2008Practice Problems for Final ExamBernhard Bodmann, PGH 636 Duration: 150 minutes First Name: Last Name:Show all work. No points will be given for numerical answers without working being shown.(1) Consider the (c
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Stochastic Processes - Spring 2008Bernhard Bodmann, PGH 636 Exercise Sheet 2, with Solutions Do all Exercises individually. (1) Let X1 , X2 , . . . , Xn , . . . be i.i.d. with P(Xi = 1) = p and P(Xi = 1) = 1 p = q. Let a, b N. Dene Sn = X1 + . . .
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Exam 2 Math 4377 November 20, Fall 2008Show all the work for full credit. In this exam no calculators are allowed. Answer all of the following questions. The maximum score is 150. 1. (15 Points) Let V = R2 and W be the vector space of all real 22 m
U. Houston - MATH - 6397
Stochastic Processes - Spring 2008Practice Problems for Final ExamBernhard Bodmann, PGH 636 Duration: 150 minutes First Name: Last Name:Show all work. No points will be given for numerical answers without working being shown.(1) Consider the (c
U. Houston - MATH - 4377
Department of MathematicsUniversity of HoustonMath 4377 Advanced Linear AlgebraFall 2008Homework Set 9, due Tuesday, Nov 4, 1pmSection 3.51 In R3 , let 1 = (1, 0, 1), 2 = (0, 1, -2) and 3 = (-1, -1, 0). (a) If f is a linear functional on R3
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Department of MathematicsUniversity of HoustonMath 4377 Advanced Linear AlgebraFall 2008Homework Set 8, due Tuesday, Oct 28, 1pmSection 3.32 Let V be a vector space over the eld of complex numbers and suppose T is an isomorphism of V onto C3
U. Houston - MATH - 4377
Department of MathematicsUniversity of HoustonMath 4377 Advanced Linear AlgebraFall 2008Homework Set 10, due Tuesday, Nov 11, 1pmSection 3.61 Let n be a positive integer and F be a field. Let W be the subspace of all vectors (x1 , x2 , . . .
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10 f f1 f2 f386420!2 !4!3!2!10123440 f f1 f2 f33020100!10!20!30!40 !4!3!2!1012341.75 1.7 1.65 1.6 1.55 1.5 1.45 1.4 1.35 1.3 0.2 a=0.3134 b=1.29490.30.40.50.60.70.80.91
U. Houston - MATH - 4377
U. Houston - MATH - 6397
U. Houston - MATH - 4377
U. Houston - MATH - 1432
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U. Houston - MATH - 3321
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U. Houston - MATH - 3334
Math 3334 Fall 2008 Professor William OttAssignment 4: due Monday, October 20, 2008Problem 1. Marsden/Tromba problems (a) MT 3.2.6 (b) MT 3.3.10 (c) MT 3.3.11 (d) MT 3.3.19 (e) MT 3.3.34 (f ) MT 3.3.41 Problem 2. A function f : R R is analytic at
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U. Houston - MATH - 3334
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U. Houston - MATH - 3334
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U. Houston - MATH - 3334
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U. Houston - MATH - 3334
Math 3334 Fall 2008 Professor William OttAssignment 3: due Wednesday, October 1, 2008Problem 1. Let A = (aij ) be an (m n)-matrix with aij R for all 1 we have a11 a12 a1n a21 a22 a2n . . . . . . . . . . . . am1 am2 amn Define 1
U. Houston - MATH - 3334
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