Clients CPU Computer Simulation Techniques: The defnitive introduction! 1 2 2 3 3 7 b 4 5 6 9 6 9 Yes Is CPU No MCL = tarr queue MCL = MCL + 1 empty? A new arrival A departure event occurs event occurs b Is MCL = tarr b ? Yes A new arrival event occurs b i Harry Perros Simulation Techniques Harry Perros Sim S ii Harry Perros Simulation Techniques Sim S Computer Simulation Techniques: The definitive introduction! Harry Perros iii Simulation Techniques Harry Perros Sim S Copyright © 2021 by Harry Perros All rights reserved. This book or any portion thereof may not be reproduced or used in any manner whatsoever without the express written permission of the author except for the use of brief quotations in a book review or scholarly journal. iv Harry Perros Simulation Techniques Sim S To Isabelle v Table of Contents FORWARD ....................................................................................................................... XI AUTHOR ........................................................................................................................ XIII CHAPTER 1: INTRODUCTION ...................................................................................... 1 1.1. INTRODUCTION ....................................................................................................................... 1 1.2. BUILDING A SIMULATION MODEL ......................................................................................... 2 1.4. A TOKEN-BASED ACCESS SCHEME ......................................................................................... 9 1.5. A TWO-STAGE MANUFACTURING SYSTEM ........................................................................ 15 PROBLEMS ..................................................................................................................................... 21 COMPUTER PROJECTS .................................................................................................................. 22 CHAPTER 2: GENERATION OF PSEUDO-RANDOM NUMBERS ........................ 25 2.1. INTRODUCTION .................................................................................................................... 25 2.2. PSEUDO-RANDOM NUMBERS .............................................................................................. 26 2.3. THE CONGRUENTIAL METHOD ........................................................................................... 28 2.3.1. GENERAL CONGRUENTIAL METHODS ............................................................................ 30 2.3.2. COMPOSITE GENERATORS ............................................................................................... 30 2.4. TAUSWORTHE GENERATORS .............................................................................................. 31 2.5. THE LAGGED FIBONACCI GENERATORS ............................................................................ 31 2.6. STATISTICAL TESTS FOR PSEUDO-RANDOM NUMBER GENERATORS ............................. 33 2.6.1. HYPOTHESIS TESTING ...................................................................................................... 33 2.6.2. FREQUENCY TEST (MONOBIT TEST) .............................................................................. 40 2.6.3 SERIAL TEST ...................................................................................................................... 41 2.6.4. RUNS TEST ......................................................................................................................... 44 2.6.5. CHI-SQUARED TEST FOR GOODNESS OF FIT .................................................................. 44 PROBLEMS ..................................................................................................................................... 45 COMPUTER PROJECTS .................................................................................................................. 45 CHAPTER 3: GENERATING STOCHASTIC VARIATES ......................................... 47 3.1. INTRODUCTION .................................................................................................................... 47 3.2. THE INVERSE TRANSFORMATION METHOD ...................................................................... 47 3.3. SAMPLING FROM CONTINUOUS-TIME PROBABILITY DISTRIBUTIONS ........................... 50 3.3.1. SAMPLING FROM A UNIFORM DISTRIBUTION ............................................................... 50 3.3.2. SAMPLING FROM AN EXPONENTIAL DISTRIBUTION ..................................................... 51 3.3.3. SAMPLING FROM AN ERLANG DISTRIBUTION ............................................................... 52 3.3.4. SAMPLING FROM A NORMAL DISTRIBUTION ................................................................. 53 3.4. SAMPLING FROM DISCRETE-TIME PROBABILITY DISTRIBUTIONS ................................. 55 3.4.1. GENERATING BINOMIAL DISTRIBUTED STOCHASTIC VARIATES ................................. 55 3.4.2. GENERATING GEOMETRICALLY DISTRIBUTED STOCHASTIC VARIATES ..................... 55 3.4.3. GENERATING POISSON DISTRIBUTED STOCHASTIC VARIATES ................................... 56 3.5. GENERATING STOCHASTIC VARIATES FROM AN EMPIRICAL DISTRIBUTION ................ 58 3.6. THE REJECTION METHOD .................................................................................................... 60 vii Simulation Techniques Harry Perros Sim S COMPUTER PROJECTS ................................................................................................................... 61 CHAPTER 4: SIMULATION DESIGNS ....................................................................... 63 4.1. INTRODUCTION ..................................................................................................................... 63 4.2. EVENT-ADVANCE DESIGN .................................................................................................... 63 4.3. FUTURE EVENT LIST ............................................................................................................ 64 4.4. EVENT LIST STORED IN A SEQUENTIAL ARRAY ................................................................. 65 4.5. EVENT LIST STORED IN A LINKED LIST .............................................................................. 66 4.5.1. DEFINING A LINKED LIST ................................................................................................. 68 4.5.2. CREATION OF A NEW NODE ............................................................................................. 69 4.5.3. DELETION OF A NODE ....................................................................................................... 70 4.5.4. INSERTING A NODE IN A LINKED LIST ............................................................................. 70 4.5.5. REMOVING THE FIRST NODE OF A LINKED LIST ............................................................ 73 4.5.6. TIME COMPLEXITY ............................................................................................................ 74 4.5.7. DOUBY LINKED LISTS ....................................................................................................... 75 4.6. UNIT-TIME ADVANCE DESIGN ............................................................................................. 75 4.6.1. SELECTING A UNIT TIME .................................................................................................. 79 4.6.2. IMPLEMENTATION ............................................................................................................ 80 4.6.3. EVENT-ADVANCE VS. UNIT-TIME ADVANCE .................................................................. 80 4.7. ACTIVITY-BASED SIMULATION DESIGN ............................................................................. 80 4.8. EXAMPLES ............................................................................................................................. 83 4.8.1. AN INVENTORY SYSTEM ................................................................................................... 83 4.8.2. A ROUND-ROBIN QUEUE .................................................................................................. 85 PROBLEMS ..................................................................................................................................... 90 COMPUTER PROJECTS ................................................................................................................... 91 CHAPTER 5: ESTIMATION TECHNIQUES FOR ANALYZING ENDOGENOUSLY CREATED DATA ........................................................................... 93 5.1. INTRODUCTION ..................................................................................................................... 93 5.2. COLLECTING ENDOGENOUSLY CREATED DATA ................................................................. 93 5.3. TRANSIENT STATE VS STEADY-STATE SIMULATION ........................................................ 96 5.3.1. TRANSIENT-STATE SIMULATION .................................................................................... 96 5.3.2. STEADY-STATE SIMULATION ........................................................................................... 96 5.4. ESTIMATION TECHNIQUES FOR STEADY-STATE SIMULATION ........................................ 97 5.5. ESTIMATION OF THE CONFIDENCE INTERVAL OF THE MEAN ......................................... 98 5.5.1. ESTIMATION OF THE AUTOCORRELATION FUNCTION (ACF) .................................. 103