PERFORMANCE MODELING OF AUTOMATED MANUFACTURING SYSTEMS

N. VISWANADHAM Department of Computer Science and Automation Indian Institute of Science

Y NARAHARI Department of Computer Science and Automation Indian Institute of Science

PRENTICE HALL, Englewood Cliffs, New Jersey 07632

CONTENTS

PREFACE xiii

Chapter 1 INTRODUCTION 1

1.1 MODELING AUTOMATED MANUFACTURING SYSTEMS 1

1.1.1 Role of Performance Modeling 2 1.1.2 Performance Measures 3

1.2 PERFORMANCE MODELING TOOLS 4 1.2.1 Simulation Models 4 1.2.2 Analytical Models 5

1.3 ORGANIZATION OF THE BOOK 6

1.4 BIBLIOGRAPHIC NOTES AND BIBLIOGRAPHY 9

Chapter 2 AUTOMATED MANUFACTURING SYSTEMS 11

2.1 INTRODUCTION 12 2.1.1 History of Manufacturing 12 2.1.2 The Product Cycle 18 2.1.3 Manufacturing Automation 26 2.1.4 Economies of Scale and Scope 28

2.2 MANUFACTURING SYSTEMS 31 2.2.1 Input-Output Model 32 2.2.2 Plant Configurations 34

2.3 PERFORMANCE MEASURES 37 2.3.1 Manufacturing Lead Time 38 2.3.2 Work-in-Process 45

CONTENTS

2.3.3 Machine Utilization 46 2.3.4 Throughput 47 2.3.5 Capacity 47 2.3.6 Flexibility 48 2.3.7 Performability 49 2.3.8 Quality 52

2.4 COMPUTER-CONTROLLED MACHINES . 55 2.4.1 Numerically Controlled Machines . . . . . 55 2.4.2 Pallets and Fixtures 57 2.4.3 Machine Centers 59 2.4.4 Automated Inspection Systems 67

2.5 MATERIAL HANDLING SYSTEMS 72 2.5.1 Introduction 72 2.5.2 Conveyors 75 2.5.3 Industrial Robots 78 2.5.4 Automated Guided Vehicles 83

2.6 PLANT LAYOUT 95 2.6.1 Group Technology 96 2.6.2 Some Typical Layouts 97

2.7 FLEXIBLE MANUFACTURING SYSTEMS 102

2.7.1 Architecture of FMS 102 2.7.2 Automated Workpiece Flow 105 2.7.3 Automated Assembly Systems 109 2.7.4 Deadlocks in Automated Manufacturing

Systems 115 2.7.5 Performance Measures 118

2.8 COMPUTER CONTROL SYSTEMS 125 2.8.1 Control System Architecture 125 2.8.2 Factory Communications 131 2.8.3 Local Area Networks 133 2.8.4 Factory Networks 140 2.8.5 Open Systems Interconnection Model . . 142

CONTENTS vii

2.8.6 Network to Network Interconnections . . 146 2.8.7 Manufacturing Automation Protocol . . . 149 2.8.8 Database Management System 151

2.9 BIBLIOGRAPHIC NOTES AND BIBLIOGRAPHY 155

Chapter 3 MARKOV CHAIN MODELS 163

3.1 MEMORYLESS RANDOM VARIABLES . 164 3.1.1 Geometrie Random Variable 164 3.1.2 Exponential Random Variable 167

3.2 STOCHASTIC PROCESSES IN MANUFACTURING 171

3.2.1 Examples of Stochastic Processes . . . . 172 3.2.2 Poisson Process 173

3.3 DISCRETE TIME MARKOV CHAIN MODELS 179

3.3.1 Definitions and Notation 180 3.3.2 Sojourn Times in States 182 3.3.3 Examples of DTMCs in Manufacturing . 182 3.3.4 Chapman-Kolmogorov Equation 188 3.3.5 Steady-State Analysis 192

3.4 CONTINUOUS TIME MARKOV CHAIN MODELS 206

3.4.1 Definitions and Notation 206 3.4.2 Sojourn Times in States 207 3.4.3 Examples of CTMCs in Manufacturing . 209 3.4.4 Equations for CTMC Evolution 215 3.4.5 Analysis of Homogeneous CTMCs . . . 218 3.4.6 Embedded Markov Chain in CTMCs . . 232

3.5 AN EXAMPLE: MARKOV MODEL OF A TRANSFER LINE 239

3.5.1 Rate Balance Equations 240

viii CONTENTS

3.5.2 Steady-State Analysis 242 3.5.3 Performance Evaluation 243

3.6 BIRTH AND DEATH PROCESSES IN MANUFACTURING 246

3.6.1 Steady-State Analysis of BD Processes . 247 3.6.2 Typical BD Processes in Manufacturing 248

3.7 TIME REVERSIBLE MARKOV CHAINS IN MANUFACTURING 254

3.7.1 Time Reversible DTMCs 255 3.7.2 Time Reversible CTMCs 258

3.8 ABSORBING STATES AND MODELING OF DEADLOCKS 263

3.8.1 Examples of Absorbing States 264 3.8.2 Analysis of Markov Chains with Absorbing

States 268 3.8.3 Application to Examples 272

3.9 SEMI-MARKOV PROCESSES IN MANUFACTURING 276

3.9.1 Definition and Examples 277 3.9.2 Analysis of Semi-Markov Processes . . . 278 3.9.3 Application to Examples 279

3.10 TRANSIENT ANALYSIS OF MANUFACTURING SYSTEMS 283

3.10.1 Solution of Forward and Backward Equations 283

3.10.2 Distribution of Time to Deadlock . . . . 288

3.11 COMPUTATIONAL ISSUES IN MARKOV ANALYSIS 293

3.11.1 Computational Issues in Steady-State Analysis 293

3.11.2 Solution Methods for Steady-State Analysis 295

3.11.3 Time Scale Analysis Technique 297

CONTENTS ix

3.11.4 Computational Issues in Transient Analysis 301

3.11.5 Uniformization 303

3.12 BIBLIOGRAPHIC NOTES AND BIBLIOGRAPHY 307

Chapter 4 QUEUING MODELS 315

4.1 QUEUES: NOTATION AND EXAMPLES. 317 4.1.1 Notation for Queues 318 4.1.2 Examples of Queues in Manufacturing

Systems 319 4.1.3 Performance Measures 322 4.1.4 Little's Result 324

4.2 THE M/M/1 QUEUE 326 4.2.1 Steady-State Analysis of the M/M/1

Queue 326 4.2.2 Waiting-Time Distributions 330 4.2.3 The M/M/l/N Queue 333

4.3 THE M/M/m QUEUE 336 4.3.1 Steady-State Analysis 337 4.3.2 Departure Process of M/M/m Queue . . 340

4.4 BATCH ARRIVAL QUEUING SYSTEMS . 343

4.5 QUEUES WITH GENERAL DISTRIBUTIONS 347

4.5.1 The M/G/l Queue 348 4.5.2 The GI/M/1 Queue 355 4.5.3 The GI/G/1 Queue 358

4.6 QUEUES WITH BREAKDOWNS 359 4.6.1 Problem Formulation 359 4.6.2 Steady-State Analysis 360

X CONTENTS

4.7 ANALYSIS OF A FLEXIBLE MACHINE CENTER 363

4.7.1 Problem Formulation 364 4.7.2 Performance Measures 365 4.7.3 Analysis for Exhaustive Service and Gated

Service 366

4.8 QUEUING NETWORKS 369 4.8.1 Examples of QN Models in

Manufacturing 370 4.8.2 Little's Law in Queuing Networks . . . . 375

4.9 OPEN QUEUING NETWORKS 378 4.9.1 The Tandem Queue 378 4.9.2 An Open Queuing Network with

Feedback 382 4.9.3 An Open Central Server Model for FMS 385 4.9.4 Jackson's Network 388

4.10 CLOSED QUEUING NETWORKS 394 4.10.1 A Closed Transfer Line 395 4.10.2 The Closed Central Server Model . . . . 396 4.10.3 Gordon-Newell Networks 399 4.10.4 Computation of Normalization Constant 402 4.10.5 Computation of Performance Measures . 404 4.10.6 Mean Value Analysis 407

4.11 PRODUCT FORM QUEUING NETWORKS 411

4.11.1 Types of Service Centers 412 4.11.2 Closed Networks with Multiple Job

Classes 414

4.12 QUEUING NETWORKS WITH BLOCKING 421

4.12.1 Types of Blocking Mechanisms 422 4.12.2 Two-Node Open Network with В AS

Blocking 423

CONTENTS xi

4.12.3 Two-Node Closed Network with BAS Blocking 425

4.12.4 Central Server Model with Blocking . . 428

4.13 APPROXIMATE ANALYSIS OF QUEUING SYSTEMS 433

4.13.1 Non-Product Form Features in AMSs . . 434 4.13.2 Approximate Analysis Through

Aggregation 435 4.13.3 Approximations Employed in the AMS

Context 444

4.14 PERFORMABILITY ANALYSIS 446 4.14.1 Reliability and Availability Measures . . 446 4.14.2 Performability Measures 451 4.14.3 Machine Center with Infinite Waiting

Space 453 4.14.4 Central Server FMS Without Repair . . . 455

4.15 BIBLIOGRAPHIC NOTES AND BIBLIOGRAPHY 462

Chapter 5 PETRI NET MODELS 473

5.1 CLASSICAL PETRI NETS 474 5.1.1 Preliminary Definitions 475 5.1.2 Transition Firing and Reachability . . . . 479 5.1.3 Representational Power 481 5.1.4 Properties of Petri Nets 485

5.2 STOCHASTIC PETRI NETS 487 5.2.1 Exponential Timed Petri Nets 489

5.3 GENERALIZED STOCHASTIC PETRI NETS 497

5.3.1 Definition and Firing Rules 497 5.3.2 Analysis of GSPNs 502 5.3.3 Computation of Performance Measures . 506

xii CONTENTS

5.3.4 Representational Power of GSPN Models 508

5.4 GSPN MODELING OF KANBAN SYSTEMS 514

5.4.1 Description of the System 515 5.4.2 GSPN Model 517 5.4.3 Numerical Results 520

5.5 DEADLOCK ANALYSIS USING PETRI NETS 524

5.5.1 Deadlock Prevention 526 5.5.2 Deadlock Avoidance 527 5.5.3 Performance Evaluation in the Presence of

Deadlocks 537

5.6 EXTENDED CLASSES OF TIMED PETRI NETS 542

5.6.1 Colored Stochastic Petri Nets 542 5.6.2 Extended Stochastic Petri Nets 547 5.6.3 Petri Nets with Deterministic and Exponential

Firing Times 550 5.6.4 Space of Timed Petri Nets 555

5.7 INTEGRATED PFQN-GSPN MODELS . . 559

5.8 BIBLIOGRAPHIC NOTES AND BIBLIOGRAPHY 571

Chapter 6 EPILOGUE 581

INDEX 585