Holdings: Introduction to discrete event systems

Introduction to discrete event systems:

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Bibliographic Details
Main Authors:	Cassandras, Christos G. (Author), Lafortune, Stéphane (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2008
Edition:	2. ed.
Subjects:	Diskretes Ereignissystem
Online Access:	http://deposit.dnb.de/cgi-bin/dokserv?id=2813682&prov=M&dok_var=1&dok_ext=htm lizenzfrei Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	XXIII, 769 S. Ill., graph. Darst.
ISBN:	0387333320 9780387333328

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adam_text	Table of Contents Preface - Second Edition XV Preface xvii Organization of Book ................................ xxi Systems and Models l 1.1 INTRODUCTION ................................. 1 1.2 SYSTEM AND CONTROL BASICS ....................... 2 1.2.1 The Concept of System .......................... 2 1.2.2 The Input-Output Modeling Process ................... 2 1.2.3 The Concept of State ........................... 6 1.2.4 The State Space Modeling Process .................... 8 1.2.5 Sample Paths of Dynamic Systems .................... 13 1.2.6 State Spaces ................................ 15 1.2.7 The Concept of Control .......................... 20 1.2.8 The Concept of Feedback ......................... 22 1.2.9 Discrete-Time Systems ........................... 25 1.3 DISCRETE EVENT SYSTEMS ......................... 26 1.3.1 The Concept of Event ........................... 27 1.3.2 Characteristic Properties of Discrete Event Systems .......... 30 1.3.3 The Three Levels of Abstraction in the Study of Discrete Event Systems 33 1.3.4 Examples of Discrete Event Systems ................... 35 1.3.5 Hybrid Systems ............................... 43 1.4 SUMMARY OF SYSTEM CLASSIFICATIONS ................. 44 1.5 THE GOALS OF SYSTEM THEORY ...................... 46 SUMMARY ..................................... 48 PROBLEMS .................................... 48 SELECTED REFERENCES ........................... 50 Languages and Automata 53 2.1 INTRODUCTION ................................. 53 2.2 THE CONCEPTS OF LANGUAGES AND AUTOMATA ........... 54 2.2.1 Language Models of Discrete-Event Systems ............... 54 2.2.2 Automata .................................. 59 2.2.3 Languages Represented by Automata .................. 62 2.2.4 Nondeterministic Automata ........................ 69 2.2.5 Automata with Inputs and Outputs ................... 72 2.3 OPERATIONS ON AUTOMATA......................... 74 2.3.1 Unary Operations ............................. 75 2.3.2 Composition Operations .......................... 77 2.3.3 State Space Refinement .......................... 85 2.3.4 Observer Automata ............................ 87 2.3.5 Equivalence of Automata ......................... 90 2.4 FINITE-STATE AUTOMATA .......................... 92 2.4.1 Definition and Properties of Regular Languages ............. 92 2.4.2 Regular Expressions ............................ 95 2.4.3 State Space Minimization ......................... 96 2.5 ANALYSIS OF DISCRETE-EVENT SYSTEMS ................ 100 2.5.1 Safety and Blocking Properties ...................... 101 2.5.2 Partially-Observed DES .......................... 102 2.5.3 Event Diagnosis .............................. 108 2.5.4 Software Tools and Computational Complexity Issues ......... 117 2.5.5 Formal Verification and Model Checking ................. 118 SUMMARY ..................................... 119 PROBLEMS .................................... 120 SELECTED REFERENCES ........................... 130 Supervisory Control 133 3.1 INTRODUCTION .................................133 3.2 FEEDBACK CONTROL WITH SUPERVISORS ................135 3.2.1 Controlled Discrete Event Systems ....................135 3.2.2 Control Under Partial Observation ....................137 3.3 SPECIFICATIONS ON CONTROLLED SYSTEM ...............139 3.3.1 Modeling of Specifications as Automata .................140 3.3.2 The Need for Formal Methods ......................143 3.4 CONTROL WITH PARTIAL CONTROLLABILITY ..............145 3.4.1 Controllability Theorem ..........................145 3.4.2 Realization of Supervisors .........................148 3.4.3 The Property of Controllability ......................151 3.4.4 Some Supervisory Control Problems and Their Solutions ........156 3.4.5 Computation of K^0 : Prefix-Closed Case ................159 3.4.6 Computation of KiC ............................161 3.5 NONBLOCKING CONTROL ...........................163 3.5.1 Nonblocking Controllability Theorem ..................163 3.5.2 Nonblocking Supervisory Control .....................164 3.5.3 Computation of K^c: General Case ...................167 3.5.4 Dealing with Blocking Supervisors ....................170 3.6 CONTROL WITH MODULAR SPECIFICATIONS ..............174 3.7 CONTROL UNDER PARTIAL OBSERVATION ................178 3.7.1 Controllability and Observability Theorem ...............178 3.7.2 Realization of P-Supervisors ........................185 3.7.3 The Property of Observability ......................188 3.7.4 Supervisory Control Problems Under Partial Observation .......193 3.7.5 The Property of Normality ........................195 3.8 DECENTRALIZED CONTROL .........................199 3.8.1 Conjunctive Architecture .........................201 3.8.2 Disjunctive Architecture ..........................205 3.8.3 Combined Architecture ..........................208 3.8.4 Realization of Decentralized Supervisors .................210 3.8.5 The Property of Coobservability .....................210 3.8.6 Undecidability in Decentralized Control .................211 SUMMARY .....................................212 PROBLEMS ....................................213 SELECTED REFERENCES ...........................219 Petri Nets 223 4.1 INTRODUCTION .................................223 4.2 PETRI NET BASICS ...............................224 4.2.1 Petri Net Notation and Definitions ....................224 4.2.2 Petri Net Markings and State Spaces ...................226 4.2.3 Petri Net Dynamics ............................227 4.2.4 Petri Net Languages ............................231 4.2.5 Petri Net Models for Queueing Systems .................233 4.3 COMPARISON OF PETRI NETS AND AUTOMATA .............236 4.4 ANALYSIS OF PETRI NETS ..........................239 4.4.1 Problem Classification ...........................239 4.4.2 The Coverability Tree ...........................244 4.4.3 Applications of the Coverability Tree ...................247 4.4.4 Linear-Algebraic Techniques ........................250 4.5 CONTROL OF PETRI NETS ..........................253 4.5.1 Petri Nets and Supervisory Control Theory ...............254 4.5.2 State-Based Control of Petri Nets ....................257 SUMMARY .....................................260 PROBLEMS ....................................261 SELECTED REFERENCES ...........................266 Timed and Hybrid Models 269 5.1 INTRODUCTION .................................269 5.2 TIMED AUTOMATA ...............................270 5.2.1 The Clock Structure ............................271 5.2.2 Event Timing Dynamics ..........................275 5.2.3 A State Space Model ............................278 5.2.4 Queueing Systems as Timed Automata .................283 5.2.5 The Event Scheduling Scheme .......................285 5.3 TIMED PETRI NETS ...............................286 5.3.1 Timed Petri Net Dynamics ........................288 5.3.2 Queueing Systems as Timed Petri Nets .................290 5.4 DIOID ALGEBRAS ................................292 5.4.1 Basic Properties of the (max, +) Algebra ................292 5.4.2 Modeling Queueing Systems in the (max, +) Algebra .........294 5.5 ALTERNATIVE TIMED MODELS .......................297 5.6 TIMED AUTOMATA WITH GUARDS .....................299 5.6.1 Model Definition ..............................300 5.6.2 Model Execution ..............................303 5.6.3 Parallel Composition ............................305 5.6.4 Untiming ..................................307 5.7 HYBRID MODELS ................................311 5.7.1 Hybrid Automata .............................312 SUMMARY .....................................318 PROBLEMS ....................................319 SELECTED REFERENCES ...........................324 Stochastic Timed Automata 327 6.1 INTRODUCTION .................................327 6.2 STOCHASTIC PROCESS BASICS ........................328 6.2.1 Continuous-state and Discrete-state Stochastic Processes .......329 6.2.2 Continuous-time and Discrete-time Stochastic Processes ........329 6.2.3 Some Important Classes of Stochastic Processes .............329 6.3 STOCHASTIC CLOCK STRUCTURES .....................333 6.4 STOCHASTIC TIMED AUTOMATA ......................334 6.5 THE GENERALIZED SEMI-MARKOV PROCESS ..............336 6.5.1 Queueing Systems as Stochastic Timed Automata ...........339 6.5.2 GSMP Analysis ...............................340 6.6 THE POISSON COUNTING PROCESS .....................341 6.7 PROPERTIES OF THE POISSON PROCESS .................347 6.7.1 Exponentially Distributed Interevent Times ...............347 6.7.2 The Memoryless Property .........................348 6.7.3 Superposition of Poisson Processes ....................351 6.7.4 The Residual Lifetime Paradox ......................353 6.8 AUTOMATA WITH POISSON CLOCK STRUCTURE ............355 6.8.1 Distribution of Interevent Times .....................356 6.8.2 Distribution of Events ...........................357 6.8.3 Markov Chains ...............................359 6.9 EXTENSIONS OF THE GSMP .........................360 SUMMARY .....................................362 PROBLEMS ....................................364 SELECTED REFERENCES ...........................367 Markov Chains 369 7.1 INTRODUCTION .................................369 7.2 DISCRETE-TIME MARKOV CHAINS .....................370 7.2.1 Model Specification ............................370 7.2.2 Transition Probabilities and the Chapman-Kolmogorov Equations . . 371 7.2.3 Homogeneous Markov Chains .......................372 7.2.4 The Transition Probability Matrix ....................374 7.2.5 State Holding Times ............................377 7.2.6 State Probabilities .............................378 7.2.7 Transient Analysis .............................378 7.2.8 Classification of States ...........................382 7.2.9 Steady State Analysis ...........................391 7.2.10 Irreducible Markov Chains ........................392 7.2.11 Reducible Markov Chains .........................397 7.3 CONTINUOUS-TIME MARKOV CHAINS ...................399 7.3.1 Model Specification ............................400 7.3.2 Transition Functions ............................400 7.3.3 The Transition Rate Matrix ........................401 7.3.4 Homogeneous Markov Chains .......................402 7.3.5 State Holding Times ............................402 7.3.6 Physical Interpretation and Properties of the Transition Rate Matrix . 403 7.3.7 Transition Probabilities ..........................405 7.3.8 State Probabilities .............................407 7.3.9 Transient Analysis .............................407 7.3.10 Steady State Analysis ...........................410 7.4 BIRTH-DEATH CHAINS .............................412 7.4.1 The Pure Birth Chain ...........................414 7.4.2 The Poisson Process Revisited ......................415 7.4.3 Steady State Analysis of Birth-Death Chains ..............415 7.5 UNIFORMIZATION OF MARKOV CHAINS ..................417 SUMMARY .....................................421 PROBLEMS ....................................422 SELECTED REFERENCES ...........................427 8 Introduction to Queueing Theory 429 8.1 INTRODUCTION .................................429 8.2 SPECIFICATION OF QUEUEING MODELS ..................430 8.2.1 Stochastic Models for Arrival and Service Processes ..........430 8.2.2 Structural Parameters ...........................431 8.2.3 Operating Policies .............................431 8.2.4 The A/B/m/K Notation .........................432 8.2.5 Open and Closed Queueing Systems ...................434 8.3 PERFORMANCE OF A QUEUEING SYSTEM ................434 8.4 QUEUEING SYSTEM DYNAMICS .......................437 8.5 LITTLE S LAW ..................................439 8.6 SIMPLE MARKOVIAN QUEUEING SYSTEMS ................442 8.6.1 The M/M/l Queueing System ......................444 8.6.2 The M/M/m Queueing System ......................448 8.6.3 The M/M/oo Queueing System ......................452 8.6.4 The M/M/l/ K Queueing System ....................454 8.6.5 The M/M/m/m Queueing System ....................458 8.6.6 The M/M/l//N Queueing System ....................459 8.6.7 The M/M/m/K/N Queueing System ..................461 8.7 MARKOVIAN QUEUEING NETWORKS ....................462 8.7.1 The Departure Process of the M/M/l Queueing System ........464 8.7.2 Open Queueing Networks .........................467 8.7.3 Closed Queueing Networks ........................471 8.7.4 Product Form Networks ..........................476 8.8 NON-MARKOVIAN QUEUEING SYSTEMS ..................478 8.8.1 The Method of Stages ...........................479 8.8.2 Mean Value Analysis of the M/G/l Queueing System .........482 8.8.3 Software Tools for the Analysis of General Queueing Networks .... 488 SUMMARY .....................................490 PROBLEMS ....................................491 SELECTED REFERENCES ...........................496 θ Controlled Markov Chains 499 9.1 INTRODUCTION .................................499 9.2 APPLYING CONTROL IN MARKOV CHAINS ...............500 9.3 MARKOV DECISION PROCESSES .......................502 9.3.1 Cost Criteria ................................503 9.3.2 Uniformization ...............................504 9.3.3 The Basic Markov Decision Problem ...................506 9.4 SOLVING MARKOV DECISION PROBLEMS .................510 9.4.1 The Basic Idea of Dynamic Programming ................510 9.4.2 Dynamic Programming and the Optimality Equation ..........514 9.4.3 Extensions to Unbounded and Undiscounted Costs ...........524 9.4.4 Optimization of the Average Cost Criterion ...............532 9.5 CONTROL OF QUEUEING SYSTEMS .....................535 9.5.1 The Admission Problem ..........................537 9.5.2 The Routing Problem ...........................542 9.5.3 The Scheduling Problem ..........................546 SUMMARY .....................................552 PROBLEMS ....................................553 SELECTED REFERENCES ...........................554 10 Introduction to Discrete-Event Simulation 557 10.1 INTRODUCTION ................................557 10.2 THE EVENT SCHEDULING SCHEME ...................558 10.2.1 Simulation of a Simple Queueing System ..... ..........561 10.3 THE PROCESS-ORIENTED SIMULATION SCHEME ...........573 10.4 DISCRETE-EVENT SIMULATION LANGUAGES .............574 10.5 RANDOM NUMBER GENERATION .....................576 10.5.1 The Linear Congruential Technique ..................577 10.6 RANDOM VARIATE GENERATION .....................578 10.6.1 The Inverse Transform Technique ...................579 10.6.2 The Convolution Technique ......................582 10.6.3 The Composition Technique ......................583 10.6.4 The Acceptance-Rejection Technique .................583 10.7 OUTPUT ANALYSIS ..............................587 10.7.1 Simulation Characterizations .....................587 10.7.2 Parameter Estimation .........................589 10.7.3 Output Analysis of Terminating Simulations .............595 10.7.4 Output Analysis of Non- Terminating Simulations ..........598 SUMMARY ...................................604 PROBLEMS ...................................605 SELECTED REFERENCES ..........................614 11 Sensitivity Analysis and Concurrent Estimation 617 11.1 INTRODUCTION ................................617 11.2 SAMPLE FUNCTIONS AND THEIR DERIVATIVES ...........619 11.2.1 Performance Sensitivities .......................620 11.2.2 The Uses of Sensitivity Information ..................621 11.3 PERTURBATION ANALYSIS: SOME KEY IDEAS .............623 11.4 PA OF GI/G/l QUEUEING SYSTEMS ...................629 11.4.1 Perturbation Generation ........................630 11.4.2 Perturbation Propagation .......................634 11.4.3 Infinitesimal Perturbation Analysis (IPA) ..............639 11.4.4 Implementation of IPA for the GI/G/l System ...........649 11.5 IPA FOR STOCHASTIC TIMED AUTOMATA ...............650 11.5.1 Event Time Derivatives ........................652 11.5.2 Sample Function Derivatives .....................655 11.5.3 Performance Measure Derivatives ...................657 11.5.4 IPA Applications ............................665 11.6 SENSITIVITY ESTIMATION REVISITED .................670 11.7 EXTENSIONS OF IPA .............................673 11.7.1 Discontinuities due to Multiple Customer Classes ..........673 11.7.2 Discontinuities due to Routing Decisions ...............678 11.7.3 Discontinuities due to Blocking: IPA with Event Rescheduling (RIPA) ..........................680 11.8 SMOOTHED PERTURBATION ANALYSIS (SPA) .............681 11.8.1 Systems with Real-Time Constraints .................685 11.8.2 Marking and Phantomizing Techniques ................687 11.9 IPA FOR STOCHASTIC HYBRID AUTOMATA ..............691 11.9.1 Stochastic Fluid Models (SFMs) ...................693 11.9.2 Sample paths of SFMs .........................695 11.9.3 Comparing SFMs to Their DES Counterparts ............697 11.9.4 IPA for a Single-Class Single-Node SFM ...............700 11.9.5 IPA for SFMs with Multiple Classes, Multiple Nodes and Feedback ..............................705 11.10 PA FOR FINITE PARAMETER CHANGES .................705 11.11 CONCURRENT ESTIMATION ........................706 11.11.1 The Sample Path Constructability Problem .............707 11.11.2 Uses of Concurrent Estimation: Rapid Learning .........709 11.11.3 Sample Path Constructability Conditions ..............710 11.11.4 The Standard Clock Approach ....................714 11.11.5 Augmented System Analysis .....................718 11.11.6 The Time Warping Algorithm ...................725 SUMMARY ...................................730 PROBLEMS ...................................732 SELECTED REFERENCES ..........................736 I Review of Probability Theory 741 1.1 BASIC CONCEPTS AND DEFINITIONS ....................741 1.2 CONDITIONAL PROBABILITY .........................743 1.3 RANDOM VARIABLES ..............................744 xiv I Table of Contents 1.4 CONDITIONAL DISTRIBUTIONS .......................745 1.5 FUNCTIONS OF RANDOM VARIABLES ...................746 1.6 EXPECTATION ..................................747 1.7 CHARACTERISTIC FUNCTIONS ........................748 1.8 RANDOM SEQUENCES AND RANDOM PROCESSES ...........751 II IPA Estimator 755 Index 761 About the Authors 771
adam_txt	Table of Contents Preface - Second Edition XV Preface xvii Organization of Book . xxi Systems and Models l 1.1 INTRODUCTION . 1 1.2 SYSTEM AND CONTROL BASICS . 2 1.2.1 The Concept of System . 2 1.2.2 The Input-Output Modeling Process . 2 1.2.3 The Concept of State . 6 1.2.4 The State Space Modeling Process . 8 1.2.5 Sample Paths of Dynamic Systems . 13 1.2.6 State Spaces . 15 1.2.7 The Concept of Control . 20 1.2.8 The Concept of Feedback . 22 1.2.9 Discrete-Time Systems . 25 1.3 DISCRETE EVENT SYSTEMS . 26 1.3.1 The Concept of Event . 27 1.3.2 Characteristic Properties of Discrete Event Systems . 30 1.3.3 The Three Levels of Abstraction in the Study of Discrete Event Systems 33 1.3.4 Examples of Discrete Event Systems . 35 1.3.5 Hybrid Systems . 43 1.4 SUMMARY OF SYSTEM CLASSIFICATIONS . 44 1.5 THE GOALS OF SYSTEM THEORY . 46 SUMMARY . 48 PROBLEMS . 48 SELECTED REFERENCES . 50 Languages and Automata 53 2.1 INTRODUCTION . 53 2.2 THE CONCEPTS OF LANGUAGES AND AUTOMATA . 54 2.2.1 Language Models of Discrete-Event Systems . 54 2.2.2 Automata . 59 2.2.3 Languages Represented by Automata . 62 2.2.4 Nondeterministic Automata . 69 2.2.5 Automata with Inputs and Outputs . 72 2.3 OPERATIONS ON AUTOMATA. 74 2.3.1 Unary Operations . 75 2.3.2 Composition Operations . 77 2.3.3 State Space Refinement . 85 2.3.4 Observer Automata . 87 2.3.5 Equivalence of Automata . 90 2.4 FINITE-STATE AUTOMATA . 92 2.4.1 Definition and Properties of Regular Languages . 92 2.4.2 Regular Expressions . 95 2.4.3 State Space Minimization . 96 2.5 ANALYSIS OF DISCRETE-EVENT SYSTEMS . 100 2.5.1 Safety and Blocking Properties . 101 2.5.2 Partially-Observed DES . 102 2.5.3 Event Diagnosis . 108 2.5.4 Software Tools and Computational Complexity Issues . 117 2.5.5 Formal Verification and Model Checking . 118 SUMMARY . 119 PROBLEMS . 120 SELECTED REFERENCES . 130 Supervisory Control 133 3.1 INTRODUCTION .133 3.2 FEEDBACK CONTROL WITH SUPERVISORS .135 3.2.1 Controlled Discrete Event Systems .135 3.2.2 Control Under Partial Observation .137 3.3 SPECIFICATIONS ON CONTROLLED SYSTEM .139 3.3.1 Modeling of Specifications as Automata .140 3.3.2 The Need for Formal Methods .143 3.4 CONTROL WITH PARTIAL CONTROLLABILITY .145 3.4.1 Controllability Theorem .145 3.4.2 Realization of Supervisors .148 3.4.3 The Property of Controllability .151 3.4.4 Some Supervisory Control Problems and Their Solutions .156 3.4.5 Computation of K^0': Prefix-Closed Case .159 3.4.6 Computation of KiC .161 3.5 NONBLOCKING CONTROL .163 3.5.1 Nonblocking Controllability Theorem .163 3.5.2 Nonblocking Supervisory Control .164 3.5.3 Computation of K^c: General Case .167 3.5.4 Dealing with Blocking Supervisors .170 3.6 CONTROL WITH MODULAR SPECIFICATIONS .174 3.7 CONTROL UNDER PARTIAL OBSERVATION .178 3.7.1 Controllability and Observability Theorem .178 3.7.2 Realization of P-Supervisors .185 3.7.3 The Property of Observability .188 3.7.4 Supervisory Control Problems Under Partial Observation .193 3.7.5 The Property of Normality .195 3.8 DECENTRALIZED CONTROL .199 3.8.1 Conjunctive Architecture .201 3.8.2 Disjunctive Architecture .205 3.8.3 Combined Architecture .208 3.8.4 Realization of Decentralized Supervisors .210 3.8.5 The Property of Coobservability .210 3.8.6 Undecidability in Decentralized Control .211 SUMMARY .212 PROBLEMS .213 SELECTED REFERENCES .219 Petri Nets 223 4.1 INTRODUCTION .223 4.2 PETRI NET BASICS .224 4.2.1 Petri Net Notation and Definitions .224 4.2.2 Petri Net Markings and State Spaces .226 4.2.3 Petri Net Dynamics .227 4.2.4 Petri Net Languages .231 4.2.5 Petri Net Models for Queueing Systems .233 4.3 COMPARISON OF PETRI NETS AND AUTOMATA .236 4.4 ANALYSIS OF PETRI NETS .239 4.4.1 Problem Classification .239 4.4.2 The Coverability Tree .244 4.4.3 Applications of the Coverability Tree .247 4.4.4 Linear-Algebraic Techniques .250 4.5 CONTROL OF PETRI NETS .253 4.5.1 Petri Nets and Supervisory Control Theory .254 4.5.2 State-Based Control of Petri Nets .257 SUMMARY .260 PROBLEMS .261 SELECTED REFERENCES .266 Timed and Hybrid Models 269 5.1 INTRODUCTION .269 5.2 TIMED AUTOMATA .270 5.2.1 The Clock Structure .271 5.2.2 Event Timing Dynamics .275 5.2.3 A State Space Model .278 5.2.4 Queueing Systems as Timed Automata .283 5.2.5 The Event Scheduling Scheme .285 5.3 TIMED PETRI NETS .286 5.3.1 Timed Petri Net Dynamics .288 5.3.2 Queueing Systems as Timed Petri Nets .290 5.4 DIOID ALGEBRAS .292 5.4.1 Basic Properties of the (max, +) Algebra .292 5.4.2 Modeling Queueing Systems in the (max, +) Algebra .294 5.5 ALTERNATIVE TIMED MODELS .297 5.6 TIMED AUTOMATA WITH GUARDS .299 5.6.1 Model Definition .300 5.6.2 Model Execution .303 5.6.3 Parallel Composition .305 5.6.4 Untiming .307 5.7 HYBRID MODELS .311 5.7.1 Hybrid Automata .312 SUMMARY .318 PROBLEMS .319 SELECTED REFERENCES .324 Stochastic Timed Automata 327 6.1 INTRODUCTION .327 6.2 STOCHASTIC PROCESS BASICS .328 6.2.1 Continuous-state and Discrete-state Stochastic Processes .329 6.2.2 Continuous-time and Discrete-time Stochastic Processes .329 6.2.3 Some Important Classes of Stochastic Processes .329 6.3 STOCHASTIC CLOCK STRUCTURES .333 6.4 STOCHASTIC TIMED AUTOMATA .334 6.5 THE GENERALIZED SEMI-MARKOV PROCESS .336 6.5.1 Queueing Systems as Stochastic Timed Automata .339 6.5.2 GSMP Analysis .340 6.6 THE POISSON COUNTING PROCESS .341 6.7 PROPERTIES OF THE POISSON PROCESS .347 6.7.1 Exponentially Distributed Interevent Times .347 6.7.2 The Memoryless Property .348 6.7.3 Superposition of Poisson Processes .351 6.7.4 The Residual Lifetime Paradox .353 6.8 AUTOMATA WITH POISSON CLOCK STRUCTURE .355 6.8.1 Distribution of Interevent Times .356 6.8.2 Distribution of Events .357 6.8.3 Markov Chains .359 6.9 EXTENSIONS OF THE GSMP .360 SUMMARY .362 PROBLEMS .364 SELECTED REFERENCES .367 Markov Chains 369 7.1 INTRODUCTION .369 7.2 DISCRETE-TIME MARKOV CHAINS .370 7.2.1 Model Specification .370 7.2.2 Transition Probabilities and the Chapman-Kolmogorov Equations . . 371 7.2.3 Homogeneous Markov Chains .372 7.2.4 The Transition Probability Matrix .374 7.2.5 State Holding Times .377 7.2.6 State Probabilities .378 7.2.7 Transient Analysis .378 7.2.8 Classification of States .382 7.2.9 Steady State Analysis .391 7.2.10 Irreducible Markov Chains .392 7.2.11 Reducible Markov Chains .397 7.3 CONTINUOUS-TIME MARKOV CHAINS .399 7.3.1 Model Specification .400 7.3.2 Transition Functions .400 7.3.3 The Transition Rate Matrix .401 7.3.4 Homogeneous Markov Chains .402 7.3.5 State Holding Times .402 7.3.6 Physical Interpretation and Properties of the Transition Rate Matrix . 403 7.3.7 Transition Probabilities .405 7.3.8 State Probabilities .407 7.3.9 Transient Analysis .407 7.3.10 Steady State Analysis .410 7.4 BIRTH-DEATH CHAINS .412 7.4.1 The Pure Birth Chain .414 7.4.2 The Poisson Process Revisited .415 7.4.3 Steady State Analysis of Birth-Death Chains .415 7.5 UNIFORMIZATION OF MARKOV CHAINS .417 SUMMARY .421 PROBLEMS .422 SELECTED REFERENCES .427 8 Introduction to Queueing Theory 429 8.1 INTRODUCTION .429 8.2 SPECIFICATION OF QUEUEING MODELS .430 8.2.1 Stochastic Models for Arrival and Service Processes .430 8.2.2 Structural Parameters .431 8.2.3 Operating Policies .431 8.2.4 The A/B/m/K Notation .432 8.2.5 Open and Closed Queueing Systems .434 8.3 PERFORMANCE OF A QUEUEING SYSTEM .434 8.4 QUEUEING SYSTEM DYNAMICS .437 8.5 LITTLE'S LAW .439 8.6 SIMPLE MARKOVIAN QUEUEING SYSTEMS .442 8.6.1 The M/M/l Queueing System .444 8.6.2 The M/M/m Queueing System .448 8.6.3 The M/M/oo Queueing System .452 8.6.4 The M/M/l/'K Queueing System .454 8.6.5 The M/M/m/m Queueing System .458 8.6.6 The M/M/l//N Queueing System .459 8.6.7 The M/M/m/K/N Queueing System .461 8.7 MARKOVIAN QUEUEING NETWORKS .462 8.7.1 The Departure Process of the M/M/l Queueing System .464 8.7.2 Open Queueing Networks .467 8.7.3 Closed Queueing Networks .471 8.7.4 Product Form Networks .476 8.8 NON-MARKOVIAN QUEUEING SYSTEMS .478 8.8.1 The Method of Stages .479 8.8.2 Mean Value Analysis of the M/G/l Queueing System .482 8.8.3 Software Tools for the Analysis of General Queueing Networks . 488 SUMMARY .490 PROBLEMS .491 SELECTED REFERENCES .496 θ Controlled Markov Chains 499 9.1 INTRODUCTION .499 9.2 APPLYING "CONTROL" IN MARKOV CHAINS .500 9.3 MARKOV DECISION PROCESSES .502 9.3.1 Cost Criteria .503 9.3.2 Uniformization .504 9.3.3 The Basic Markov Decision Problem .506 9.4 SOLVING MARKOV DECISION PROBLEMS .510 9.4.1 The Basic Idea of Dynamic Programming .510 9.4.2 Dynamic Programming and the Optimality Equation .514 9.4.3 Extensions to Unbounded and Undiscounted Costs .524 9.4.4 Optimization of the Average Cost Criterion .532 9.5 CONTROL OF QUEUEING SYSTEMS .535 9.5.1 The Admission Problem .537 9.5.2 The Routing Problem .542 9.5.3 The Scheduling Problem .546 SUMMARY .552 PROBLEMS .553 SELECTED REFERENCES .554 10 Introduction to Discrete-Event Simulation 557 10.1 INTRODUCTION .557 10.2 THE EVENT SCHEDULING SCHEME .558 10.2.1 Simulation of a Simple Queueing System .'.561 10.3 THE PROCESS-ORIENTED SIMULATION SCHEME .573 10.4 DISCRETE-EVENT SIMULATION LANGUAGES .574 10.5 RANDOM NUMBER GENERATION .576 10.5.1 The Linear Congruential Technique .577 10.6 RANDOM VARIATE GENERATION .578 10.6.1 The Inverse Transform Technique .579 10.6.2 The Convolution Technique .582 10.6.3 The Composition Technique .583 10.6.4 The Acceptance-Rejection Technique .583 10.7 OUTPUT ANALYSIS .587 10.7.1 Simulation Characterizations .587 10.7.2 Parameter Estimation .589 10.7.3 Output Analysis of Terminating Simulations .595 10.7.4 Output Analysis of Non- Terminating Simulations .598 SUMMARY .604 PROBLEMS .605 SELECTED REFERENCES .614 11 Sensitivity Analysis and Concurrent Estimation 617 11.1 INTRODUCTION .617 11.2 SAMPLE FUNCTIONS AND THEIR DERIVATIVES .619 11.2.1 Performance Sensitivities .620 11.2.2 The Uses of Sensitivity Information .621 11.3 PERTURBATION ANALYSIS: SOME KEY IDEAS .623 11.4 PA OF GI/G/l QUEUEING SYSTEMS .629 11.4.1 Perturbation Generation .630 11.4.2 Perturbation Propagation .634 11.4.3 Infinitesimal Perturbation Analysis (IPA) .639 11.4.4 Implementation of IPA for the GI/G/l System .649 11.5 IPA FOR STOCHASTIC TIMED AUTOMATA .650 11.5.1 Event Time Derivatives .652 11.5.2 Sample Function Derivatives .655 11.5.3 Performance Measure Derivatives .657 11.5.4 IPA Applications .665 11.6 SENSITIVITY ESTIMATION REVISITED .670 11.7 EXTENSIONS OF IPA .673 11.7.1 Discontinuities due to Multiple Customer Classes .673 11.7.2 Discontinuities due to Routing Decisions .678 11.7.3 Discontinuities due to Blocking: IPA with Event Rescheduling (RIPA) .680 11.8 SMOOTHED PERTURBATION ANALYSIS (SPA) .681 11.8.1 Systems with Real-Time Constraints .685 11.8.2 Marking and Phantomizing Techniques .687 11.9 IPA FOR STOCHASTIC HYBRID AUTOMATA .691 11.9.1 Stochastic Fluid Models (SFMs) .693 11.9.2 Sample paths of SFMs .695 11.9.3 Comparing SFMs to Their DES Counterparts .697 11.9.4 IPA for a Single-Class Single-Node SFM .700 11.9.5 IPA for SFMs with Multiple Classes, Multiple Nodes and Feedback .705 11.10 PA FOR FINITE PARAMETER CHANGES .705 11.11 CONCURRENT ESTIMATION .706 11.11.1 The Sample Path Constructability Problem .707 11.11.2 Uses of Concurrent Estimation: "Rapid Learning" .709 11.11.3 Sample Path Constructability Conditions .710 11.11.4 The Standard Clock Approach .714 11.11.5 Augmented System Analysis .718 11.11.6 The "Time Warping" Algorithm .725 SUMMARY .730 PROBLEMS .732 SELECTED REFERENCES .736 I Review of Probability Theory 741 1.1 BASIC CONCEPTS AND DEFINITIONS .741 1.2 CONDITIONAL PROBABILITY .743 1.3 RANDOM VARIABLES .744 xiv I Table of Contents 1.4 CONDITIONAL DISTRIBUTIONS .745 1.5 FUNCTIONS OF RANDOM VARIABLES .746 1.6 EXPECTATION .747 1.7 CHARACTERISTIC FUNCTIONS .748 1.8 RANDOM SEQUENCES AND RANDOM PROCESSES .751 II IPA Estimator 755 Index 761 About the Authors 771
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spelling	Cassandras, Christos G. Verfasser aut Introduction to discrete event systems Christos G. Cassandras ; Stephane Lafortune 2. ed. Berlin [u.a.] Springer 2008 XXIII, 769 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Diskretes Ereignissystem (DE-588)4196828-1 gnd rswk-swf Diskretes Ereignissystem (DE-588)4196828-1 s DE-604 Lafortune, Stéphane Verfasser aut http://deposit.dnb.de/cgi-bin/dokserv?id=2813682&prov=M&dok_var=1&dok_ext=htm http://www.gbv.de/dms/ilmenau/toc/512945640.PDF Inhaltsverzeichnis lizenzfrei http://www3.ub.tu-berlin.de/ihv/001780437.pdf Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015011003&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Cassandras, Christos G. Lafortune, Stéphane Introduction to discrete event systems Diskretes Ereignissystem (DE-588)4196828-1 gnd
subject_GND	(DE-588)4196828-1
title	Introduction to discrete event systems
title_auth	Introduction to discrete event systems
title_exact_search	Introduction to discrete event systems
title_exact_search_txtP	Introduction to discrete event systems
title_full	Introduction to discrete event systems Christos G. Cassandras ; Stephane Lafortune
title_fullStr	Introduction to discrete event systems Christos G. Cassandras ; Stephane Lafortune
title_full_unstemmed	Introduction to discrete event systems Christos G. Cassandras ; Stephane Lafortune
title_short	Introduction to discrete event systems
title_sort	introduction to discrete event systems
topic	Diskretes Ereignissystem (DE-588)4196828-1 gnd
topic_facet	Diskretes Ereignissystem
url	http://deposit.dnb.de/cgi-bin/dokserv?id=2813682&prov=M&dok_var=1&dok_ext=htm http://www.gbv.de/dms/ilmenau/toc/512945640.PDF http://www3.ub.tu-berlin.de/ihv/001780437.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015011003&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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