Modelling with Generalized Stochastic Petri Nets

INTRODUCTION......Page 20
Shared Resources......Page 23
Fork and Join......Page 27
Token Ring LAN......Page 30
Petri Net Models......Page 34
Models, Systems, and Nets......Page 37
System Dynamics......Page 38
Enabling and firing rules......Page 39
Reachability set and reachability graph......Page 41
Modelling issues......Page 44
Typical situations in the PN system evolution......Page 47
Properties of Petri Nets......Page 52
Structural Analysis Techniques......Page 54
Linear algebraic techniques......Page 55
Graph-based structural techniques......Page 63
State Space Analysis Techniques......Page 66
The Motivations for Timing......Page 70
Timed Transitions......Page 72
Immediate transitions......Page 74
Two examples......Page 75
Parallelism and Conflict......Page 77
Memory......Page 80
An example with the enabling memory policy......Page 82
Multiple Enabling......Page 84
Performance Measures......Page 89
Definition and Dynamics......Page 92
Conflicts, Confusion and Priority......Page 96
Properties of Priority PN Models......Page 100
Linear algebraic techniques......Page 103
Graph based analysis......Page 104
Reachability Analysis Techniques......Page 106
Exponential Distributions for Transition Delays......Page 112
Mixing Exponentially Distributed and Null Delays......Page 117
The Definition of a GSPN Model......Page 121
An Example of a GSPN Model......Page 123
Some Fine Points......Page 126
The Stochastic Process Associated with a SPN......Page 128
SPN performance indices......Page 130
An example SPN system......Page 131
The Stochastic Process Associated with a GSPN......Page 136
Marking dependency......Page 142
An example GSPN system......Page 144
Numerical Solution of GSPN Systems......Page 147
Evaluation of the steady-state probability distribution for the example GSPN system......Page 155
Performance analysis of the example GSPN......Page 157
Reducing GSPNs to SPNs......Page 159
Simulation of GSPN Systems......Page 166
Simulation of the example GSPN system......Page 168
The Central Server Model Example......Page 170
CPU interruptions......Page 173
CPU memory policies......Page 177
Phase-Type Distributions......Page 179
Erlang distributions......Page 180
Numerical evaluation......Page 189
General Phase-Type Distributions......Page 190
MODELLING FLEXIBLE MANUFACTURING SYSTEMS......Page 192
Flexible Manufacturing Systems......Page 193
A Kanban System......Page 194
Structural analysis of the GSPN model of the Kanban system......Page 197
Performance analysis of the Kanban system......Page 198
Push Production Systems......Page 201
Structural analysis of the push production systems......Page 208
Performance analysis of the system with AGV transport......Page 211
Polling Systems......Page 220
Modelling Random Polling the Easy Way......Page 225
The first complete random polling model......Page 226
Beginning to Exploit Symmetries......Page 229
Walking before choosing?......Page 230
Abstracting from the Queue Identifiers......Page 232
The abstract GSPN model......Page 234
Walking before choosing!......Page 237
From GSPNs to SPNs......Page 238
Introduction to the Static Analysis of Concurrent Programs......Page 246
Languages of interest......Page 248
The translation procedure......Page 250
An Example of Translation......Page 254
Modelling Control Variables to Reduce Nonfaults......Page 260
Stochastic Analysis......Page 261
Concurrent Architectures......Page 266
Single Processor Model......Page 268
Single Processor Model with Multitasking......Page 270
Mesh models without multitasking......Page 273
Mesh models with multitasking......Page 275
Basic Definitions......Page 280
Markov Processes......Page 282
Discrete-Time Markov Chains......Page 284
Steady-State Distribution......Page 285
Matrix Formulation......Page 287
Example......Page 288
Continuous-Time Markov Chains......Page 290
Steady-state distribution......Page 291
Matrix Formulation......Page 292
The Embedded Markov Chain......Page 293
Example......Page 295
Aggregation of States in Markov Chains......Page 297
Aggregation in Discrete-Time Markov Chains......Page 298
Aggregation in Continuous Time Markov Chains......Page 300
Semi-Markov Processes......Page 301
Semi-Markov Reward Processes......Page 304
Glossary......Page 306
Index......Page 318