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Acknowledgements |
6 |
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Contents |
7 |
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Authors and Contributors |
10 |
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Introduction |
13 |
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1 Introduction to Digital Simulation |
14 |
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1.1 Introduction |
14 |
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1.2 Definition of Simulation |
14 |
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1.3 When to Use Simulation |
15 |
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1.4 Concepts of Systems |
17 |
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1.4.1 Construction by Composition |
18 |
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1.4.2 Construction by Decomposition |
18 |
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1.4.3 Definition of System |
19 |
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1.4.4 State of a System |
19 |
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1.5 Types of Models |
21 |
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1.5.1 Static Models Versus Dynamic Models |
23 |
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1.5.2 Deterministic Models Versus Stochastic (Probabilistic) Models |
23 |
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1.5.3 Continuous Models Versus Discrete Models |
24 |
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1.6 Advantages, Disadvantages and Risks of Simulation |
24 |
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1.7 Lifecycle of a Simulation Project |
26 |
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References |
30 |
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2 Elements of Statistics for Simulation |
31 |
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2.1 Introduction |
31 |
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2.2 Generation of Random Numbers |
35 |
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2.3 Properties of a Good Random Number Generator |
36 |
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2.4 Generation of Random Numbers with a Uniform Distribution Between Zero and One |
38 |
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2.5 Selection of a Distribution Function |
40 |
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2.6 Continuous Distribution Functions |
41 |
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2.6.1 Exponential Distribution Function |
42 |
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2.6.2 Gamma Distribution Function |
43 |
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2.6.3 Log-Normal Distribution Function |
44 |
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2.6.4 Normal Distribution Function |
44 |
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2.6.5 Triangular Distribution Function |
46 |
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2.6.6 Uniform Distribution Function |
46 |
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2.6.7 Weibull Distribution Function |
47 |
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2.7 Discrete Distribution Functions |
49 |
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2.7.1 Bernoulli Distribution Function |
49 |
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2.7.2 Discrete Uniform Distribution Function |
50 |
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2.7.3 Binomial Distribution Function |
50 |
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2.7.4 Poisson Distribution Function |
51 |
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2.7.5 Geometric Distribution Function |
52 |
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2.8 Development of a Statistical Model |
53 |
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2.9 Statistical Analysis of the Simulation Results |
56 |
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2.10 Conclusions |
59 |
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References |
59 |
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3 Modeling Discrete Event Systems Using Petri Nets |
61 |
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3.1 Introduction |
61 |
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3.2 Petri Nets |
62 |
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3.2.1 Description of Petri Nets |
62 |
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3.2.2 Formal Definition of Petri Nets |
64 |
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3.2.3 Behavior or Dynamics of Petri Nets |
65 |
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3.3 Development of Petri Net Models of Systems |
67 |
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3.4 Redundant Place Nodes |
77 |
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3.5 Limitations of Petri Nets |
78 |
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3.6 Colored Petri Nets |
78 |
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3.6.1 Elements Involved in the Modeling of Colored Petri Nets |
79 |
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3.6.2 Formal Definition of Colored Petri Nets |
81 |
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3.6.3 Behavior or Dynamics of Colored Petri Nets |
82 |
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3.7 Timed Colored Petri Nets |
88 |
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References |
97 |
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4 The Coupling of Coloured Petri Nets with SIMIO |
98 |
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4.1 Introduction |
98 |
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4.2 Review of the Methodology |
99 |
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4.3 SIMIO: Modelling Environment |
99 |
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4.3.1 Objects |
101 |
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4.3.2 Useful Elements for Implementation |
101 |
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4.4 SIMIO/Petri Nets Equivalence |
103 |
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4.4.1 Equivalence Between the Dynamics of SIMIO and the Coloured Petri Nets |
103 |
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4.4.2 Conditioned Events and Satisfaction of Constraints |
106 |
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4.4.3 Modelling Synchrony |
109 |
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4.4.4 Modelling Parallelism |
111 |
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4.4.5 Modelling Processes |
113 |
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4.4.6 Modelling Queues |
115 |
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4.4.7 Shared Resources |
116 |
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4.4.8 Time Consumption |
117 |
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4.4.9 Insertion of Petri Net Transitions in SIMIO |
118 |
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4.4.9.1 Process Activators |
119 |
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4.5 Examples of Coloured Petri Net Implementation in SIMIO |
120 |
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4.5.1 Example 1: Boarding of Passengers at an Aircraft Cabin |
120 |
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4.5.1.1 Coloured Petri Net Model |
122 |
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4.5.1.2 Modular Integration |
124 |
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4.5.2 Example 2: Sequential Manufacturing System |
128 |
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4.5.3 Modelling of Place Nodes in SIMIO |
130 |
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4.5.4 Definition of Token Colours |
132 |
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4.5.5 Modelling Transitions |
133 |
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4.5.6 Time Consumption |
136 |
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4.5.7 Modelling Exit Arcs |
138 |
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4.5.8 Final Model |
139 |
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4.6 Conclusion |
140 |
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References |
141 |
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5 Simulation Examples |
142 |
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5.1 Introduction |
142 |
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5.2 Canal-Lock System |
143 |
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5.3 Two-Robot and 5-Machine Process |
148 |
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5.4 The Philosophers’ Dinner |
153 |
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5.5 Manufacturing Process |
159 |
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5.6 Automated Warehouse |
167 |
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References |
173 |
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