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