Regenerative Stochastic Simulation Book

	Preface
1	Discrete-Event Simulations	1
1.1	Methodological Considerations	2
1.2	State Definitions	5
1.3	Time-Advance Procedures	11
1.4	Generalized Semi-Markov Processes	23
2	Regenerative Stochastic Processes	51
2.1	The Regenerative Property	51
2.2	Limit Theorems	73
2.3	Regenerative Generalized Semi-Markov Processes	76
3	Regenerative Simulation	97
3.1	The Regenerative Method	98
3.2	Implementation Considerations	122
3.3	Discrete Time Conversion	125
3.4	Theoretical Values for Markov Claims	127
3.5	Statistical Efficiency	138
4	Networks of Queues	143
4.1	The Job Stack Process	144
4.2	Regenerative Job Stack Processes	159
4.3	Geometric Trials Criteria for Recurrence	168
4.4	Preemptive-Resume Priorities	172
5	Passage Times	193
5.1	The Augmented Job Stack Process	194
5.2	The Marked Job Method	209
5.3	The Labelled Jobs Method	217
5.4	Comparison of Statistical Efficiency	228
5.5	Abstract Passage Times	240
6	Simulations With Simultaneous Events	283
6.1	Simultaneous Trigger Events	284
6.2	Compound Events	290
6.3	Formal Specification	308
6.4	Regeneration Theorems	329
	Appendix A. Limit Theorems for Stochastic Processes	345
A.1	Probability Spaces and Random Variables	345
A.2	Modes of Convergence	347
A.3	Convergence Tools	349
A.4	Stochastic Processes	351
A.5	Laws of Large Numbers	360
A.6	Central Limit Theorems	363
A.7	Recurrent Events	365
A.8	Wald's Moment Identities	366
	Appendix B. Random Number Generation	367
B.1	Linear Congruential Generators	367
B.2	Inverse Transformation	372
B.3	Rejection-Acceptance Methods	375
B.4	Decomposition Methods	378
	Bibliography	385
	Index	393