Changes and additions are sprinkled throughout. Among the significant new features are: ¿ Markov-chain simulation (Sections 1. 3, 2. 6, 3. 6, 4. 3, 5. 4. 5, and 5. 5); ¿ gradient estimation (Sections 1. 6, 2. 5, and 4. 9); ¿ better handling of asynchronous observations (Sections 3. 3 and 3. 6); ¿ radically updated treatment of indirect estimation (Section 3. 3); ¿ new section on standardized time series (Section 3. 8); ¿ better way to generate random integers (Section 6. 7. 1) and fractions (Appendix L, program UNIFL); ¿ thirty-seven new problems plus improvements of old problems. Helpful comments by Peter Glynn, Barry Nelson, Lee Schruben, and Pierre Trudeau stimulated several changes. Our new random integer routine extends ideas of Aarni Perko. Our new random fraction routine implements Pierre L'Ecuyer's recommended composite generator and provides seeds to produce disjoint streams. We thank Springer-Verlag and its late editor, Walter Kaufmann-Bilhler, for inviting us to update the book for its second edition. Working with them has been a pleasure. Denise St-Michel again contributed invaluable text-editing assistance. Preface to the First Edition Simulation means driving a model of a system with suitable inputs and observing the corresponding outputs. It is widely applied in engineering, in business, and in the physical and social sciences.