By Walter Philipp

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John Wiley & Sons, New York, 1998. 1 INTRODUCTION This chapter deals with the computer generation of random numbers, random variables, and stochastic processes. In a typical stochastic simulation, randomness is introduced into simulation models via independent uniformly distributed random variables. These random variables are then used as building blocks to simulate more general stochastic systems. The rest of this chapter is organized as follows. 2, with the generation of uniform random variables.

Xtn)has the same distribution as ( X t l + r ,. . , X t n + r ) . 35) hold when the index set is Z, holds is called a stationary distribution. 35) as the system of equations C nip,, = C n j p j i for all i E 8 . 36) 3 3 These are called the global balance equations. 35) as the statement that the “probability flux” out of i is balanced by the probability flux into i. 36), states that the same balancing of probability fluxes holds for an arbitrary set a“. That is, for every set a” of states we have c lEd,#d =1 Pz, = cc n3 P3r .

Kriman and R. Y. Rurbinstein. Polynomial time algorithms for estimation of rare events in queueing models. In J. Dshalalow, editor, Fronfiers in Queueing: Models and Applications in Science and Engineering, pages 421-448, New York, 1995. CRC Press. 13. E. L. Lehmann. TesfingSfatistical Hypotheses. Springer-Verlag, New York, 1997. 14. S. M. Ross. A First Course in Probability. Prentice Hall, Englewood Cliffs, NJ, 7th edition, 2005. 15. R. Y. Rubinstein and B. Melamed. Modern Simulation and Modeling.