| P. Bratley, B. Fox, and L. Schrage. A guide to simulation. Springer Verlag, 2nd edition, 1996. |
....with the specified mean and variance. The normal random variates were generated using the Box Muller method. The gamma variates were generated using the RGS and RGKM3 algorithms (depending on the value of the shape parameter) For details of these pseudo random number generators see Bratley et al. [2]. For each problem, 15,000 replications were used in the simulation to obtain reliable start 26 time (co)variance estimates. Preliminary experimentation suggested the need for at least 15,000 replications to accurately model processing time variances. All the code was written in C. The CNC ....
Bratley, P., Fox B. L., and Schrage L. E., A Guide to Simulation, Second Edition, Springer Verlag, 1987.
....distribution over [0, 1) so# can be interpreted as a uniform random vector. Many well known variance reduction techniques, including antithetic variates, rotation sampling, Latin hypercube sampling, randomly shifted lattice rules, and other types of randomized quasi Monte Carlo point sets [3, 4, 12, 15, 17, 22] can be seen as special cases of GA transformations. To improve the quality of our estimator of ,wealsowanttousem measurable functions C l : 0, 1) as control variables (CV) where we assume that E[C l (U) 0 for l =1, m. We are thus interested in approximating by estimators of the ....
....m,1 )thanfor computing (X 0 ,C 1,0 , C m,0 ) alone, then using the GA scheme is more e#cient than using independent replications only if it reduces the variance by a factor larger than 2 compared with the case n = 1. Several other articles and books concentrate on this e#ciency issue (e.g. [3, 4, 9, 11]) usually assuming equal weights a priori in the case of GA methods. The remainder of this paper is organized as follows. In Section 2, we introduce some notation, state our basic result, and prove it. Section 3 considers settings where the u i s form an abelian group of random variables and our ....
P.Bratley,B.L.Fox,andL.E.Schrage. A Guide to Simulation. Springer-Verlag, New York, second edition, 1987.
....expressiveness because we can encapsulate probabilistic computations and treat probability distributions as values. For instance, we can now specify a probability distribution over probability distributions of the same type. The examples below demonstrate the expressive power of our language. See [2] for the simulation methods used in the examples. We first introduce new base types and primitive constructs such as if M then M else M . let x = M in N is syntactic sugar for (#x : A.N) M , and let rec x = M in N for let x = fix x : A. M in N , where A is an appropriate type for M . unprob M is ....
P. Bratley, B. Fox, and L. Schrage. A guide to simulation. Springer Verlag, 2nd edition, 1996.
....is available, cf. item 3 at the end of Section 2. This is then combined with a conditioning argument using the renewal representation and thus the algorithm contains the ingredient of conditional Monte Carlo, more precisely extended conditional Monte Carlo in the sense of Bratley, Fox ; Schrage [12] (see also Glasserman [19] Algorithm IV We use the representation lP( x) T) oTY(T t; x)U(dt; x) 3.2) where f(t; x) lP( x) t C) as in Theorem 2.5 and U(A;x) IP(C . C A, x) C . C) 0 (to obtain (3.2) condition upon the time t = C . Ck where the cycle ....
P. Bratley, B.L. Fox & L. Schrage (1987) A Guide to Simulation. Springer, New York.
....because we must be able to run multiple independent simulation runs, each being statistically different, and we must avoid any correlatory effects between the random variables within each simulations run. MAGELLAN borrows theory and implementation of RNGs from various sources [Knuth, 1973] [Bratley et al. 1987], L Ecuyer, 1988] and [Jain, 1991] D.4.1 The Multiplicative Linear Congruential Generators MAGELLAN uses MLCG RNGs [Jain, 1991] This class of random number generators has many useful properties. These include: 155 1. In [L Ecuyer, 1988] the RNG has been subjected to a battery of ....
....1988] the RNG has been subjected to a battery of statistical tests and has derived robust implementations, 2. A public domain portable implementation from GNU s libg [Lea, 1992] is available, 3. The RNG has a very long period, and 4. A systematic technique to generate seeds is given in [Bratley et al. 1987]. The MLCG used in M IGELL IN is a portable implementation on 32 bit machines as described in [L Ecuyer, 1988] L Ecuyer suggests a mix of two MLCGs: 2147483563, al 40014 m2 = 2147483399, a2 = 40692 Note that (Zl 1) 2 = 3 x 7 x 631 x 81031 and (m2 1) 2 = 19 x 31 x 1019 x 1789 are ....
[Article contains additional citation context not shown here]
P. Bratley, B.L. Fox, and L.E Schrage. A Guide to Simulation. Springer Verlag, New York, NY, 2 edition, 1987.
....random number generator, random variate, alias, bucket, rejection, dynamic data structure, update, approximate priority queue. 2 1 INTRODUCTION 1 Introduction The generation of random variates based on arbitrary nite distributions has long been a key component of many computer simulations [1], 7] 14] 25] Given elements 1, 2, N and their respective weights w 1 , w 2 , wN 0, we want to design an algorithm to generate a random variate that has value j with probability w j = 1 i N w i . In the static case, when the N weights are xed, we can utilize the clever ....
P. Bratley and B. L. Fox and L. E. Schrage, A Guide to Simulation. Springer-Verlag, Second Edition, 1987.
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P. Bratley, B. Fox, and L. Schrage. A guide to simulation. Springer Verlag, 2nd edition, 1996.
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P. Bratley, B. Fox, and L. Schrage. A guide to simulation. Springer Verlag, 2nd edition, 1996.
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P. Bratley, B. Fox, and L. Schrage. A guide to simulation. Springer Verlag, 2nd edition, 1996.
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P. Bratley, B.L. Fox, and L.E. Schrage. A Guide to Simulation. Springer Verlag, 1983.
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Paul Bratley, Bennett L. Fox, Linus E. Schrage, A Guide to Simulation, Second Edition, 1987, Springer Verlag.
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P. Bratley, B. Fox, and L. Schrage. A guide to simulation. Springer Verlag, 2nd edition, 1996.
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P. Bratley, B. Fox, and L. Schrage. A guide to simulation. Springer Verlag, 2nd edition, 1996.
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Bratley, P., Fox, B.L., and L.E. Schrage (1987) A Guide to Simulation. SpringerVerlag, New York.
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P. Bratley,B.L. Fox, and L. E. Schrage, A Guide to Simulation, Springer-Verlag, New York, 1986.
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P. Bratley, B. L. Fox, and L. E. Schrage, A Guide to Simulation, Springer-Verlag, New York, second ed., 1987.
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P. Bratley, B.L. Fox and L.E. Schrage, Guide to Simulations. (Springer-Verlag, New York, 1983).
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P. Bratley, B.L. Fox & L.E. Schrage, "A guide to Simulation", Springer Verlag, New-York, 1983.
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Bratley, P., B. L. Fox and L. E. Schrage (1987). A Guide to Simulation, second edition. Springer-Verlag, New York.
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P. Bratley, B. Fox, and L. Schrage. A guide to simulation. Springer Verlag, 2nd edition, 1996.
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Bratley, P., B.L. Fox, and L.E. Schrage. 1987 A Guide to Simulation, Second Edition. New York, NY: Springer Verlag.
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Paul Bratley, Bennet L. Fox, and Linus E. Scharge. A Guide to Simulation. Springer-Verlag, 1987.
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Paul Bratley, Bennett L. Fox, and Linus E. Schrage. A Guide to Simulation. SpringerVerlag, 1983.
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P. Bratley, B. L. Fox and L. E. Schrage, A Guide to Simulation, Springer-Verlag, New York, 1983.
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Paul Bratley, Bennett L. Fox, and Linus E. Schrage. A Guide to Simulation. SpringerVerlag, 1983. 4
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