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# genrate-rv - CDA6530 Performance Models of Computers and...

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DA6530: Performance Models of Computers and Networks CDA6530: Performance Models of Computers and Networks hapter 5: Generating Random Number Chapter 5: Generating Random Number and Random Variables

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bjective Objective se computers to simulate stochastic Use computers to simulate stochastic processes earn how to generate random variables Learn how to generate random variables Discrete r.v. Continuous r.v. Basis for many system simulations 2
Pseudo Random Number Generation (PRNG) x = a x - mod m n n 1 Multiplicative congruential generator x n = {0, 1, , m-1} x /m is used to approx. distr. U(0,1) n x 0 is the initial “seed” Requirements: No. of variables that can be generated before o o a ab es a ca be ge e a ed be o e repetition begins is large For any seed, the resultant sequence has the “ ppearance” of being independent appearance of being independent The values can be computed efficiently on a computer 3

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x = a x mod m n n-1 m should be a large prime number For a 32-bit machine (1 bit is sign) m=2 31 -1 = 2,147,483,647 a = 7 5 = 16,807 or a 36- it machine For a 36 bit machine m= 2 35 -31 a = 5 5 x n = (ax n-1 + c) mod m Mixed congruential generator 4
C Programming Language In C Programming Language Int rand(void) Return int value between 0 and RAND_MAX RAND_MAX default value may vary between

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genrate-rv - CDA6530 Performance Models of Computers and...

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